Teachersmanualfortheandrewsl

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Copyrigbted by

H D OW AR ‘ GR SS H O ,

H C GO 1 88 r. C I A , I n trodu cti on .

To THE TEACHER In the preparati o n o f this M an ual the writer has endea v ored to treat the u b ec t re en ted in a m e et forc b e man n er a o d s j s p s , si pl y i l , v i c a r Th u trat o n en in a s m u c as o s b e tec n te m . e g, h p si l , h i l s ill s i s gi v ,

- he outline the work that sho u ld be do n e in the c lass ro o m . T teac her ho u d and n o do ubt w u em en t the e u trat o n s l , ill s ppl s ill s i s in man w a re en t n the ub ec t treated te b te in a y ys , p s i g s j s , s p y s p,

r an n tho o u gh and yet attracti v e m er. The a u e o f demonstra tion n o o n er do ubted and in t o e v l is l g , h s o o er it m o d h t t f o w T sch ls wh e is st u s e t e bes res u l s o ll . his is

- r The pre emi nen tly t u e in geographi cal and astro n o mi c a l w ork . Lu nar Telluri an is de sign ed to furn ish the ill u stratio n s n ecessary to giv e the pupils a co mprehen si v e u n ders tandi ng o f the relatio n n mo n m in c o n tru t o n s h s o f the earth su and o . It so e c ip , i s si pl s i that the a v erage teacher may u se it to adv antage after a few ’ r d t the an ua h o u s s tu y wi h M l . The teacher will ﬁ nd it adv antageou s to now and then a ssign a to c to o n e o f the u and re u re him to furn c ear and pi p pils , q i ish l n trat o n b u s forc ible demo s i s y e o f the apparatu s . ’ The teacher s atten ti o n is parti c ul arly c alled to the s ectio n in b rt n w en t ﬁ d th o w h c P ro f. E . o e o c c e tor o f e ca i h C l , s i i i Chi g Tribune and we n o w n as a rac t ca a tro n o m er treat the , ll k p i l s , s

s ub ec t o f T de . re en tatio n n ew a n redu c ed the j i s H is p s is , h vi g

t a ct to th conc ete The au t or c o n at te h r a a bs r e r . h gr ula s t e e ders b r n u o n be n a e to e e t an art c e fro m the en o f P ro f. o bert p i g l p s i l p C l , a nd here ack nowledges o bligatio n s to that es timable and s cho larly

gentl eman .

The wr ter ac now ed e o b i at o ns to . acv c ar Ph . i k l g s his l g i M M i , — D . o f the c an State No rm a S c o o than w o m there , Mi hig l h l h is — n o b etter au thori ty o n mathemati cal geo graphy so me o f whose i u trat o n th w r ter has embo d d h ll s i s e i i e in t is wo rk .

C G arc 1 88 1 . CHI A O , M h I ,

1 1 1 8 61 I N D E X .

I ntroduction ,

’ A ndrews Lunar Telluria n Descr ti n , ip o ,

How to Ad ust tize Lunar Tellu ia n j r ,

P re ara tor ork p y W ,

General D initions gf ,

Distribution o L /zt a nd Heat f ig ,

Da s a nd N i /zts E ua l a nd Une ual y g q q ,

’ Tbe S u n s A a rent atﬁ pp P ,

Clza n e S eason g of ,

’ TIze S un s Dec ination l ,

To nd the Latitude a nd Lon itude o P laces ﬁ g f ,

Lon itude a nd Time g ,

T0 ﬁnd tlze Dif erence of Longitude between Two

aces P l ,

T0 ﬁ nd t/ze Time of S unrise a nd t/ze Length of

e un Tb S ,

Tbe E a rt/z ,

’ Moons Motions P /zases E tc . T/ze ; , ,

Tlze Z odia c S i ns o E ta , g f , ,

c i ses S ola r a nd Lunar E l p , ,

eces sion o til e E uinoxes P r f q ,

ua tion o Time E q f , — I c Tides B P OF. B T n y R COL ER ,

’ i s o rews Lunar Telluria n Commendat on f And , ’ n rews "mar uria .

’ A The obe a l. dr wn . b S . A rc o u n ir u mference gl l f the s s c c , a u on the same ca e as the n d h arc S u nti a c rc e p s l globe . Exte t e l i l

co m eted and t c rc e o w the z e o f su n u on the ame is pl , his i l sh s si p s ca e as the obe re r s nts th a c rc e o f i u B . he s l gl p e e e e rth . T i l ll m nat o n owin ho a th n The tw t i w f r e u i t e tend . . i , sh g s l gh x s C iligh r ho n ho f r h o o n a c c e w w a th t t . T e m b e w e tend D . i l s i g iligh x s ll , n th t and d n he ear sho wi g e ligh ark hemispheres o f the moo . T g

h n . ing a t F k eeps the light hem isphere alw ays to ward t e su . E ’ ca en Plate showi ng the in c linatian Of the mo o n s orb i t. G . A l ’ r d L. o nter o w n the o t o n o f the u n ert ca da i n ex . P i sh i g p si i s s v i l d n r m nd ﬁ n d t me o f s u n ra . . A on itu a o t e e u ed to y H l g i l i i x , s i The r e and sun et en t of da s ni ts and tw t. . is s , l g h y , gh iligh J K h ua c t T e e tor. e lip i c . . q L 6 UNAR TELLURIAN MANUAL .

To Adjust the Lunar Tellurian .

To to n adjust the apparatus agree with the cale dar, m o ve the arm IX u ntil the calendar i nde x G is Opp o site the 21 5t o f Ju ne place the arm i n which the s o uth po le

o f o f n arm the gl be is aste ed parallel with the IX , as

o n in o r r n n n to n 2 l st sh w cut, b i g the cale dar i dex Ju e and place the ce nter o f the s o cket at the s o uth po le Op

po site the mark I o n the semi - circular b race j o i ni ng the n o f o n L o r h e ds circle C . The p i ter sh uld be pa allel wit

the arm IX . Raise the m o o n ball u n til the gear wheels at F are

dis en a ed rn co - to o r n g g , tu the g wheel the right left u til w/z ite s ide o f o o n o sun o the the m ball is t ward the , dr p

o n o r n the c gs i t gear . The gea i g will keep the bright S side o f the m o o n ball to ward the arc .

h no fo r T eapparatus is w fully adjusted use .

For G eo grap h i c a l S tu dy.

(The Globe may be u s ed fo r geographi c al purpo s es and is an e ce ent o n e for u c u se h a n the I o t erma L ne nd cated x ll s h , v i g s h l i s i i b u and r c t n he o ean c urr n t ar a o n . n u s i l e ed. T e s e ls show Whe h u ed the teac er w remo e the c rc e B a o the cur ed s , h ill v i l s C , ls v s tandards s upporti ng the s am e (after li fti ng o ff the globe ball

a o n w t the a . Re ace the obe detac the moo n a o l g i h xis ) pl gl , h ls , at F b t n th b a ma e toward the obe. The s un arc S , y ippi g ll gl , y a o be r m A ll an n n e o ed. t e e c e ta e b u t a mo me t ls v h s h g s k , givi g an u nob struc ted v iew o f the Globe. ) L T . UNAR ELLURIAN MANUAL 7.

r rk Preparato y W o .

T he s tu dy of th e m eth o d of a dj u s ti n g a n d h a n dli n g th e L UN A""TE LL URI AN G L OB E i n i llu s tr a ti n g

a n d s o win g p r o blem s .

o n o in o n o o n Bef re usi g the gl be illustrati s , the f ll wi g n p oin ts sh o uld be carefully studied . Each adjustme t

o r r sh uld be made familia by actual p actice . The teacher nno be to o r o n o n o o f ca t pa ticular this p i t , as the p wer any illustrati o n depends largely up o n the tact with which

the piece o f apparatus used is handled .

The cut o n the precedi ng page represents the gl obe

n i o o n Let with all the attachme ts n p siti . every part be remo ved and replaced and set in the po siti o ns i ndicated n and n n n r can o n agai agai , u til everythi g requi ed be d e

and r W ith ease apidity .

Be particular to no tice the fo ll owi ng su ggesti o ns

arc S n o f 1 . The represe ts the curvature the surface of a ball which bears the same rel ati on in si z e to the sun n that the gl o be A bears to the earth . He ce by co m

letin o f arc S r and co m p g the circle which the is a pa t , n o n o pari g it with a great circle the gl be , we have a c o rrect representati o n Of the relative si z e o f the earth

and sun .

o n L n 2 . The p i ter represents a li e c o nn ecti n g the

n r and sun n n o o ce te Of the earth , he ce , i dicates the p siti n of the o nly vert ical ray o f light o r heat which c o mes ro su n to r f m the the ea th .

The r B 3 . ci cle is u sed to i ndicate the li ne which sep arates light fro m dark n ess hen ce is called the Circle " o f n o n o r Da and r Illumi ati , y Night Ci cle . 8 LUNAR TE LLUR i A N MANUAL .

G eneral Deﬁ nitions .

The fo ll owi ng deﬁ niti ons sh o uld be made familiar

n o f o befo re c o mmenci g the use the gl be .

A o o n o 1 . Point is that which has p siti with ut mag

n itude.

2 A ine o f o n o n . , L is the path a m vi g p i t 3 A Straight Lin e is o n e which has the same di n rect i o n thro ugh o ut its entire le gth . hi di A o ne . w ch n rec 4. Curved "zine is cha ges its

o r o n ti n at eve y p i t .

r ll l in s are n 5 . Pa a e L e li es which have the same o n directi .

A n n n n two n w 6 . Angle is the Ope i g betwee li es hich

in o o n o n ver tex meet a c mm p i t called a .

n o f n There are three ki ds a gles , thus

(2)

ﬁ O Rl Z O NTM - o

n n mee s no r. n a n 7 . Whe a li e t a the li e , m ki g, as is

o n in tw o e u a l a n les n sh w ( q g , each a gle is a Ri ght

' and n to n to An gle, the li es are said be perpe dicular o each ther .

A n an n o n in 8 , Obtu se Angle is a gle (as sh w 6

r ea ter n r i ht a n le that is g tha a g g .

A n an n o n in 9 . Acute An gle is a gle (as sh w 6

less n r i ht a n l that is tha a g g e. LUNAR TELLURIAN MANUAL . 9

0 A l ne s u r a ce r r n 1 , P a is a f t aced by a st aight li e n o n m o vi ng i the same directi .

A r 1 1 . Circle is a su face

n o cu rved lin e e cl sed by a , . eve ry po i n t o f which is eq u a lly dis ta nt fro m a p o i nt

n center withi called the .

A 1 2 . Circumference is the li ne that b o u nds the

r ci cle .

I n describi ng the li nes o n

s rface o f o the b the gl be , the o r in Of i r r n n w rd ci cle is used place c cumfe e ce . Whe a “ " circle ro er intended the o r n n o p p is , w d pla e is i tr duced .

3 A o n e 360 r n o 1 . Degree is Of the equal pa ts i t which the circu mfer en ce o f a circle is supp o sed to be divided .

06s er ve n Of va ries i s i z e o f , the le gth a degree w th the

r the ci cle .

i t r o f circle r n 1 4. The D ame e a is a st aight li e pass ing th ro u gh its center and terminating at 60th ends in

c ircu m eren ce the f .

1 o f circle an r n 5 . The Radius a is y st aight li e ex n n fro c n t r ir u m eren ce te di g m its e e to the c c f .

1 A o o r o o n 6 . Sph ere is a s lid v lume b u ded by a r o n in are curved su face , such that all p i ts it equally dis n n ta t fro m a p o i nt withi n called the ce ter . L T UNAR ELLURIAN MANUAL .

Observe the p oi nt e: in the in n n cut the margi , is the ce ter o f a sphere o f which c l) d is

the l ower half.

The o f a 1 7 . Diameter sphere is a st raight li ne passin g thro ugh its center and termin ati ng at b o th ends in the sur

face . 0 In a 5 and cd dia meters the cut , are .

1 i s o f s here n n 8 . The Rad u a p is a straight li e draw f o n to an mn in rf r m the ce ter y"i t the su ace . In e c e ae e and de are radn . the cut , , f , , g

1 9 A re t ir le o f s here one o ne . G a C c a p is wh se pla a ro n o f r p sses th ugh the ce ter the sphe e .

Hence the planes o f all great circles divide the Sphere

n o two . i t equal parts . Each part is called a Hemisphere

A o f s here o ne o ne 2 0. Small Circle a p is wh se pla d oes n o t pass through the ce nter o f the sphere .

n n of on He ce , the pla es all small circles a sphere di vide the Sphere i nto two u nequal parts .

o f on 2 1 , The Ax is the Earth is that diameter

- r which it ro t ates o nce in twenty fo u r h o u s .

2 2 ol s o f rth are two o n o n . The P e the Ea the p i ts its surface at the extremities o f its axis .

i The o directed to the 2 3 . North Pole is the P le

o r r o os ite N th Sta . The South Pole is the pp extrem ity Of the axis . LUNAR TELLURIAN MANUAL . I I

tor r n 2 4. The Eq ua is a great ci cle midway betwee ’ the p o les wh o se plan e is at right angles to the axis of the earth .

2 r llels o f tit d s 5 . The Pa a La u e are small circle r to o pa allel the Equat r .

A - x n n f o 2 6. Meridian is a semi circle e te di g r m o to o P le P le .

o f n in 2 7 . The Latitude a place is its dista ce de r no r o r o o f o g ees th s uth the Equat r.

Places no rth o f the Equato r are said to be in N orth

Latitu de and o in S ou th La titu de , places s uth .

2 8 on it o f n in . The L g ude a place is its dista ce de grees east o r west o f a give n meridian called the Firs t

r P r e o im Meridian .

n o f o O r o at n The meridia the R yal bse vat ry Gree wich, i n n o o n o P r ime Merid E gla d , is c mm ly empl yed as the

a n n r n o f r i . The Fre ch use the me idia Pa is the Ger

' n o f r o o ne o f n n and ma s that Fe r , the Ca ary Isla ds ;

A n n o f n o n merica s freque tly use that Washi gt .

2 i o f n Of e 9 . The Trop c Ca ceris a parallel latitud 23 r no o f o % deg ees rth the Equat r.

o f o f 3 0. The Tropic Capricorn is a parallel lati 2 3 r o o f o tude % deg ees s uth the Equat r .

o f in 3 1 . The Orbit the Earth is the path which it o o n su n m ves r u d the .

’ O la ne o f ea rth s or it bserve , the p the h is the plane in o which the rbit is described . 1 2 LUNAR TELLURIAN MANUAL .

’

3 2 . Zones are o o r o n The , br ad belts divisi s Of the ’ e o n o and o arth s surface b u ded by the Tr pics P lar Circles .

These fo ur lines divide the surface o f the earth i nto ﬁve

z o n o r no n Torrid Z one tw o Tem es belts k w as the , the

era Z n n o Fri id Z on es te o es a d tw . p , the g

The width Of the Z o nes depends entirely up o n the in

clin ati o f o rr Zo n on Of the axis . The width the T id e is

dou hle n n o n o f 23 o r 47 the i cli ati the axis ( % degrees), o f r Zo n e u a l to degrees . The width the F igid e is q the n n o n Z o n i cli ati . The Temperate es embrace whatever su rface lies betwee n the Tro pics and P o lar Ci rcles (43

r n n o n o f r 30 r , deg ees). If the i cli ati the axis we e deg ees in n S rn Zo n o as the case Of the pla et atu , the es w uld be as fo ll ows

° ° o rr Zon o n n o n 30 o r 60 T id e , d uble the i cli ati , ° ° r Zo n to n n o n 30 o r 60 F igid es , each equal the i cli ati , ' ° ° Z o n to the n n o n 30 o r 60 Temp . es , each equal i cli ati ,

° o r ro o to o 1 80 T tal deg ees f m p le p le ,

’ 3 li ti n n r 3 . The Ec p c is the su s appare t yea ly path ’ o r o r ea rth s o r orhit. thr ugh the ﬁxed sta s , the real path

o i l o f n 1 6 3 4. The Z d ac is a be t the heave s degrees d n 8 r o n E n wi e , lyi g deg ees each side Of the cliptic , withi

un o o n and n n to o . which the s , m pla ets are see m ve

This belt is divided i nto twelve equal parts called r n S i n the Z odia c . o n g s of These divisi s , with thei ames , n are represented o n the base o f the Lu n ar Tellu ria .

3 5 no ti l o r elesti l tor . The Eq ui c a C a Eq ua is a g reat circle Of the Celestial Sphere di rectly o ver the terres tria l e u ator and n in n . q , he ce is the same pla e LUNAR TELLURIAN MANUAL . 1 3

no i al oints o r i n ox es are 3 6. The Eq ui ct P Eq u u n octia l the p o ints whe re the E cliptic cro sses the E q i .

The p o i nt which the su n passes in March is called the

Verna l E u inox and as in S q , that which he p ses eptember

A u tu mna l E u inox the q .

olsti i l oints o r olsti es a re the 3 7 . The S t a P S c o o n no tw p i ts where the sun is farthest fro m the Equi ctial .

The p o i n t no rth o f the E quino ctial is called the S u m mer S olsti e and n o inter S ols tice c o e W . , the s uth the

i o f n o 3 8 . The Declin at on a heave ly b dy is its dis no t ance no rth o r s o uth fro m the E qui ctial .

o o n to Decli natio n c rresp ds terrestrial latitude .

’ erih eli on o n in r o t 3 9. P is the p i t the ea th s rbi nearest to the su n .

’ o n in o far 40. Aphelion is the p i t the earth s rbit thest fro m the su n .

1 fr tion in A o no n o f 4 . Re ac str my is the cha ge di recti o n which the rays o f light u ndergo in passing thro ugh o the atm sphere .

This may be illustrated to a class by placing on the o blackb ard a diagram thus , 1 4 LUNAR TELLURIAN MANUAL .

Let S n sun D r and and represe t the , the ea th, F E tw o strata o f the atm o sphe re o f which E is the m o re d n . e se .

A sk i to r the pup l Obse ve ,

(a ) That if a ray o f light fro m S e nte r the stratum F at n o r the r n r and 3 it will be be t t wa d pe pe dicula 3 b ,

n r r n o r e ter the st atum E at 2 . The st atum E bei g m e

. n n r n n o r de se tha the st atum F , it is agai be t t wa d the

r n r and r r r 1 pe pe dicula 2 a, st ikes the su face Ofthe ea th at

5 o r n o t r r n ( ) That the atm sphe e is made up , as ep ese ted in o f r r ff r n n the diagram , sepa ate st ata Of di e e t de sities , but beco mes gradually m o re de nse the n earer it is to the

s r r n r in n u face Of the ea th . He ce , the ays Of light passi g th ro ugh the atm o sphe re cu rve gradually to wa rd a per pendicu lar to the su rface o f the earth fro m the po i nt

r n o whe e they e ter the atm sphere . (c) That there is n o refractio n when a ray o f light

’ s r o r r n r o n b t ikes the atm sphe e pe pe dicula ly , as sh w v the line ~ l z and o o ra n r , that the m re bliquely a y e te s , the

r r o n o n n 1 3 n s g eater the ref acti , as sh w by the li e S. He ce LUNAR TELLURIAN MANUAL . I 5

o n ro an en o in o ur z n u n light c mi g f m y heav ly b dy e ith ,

r oe no o n and o o ro de g s refracti , as a b dy m ves f m the

z n to o z o n r r o n n r . e ith the h ri , the ef acti i c eases

(d) That si nce all Objects are seen in the di recti o n in which the light fro m them falls upo n the reti n a o f the

s u n in n an v eye , the S the diagram is see by Obser er at in r o n o f I In o n n o f ff 1 the di ecti S . c seque ce this e ect

Of o n n o n o n in z n refracti heave ly b dy , u less the e ith , is

n in r o t o n See its eal p si i .

In o f su n and o o n o n o f refrac the case the m , the am u t ti o n at the h o ri z o n is a little greater than thei r apparent d n in r n o r n r iameters . He ce , isi g setti g , they appea

o o z o n n re o ab ve the h ri whe they a actually bel w it .

42 n to . The Radiation Of heat with refere ce the e a rth is the emissio n anddiffusio n o f heat fro m its surface in o o t the atm sphere .

A sk to o r the pupil bse ve ,

(a) That du ri ng the day the surface of the earth is

r o f sun heated by the ays the .

(6) That when the su n sets the earth radiates its heat n o o r n n in i t the atm sphe e he ce , the cha ge the tempera r o su n r tu e bef re the ises .

’ In the summer seas o n the earth s su rface abs o rbs o r takes in m o re heat fro m the su n duri n g the l o ng day than r o r o ut n o n it adiates gives duri g the sh rt ight, the tem erature fo r o n r n n p must this reas ise . Whe the su leaves

US ‘ and o o o u r o r n and n n n g es s uth days sh te ights le gthe , r n o r on ni o n n du i g which abs pti dimi shes , radiati i creases , a nd r o on n o the tempe ature is c rresp di gly l wered .

The blacksmith puts the h o rsesh o e i nt o the fo rge that 1 6 LUNAR TE LLURIAN MAN UAL .

a hs or h n o s o c an it may heat u til it gets s ft, that he easily shape it up o n the anvil while w o rki ng with it the sh o e radia tes n o and o r fﬁ to heat , getti g thereby m re m e di cult

o o o n in o n to w rk . It must s be replaced the f rge agai abso rb the required quantity o f heat to be easily and econo mically wro ught when the smith is through with the sh o e he d rops it i n to his tub o f water that it may quickly radiate the heat and be ready to n ail to the ’ o o o h rse s h f.

Distrib tion of i ht H u L g and eat.

’ To Illu s tr a te th e diﬁ eren ce b etween th e S u n s V er

ti ca l a n d Obli q u e R a ys .

f o o o o r In Take two pieces o cardb ard ab ut a f t squa e . the cen ter o f On e o f them cut a ro u nd h o le ab o ut o ne inch in diameter h o ld this o ne up to the sun at a right

n to so o a gle the rays , that the light will pass thr ugh the Open i ng place the o ther piece abo ut a fo o t behi nd the ﬁ rst and parallel to it ask the pupils to observe that the su nlight passi ng th ro ugh the i nch Openi n g falls upon the

on to and o rs o f o n e sec d piece vertical it, c ve a like surface

n u r ho w the n n verti i ch . This ill st ates su light, falli g

ca l o n r o r e u a l to volu me ly up the ea th , c vers a su face q the

o f s u ch li ht g .

Cha nge the p o sitio n o f the back piece o f cardb o ard

s lowl so not to r and y, that it will be parallel the ﬁ st , ask the pupils to Obse rve that while n o m o re su nlight passes th ro ugh the Open i ng in the ﬁ rs t cardbo ard than in the o r o n o n o rea ter ther illust ati , yet that, am u t is Spread ver a g

s u r a ce o n o n o n entirel to f the sec d piece , wi g y the fact now ohli u e in n nc that it falls q ly whereas , the ﬁrst i sta e ,

r to r o f r it fell ve tical the su face the ca dbo ard . This illus

L N‘ 1 8 UNAR TELLURIA MANUAL .

o r in n n are r n and o h u s su light, wherei we wa mi g, ab ut

9 o r rn in r n to o o i in h u s are tu ed away da k ess c l , wh le midwi nter we have ab o ut 9 ho urs o f su nlight and 1 5

r o f r n A s n o n n h o u s da k ess . we depe d up su light fo r o o r r in heat, it f ll ws that the tempe atu e must rise summer

and in n o n to o n and S o r fall wi ter , wi g the l ger h ter periods o f n n o n su shi e at these respective seas s .

’ 2 o n on e- ha l a . That ly f Of the earth s surface c n at ’ an o to n and y time , be exp sed the su s light heat. This I llu min a ted Hemis here half is called the p .

R o tate the gl obe o n its axis fro m wes t to eas t 1 0 de

and to in grees , ask the pupils Observe , case the earth m o ves in like manner

(a ) That a distributi o n o f light and heat will have n take place .

(b) That the ve rtical rays o f the su n will have been ’ r wes twa rd 1 0 r U o n r ca ried deg ees p the ea th s surface , ’ o n to o o n to ea s t o r n wi g this r tati the , the su s vertical

n dis tr ibu ted and 1 0 r ray will have bee east west deg ees .

’ (c) That the b o u ndary o f su n s light and heat will have bee n carried wes tward fro m 90 degrees west l o ngitude to 1 00 r and n deg ees , that all places situated betwee these

* — NOTL . If c o n en en t ac e a c o n e en o er the a erture in v i , pl v x l s v p the c ardbo ard ace the ec o nd b oard b eh nd as d rec ted in the pl s i , i ﬁ r t n tan c e and at u c h a d tan c e as n ece ar to ma e the s i s , s is ss y k c o n v ergi ng rays co v er the l east po ssible s u rface ho ld the s u nlight u po n the s am e po i n t fo r a few mo m en ts and if the l en s i s a goo d o n e c o mb u t o n w en u e at the o n t o f c o n tac t thu illu strat , s i ill s p i , s ing the i nten s e heat pro du ced by reducing the spac e co v ered by a n r n he intensit so a r heat is inverse giv e po ti o n o f s u light. T y of l ly r t na p of or io l to the space covered by a given volume. 1 LUNAR TELLURIAN MANUAL . 9

m e ridians will have be e n by this distributi o n bro ught in to n r whi e ' tho se the illumi ated hemisphe e , l places situ ated betwee n the 90th and 80th meridians ea s t l o n gitude

u f will have bee n carried o t o it .

(d) That the Day and Night Circle is parallel with i n e the mer di ans as they pass u d r it .

o o o n o n fro s t o R tate the gl be ce up its axis m we t east, and ask the pupils to o bserve

(a) That by reas o n o f this ro tati o n the sun has cro ss ed r n r o n e ve ry me idian a d retu ned t the place Of starti g.

(b) That every meridian has passe d thro ugh the illu

minated and r r . n o ne co m the da k hemisphe es He ce , plete distributi o n o f light and heat ea s t and wes t has

n n ro ro o n o f r take place , bei g p duced by the tati the ea th u o n As r rn o n o n its p its axis . the ea th tu s ce up axis daily , the re must o ccu r a da ily dis tribu tion of lig ht a nd hea t ’ eas t a n d w es t u on the ea rth s s u r a ce p f .

c n su n r to o o n ( ) That whe the is ve tical the equat r , as r 20th and S 2 3 rd and M a ch eptember , the light heat Of the su n is eq u a lly dist ributed in the n o rth and s o uth h emisphe res .

To Illu s tra te th e Di s tri b u ti on of Li gh t a n d Hea t o n a r ch 2 oth M .

’ To pro duce a dis tribu tion o f the Su n s light and heat ’ o n r e r o r su n n up the ea th s surface, the a th must cha ge t r o o n in to o n hei p siti respect the ther . This ecessitates

a movemen t and o o e n n o , with ut a m vem t dis tr ibu tion c an take place .

It is very necess ary tha t the pupils get a clear co ncep t o n e andmas ter as on i Of this subj ct it, up the distributi o n 2 0 LUNAR TELLURIAN MANUAL .

of and n e o n o f and n light heat depe d the succ ssi day ight,

n o f o n and in o u r ver the twilights , cha ge seas s , , fact , y

ex isten ce.

B ring the cale ndar i ndex to the 20th o f March rotate

) the gl o be upo n its axis u ntil the sun is vertical to the

rime n and to r p meridia , ask the pupils Obse ve

a sun to o ( ) That the is vertical the equat r .

’ (b) That the su n s light and heat extends n o rth and ' o ro o o o o n Da and s uth f m p le t p le , as Sh w by the y Night

Circle B .

’ (c) That the su n s light and heat extends eas t and west o f n 90 r o n the prime meridia deg ees , as sh w by the

Da and y Night Circle B .

To Illu s tr a te th e Di s tri bu ti on of Li gh t a n d Hea t

o n th e 2 1 s t of J u n e.

n a n n to 2 l st of n and Bri g the c le dar i dex the Ju e , ask the pupils to observe

a T sun to rO io o f n ( ) hat the is vertical the T p Ca cer,

3 n orth of o . 2 54 degrees the equat r

(b) That the Illum i n ated Hemisphere n o w extends 3 be on d no r o and to 2 % degrees y the th p le , that it fails n r o f reach the s o uth p o le by the same umbe degrees .

’ (c) That the placeup o n the earth s surface where the r ra n r n ve tical y falls , is the ce te Of the Illumi ated Hemi r and an n in o o n o f o n ro sphe e , that y cha ge p siti this p i t p

ihe n in I llu min ated and an o duces a l cha ge the , Opp site change in the Da rh Hemispheres .

d On n 2 l st h and o f su n ( ) That Ju e the lig t heat , the is u n equa llydistributed in the n o rth and south hemispheres LUNAR TE LLU R1 AN MANUAL . 2 1

that the Illumi n ated Hem i sphere pred o mi n ates n o rth o f

o and D r r r o n the equat r, the a k Hemisphe e p ed mi ates

s outh Of it .

o o on and to R tate the gl be up its axis , ask the pupils o bserve

a un ro o f n ( ) That the vertical s traces the T pic Ca cer .

b ro on in man ( ) That as the earth tates up its axis , this n er n A rctic rema in i , all places withi the circle will n

s n o r on n n A nta rctic u light , while c resp di g places withi the

r n withou t n Will emai su light .

th o f o f n (c) That fro m the 20 March t the 2l st o Ju e , su n n no 23 o r the vertical has bee carried rth % degrees , north and o o n to x n o f 2 that a . s uth distributi the e te t 3 % d n egrees has take place .

To Il lu s tra te th e Di s tri bu ti on of Li ght a n d Hea t n o the 2 3 d of S ep tem b er .

Bri ng the calendar index to the 2 3d o f September ; this illustrates the relati o nship that exists betwee n the e and sun o n A sk to arth that day. the pupils Observe

a l sun f o 2 l st o f n ( ) That the vertica has , r m the Ju e to 23d o f S n r s outh ro the eptember , bee car ied f m the

‘ Tro pic o f Cance r to the equato r and that the Illu min r n o o n n n ated Hemisphe e has bee c rresp di gly cha ged , so ’ o n S 2 3d n and that eptember , the su s light heat is again e ua l r in no r q ly dist ibuted the th and s o uth hemispheres , a nd n n fro o to o o n h exte di g m p le p le , as March 20t .

b h o n w as o n o r ( ) That w atever distributi sh w , what

o r o n o o n 2 h a ever bse vati s c uld be made March 0t , re a an oduc on S g i repr ed eptember 2 3d. 2 2 LUNAR TELLURIAN MANUAL .

To Illu s tra te the D is tri b u ti on of Ligh t an d Hea t

on D ecem b er 2 2 d .

r n n n to 22d o f D and B i g the cale dar i dex the ecember, ask the pupils to o bse rve

(a ) That the sun is vertical 23 % deg rees s ou th o f the

o r eq uat .

(b) That the Illumi n ated Hemisphere no w extends r o n s ou th o and to 2 3 % deg ees bey d the p le , that it fails

no r ol the n o f r reach the th p e by same umber deg ees .

c o n D 22d and o f ( ) That , ecember , the light heat the su n is again u n eq u a lly distributed in the n o rth and s o uth

and n r re hemispheres , that the Illumi ated Hemisphe e p

s ou th o f o r and D r d o mi n ates the equat , the a k Hemi

n rth Sphe re p red o mi n ates o Of it .

ob o n and to Ro tate the gl e up its axis , ask the pupils o bserve

(a) That t he ve rtical su n t races the TrOpic o f Capr i

corn .

(b) That as the ea rth ro tates up o n its axis i n this n n r n A nta rctic rema in in ma e , all places withi the circle l i i n o rr o n n aces , w th n A rctic su light , while c esp di g p the

it o u t n ci rcle w ill remai n w h su light .

r o r a n o and o o n has n deg ees , that rth s uth distributi take place .

B ri ng the calendar i ndex sl o wly to starti ng p o i n t

r 20th and r r su n (M a ch ,) Obse ve That the ve tical is rr ro ro o f o rn to to r the ca ied f m the T pic Capric the equa , place o f beginning ; and that a no rth and s o uth distribu LUNAR TELLURIAN MANUAL . 2 3

’ tion o f the su n s light and heat has taken place fro m the

o o and n and equato r to b th tr pics retur , that the time

o do o ne and as the vertica l ra n ecessary t this is year , y

dis tribu ted s o mu s t a ll other ra s that touch the is , y ’ ’ r a ce e a ectea ea rth s s u f b f .

Thus we see that there is a dou ble distributio n east

d da i and no and o a nn u a l . an west ly, rth s uth ly

Th e Ca u s es of the E at i s ti n g Di s tri b u ti on of Li gh t

o n and 1 . The daily distributi east west is caused by o n o t o n the daily rotati f the ear h its axis .

nn o n no r and o s 2 . The a ual distributi th s uth is cau ed

(a) By the revolu tion qf the ea rth in its orbit a round h u n r i r t e s . n n o and If the ea th remai ed ﬁxed its bit ,

o o n o n e o n o rev lved up its axis , but distributi c uld take — place the daily .

’ 5 B the i n clina tion o the ea rth s a x is o ( ) y f . N tice that on 20th o f r n n 23 the Ma ch the axis is i cli ed % degrees ,

n n o n n either to no r rom sun but that the i cli ati is f the , and su n n o o o that the is the vertical t the equat r . N tice that o n the 2 l st o f ju ne the n or th po le is i n cli ned to the sun u ll in clin a tion o f 23 r and fo r the f % deg ees , this reaso n the sun is vertical the s a me number o f degrees n o o f o n D d no o . O 22 rth the equat r ecember , the rth p le

n n rom sun n n o n r n is i cli ed f the the full i cli ati , this b i g in o rn n the u n r g Capric u der s . E ect the axis by sup ’ o n o o n o o p rti g the gl be the ther s cket , call the pupil s attentio n to the fact that the equato r and the ecliptic n o w in n o r ro n lie the same pla e . Rev lve the ea th a u d the sun and observe that the vertical ray falls co nstantly 2 4 LUNAR TELLURIAN MANUAL .

‘ up o n the equato r with o ut an i ncli n ati o n n o annual

r o n o f and o dist ibuti light heat c uld take place .

’ c B the a ra llelis m o the ea rth s a x is ( ) y p f . The axis t r o n o n n to is said o be pa allel , because it p i ts c ti ually the

r o f heav ens z n o r o o n same pa t the thus , the th p le p i ts

o n n o r o r S r r re ~ c sta tly t wa ds the N th ta , While the ea th o ro n u n o o ro n v lves a u d the s . Rev lve the gl be a u d the arc S and o bserve that the a x is p o i n ts c o nstan tly in the

r o n r o f and same di ecti . This is t ue the earth all the

an re iolv e in o pl ets as they s their several rbits . This is

r o f te rmed the pa allelism the axis .

Eq u a l D a ys a n d Ni gh ts .

1 . n n n to 20th o f r Bri g the cale dar i dex the Ma ch , and ask the pupils to o bserve

(a ) That the Day and Night Ci rcle B divides the — earth i nto tw o divisi o ns day and Night that all places

o n o f r n ex t to the s u n the side this ci cle have day , while

o o n o n th se places the Opp site side have ight .

(6) That at this seas o n o f the year the s u n is ve rtical to o r and Da and r the equat , the y Night Circle is pa allel

r to Opp o site me idians .

(c) That in this p o siti o n the Day and Night Circle r r o f ro o to o divides eve y pa allel latitude , f m p le p le ,

n o two e u al r i t q pa ts .

o o o o n and R tate the gl be sl wly up its axis , ask the pupils to o bserve

(a) That a ll places upo n a given me ridian enter the n s a e moment su light at the m .

(3) - That one- ha lf a ro tati o n o n the axis ca rries these

2 6 L T A UNAR ELLU RIAN MANU L .

(a ) That no su nlight o r day reaches that po rti o n o f ’ the r n A n ea th s surface withi the tarctic circle , alth o ugh

r o o n the ea th may rev lve up its axis .

’ (5) That the entire area o f the earth s surface withi n

A l no t ou t o f n the rctic circ e , is carried the su light by the o o n o f o n r tati the earth up its axis .

(c) That the Day and Night Circle cuts the equator at o o o n and there and n pp site p i ts , that the days ights are eq u aL

d T o u o n orth ro to to ( ) hat, as y pr ceed f m the equa r

Ar i n creas e in n r the ctic circle , the days le gth g adually o 1 2 o o to 24 o r n A rc fr m h urs at the equat r, h u s withi the tic Circle .

e o u o s ou th o o to ( ) That , as y pr ceed fr m the equat r the A n decreas e in n r tarctic circle , the days le gth g adually ,

ro 1 2 o r o r to 0 o r n A nt f m h u s at the equat , h u s withi the

r a ctic Circle .

n the n r n to the 22d o f D and Bri g cale da i dex ecember, ask the pupils to o bserve : that what was true o f the

n orther n in u n e no w r o f s ou thern 7 , is t ue the hemi

r in ecemher n Sphe e D . Thus it is evide t

1 . n su n o n o That whe the is up the equat r, the days an r d nigh ts are everywhe e equal .

2 n r su n o ne o r o r . That whe the ve tical is m re deg ees

no r o r o o f o r o n n da th s uth the equat , c ti ual y must exist

ro n o n ea rer sun and o n n n i ht t a u d the p le the , c ti ual g mus

' exist aro u nd the po le f a rther fro m the su n the ex tent o f this area o f co ntinual day and n ight depe nding upo n the distance o f the vertical su n n o rth o r So uth of the

or equat . LUNAR TELLURIAN MANUAL . 2 7

and n t o a l 3 . That the days ights a the equat r must

a w ys be equal .

4 o u ro o o n . That as y depart f m the equat r, the variati in n o f and n incr eas es and o u a the le gth day ight , as y p pro ach the equato r the va riatio n beco mes les s the ma x imu m r o n n in o a and n in va iati bei g the p l r, the mi imum

o r o n the equat ial regi s .

n o f an a o n an r 5. That the le gth y dy up y pa allel o f n orth to n o o n o n co r latitude , is equal the ight f ll wi g the r o n n o f ou th la titu de esp di g parallel s . — No r m In this wo rk we regard day as the time when the su n

is resent and n t as the t m e w en he absent. N t do es f , igh i h is igh no t n ec e ar m an arkness N t be n at u n et and ends ss ily e d . igh gi s s s at s u nris e.

’ Th e S u n s Ap p a r en t P a th .

’ n n r n x to 2l st o f n ro Bri g the cale da i de the Ju e , tate the gl o be o n its axis u ntil the E cliptic ma rked upo n the

o o n r r u n o r gl be is br ught u de the ve tical S . M ve ve y sl o wly the calendar i ndex th ro ugh the succeedi n g m o n ths un n o to 2 l st o f n and til it agai c mes the Ju e , ask the pupils to n o tice that the ve rtical su n t races the ecliptic and r no da i o o n o n its x if the ea th had ly r tati a is , that the ecliptic w o uld mark the true path o f the S u n up o n the earth .

R o tate the earth up o n its a x is and ask the pupils to o r S un tra ces Tro ie Ca ncer and bse ve that the the p qf , that if the su n sho uld leave behi nd it a th read o f light ,

r o o n r0 i o n that th ead w uld lie up the t p c . M ve the cale

n x 0 ' 22d o f n and o o o n dar i de t the Ju e , r tate the gl be up

and no su n r n a ra llel to its axis , tice that the t aces a li e p

ro o f n o o f r o of the T pic Ca cer , but ab ut a deg ee s uth

it In r r in . the same manne p o ceed with several days 2 8 LUNAR TE LLURIAN MAN UAL .

‘ successi o n and o bserve that by reas o n o f the ro tation o f

' the earth upo n its axis and the m o vement fo rward o f

r in o r s o f the ea th its bit at the ame time , the path the vertical su n will be a conti nu o us li ne ru n n i ng fro m eas t to and n n o ro n r to r o n west , wi di g s uth f m Ca ce Cap ic r , and rn n r n r o n retu i g du i g the yea , much as a thread is w u d

o n o o up a sp l .

h n of sons C a ge Sea .

To p ro duce what is called a chan ge o f seas o n at any

o ol o n r n place , m re s ar heat must fall up that place du i g one o f r n a nother n th e ro part the yea tha at . Withi t pics the am o u nt o f heat received fro m the su n is n early u ni

o r ro o r so r n o f f m th ugh ut the yea , that ve y little cha ge seas o n takes place the greatest changes o ccurri ng in

r the highe latitudes .

B ri ng the cale ndar i ndex to the 20th o f March and ask the pupils to o bserv e

(a) That the light and heat o f the su n are equally dis in n o r and o r tributed the th s uth Hemisphe es .

(6) That if the earth remai ned ﬁxed in its o rbit and o o n o no cha n e o f was r tated up its axis , there c uld be g o n seas s .

Bri ng the calendar i ndex to the 2l st o f Ju ne and ask the pupils to o bserve

(a) That the sun is n ow vertical to the tr0 pic o f can ’ and n and n cer, that the su s light heat is u equally dis

m no and o no tributed the rth s uth hemispheres , the rth hemisphere havi ng the g reater and the s o uth hemisphere

o n the lesser am u t . LUNAR TELLURIAN MANUAL . 2 9

(5) That o wi n g to this ineq u ality‘ he no rth hemisphere n o n o f and is havi g its greatest am u t light heat , its on o r S r and the o warmest seas umme , that s uth hemi

o r n sphere is havin g its coldest seas on Wi ter .

B ri ng the calendar i ndex to the 2 3d o f September and ask the pupils to o bserve that the light and heat is again equally distributed n o rth and s outh o f the equato r as in

r h Ma ch 20t .

B rin g the calendar i ndex to the 22d o f December and ask the pupils to observe that the su n is vertical to the ’ trO ic o f o n n and n n p Capric r , the su s light heat bei g agai u ne all r in no r and o q y dist ibuted the th s uth hemispheres , the s o uth havi n g the g reater and the no rth the lesser am ou nt and that at this time in the year the s o uth n on o r S hemisphere is havi g the warmest seas ummer, in n o r in o o r n while the th it is the c ldest Wi ter season .

n n n to 20th o f an Bri g the cale dar i dex the March , d observe that the sun is bro ught to the equator g oing n orth and cros s es S r n n that as it , p i g begi s m the n o rth

and A n o r n in o utum Fall begi s the s uth hemisphere .

Th e Causes that produce the Change of

Season s .

n e o f o n o The cha g seas s is pr duced by ,

(a) The rev o luti on o f the earth in its o rbit arou nd the

sun .

5 ’ ( ) The i ncli nati on of the earth s axis to the plane of o the rbit .

\ ’ (c) The parallelism o r ﬁ x ed position o f the earth s x a is . 0 L TE LLU R rAN 3 UNAR MANUAL .

d o o n r o n x ( ) The r tati the ea th up its a is .

TO illustrate that the ro tatio n o f the earth upo n its axis is o ne o f the causes that p roduce the changes Of sea s o ns as they now exist b ring the calendar i ndex to the

2 0th r o n o n o h Of Ma ch , mark the p i t up the equat r w ere the sun is vertical at that time no w m o ve the calendar i ndex sl o wly through the succeedi ng m onths o f the year

n n r i o n u til it is agai ve t cal to the same p i t . Call the ’ pupil s attenti o n to the fact that if the earth did not ’ o o n the sun o O ne to r tate up its axis w uld require " year

ro th e n once and in c ss all meridia s , that this case it w o uld c ro ss them fro m west to east i nstead o f fro m east to west ; that the su n w o uld in that event rise in the wes t a nd in eas t and o u r and o o f set the , day year w uld be the l n and h r o f same e gth , that if t is we e true , the side the earth t o wards the su n w o uld be parched by the ex tr o o l o roz n eme heat, while the Opp site side w u d bec me f e

and e s . S O the rt n o t o o n lif le s , if ea h did r tate her axis , n o n o f o n n ow s o cha ges seas s as they exi t c uld take place , no r in fact co uld animal o r vegetable life as no w con s tituted endu re the extremes O f heat a nd co ld to which they w o uld be subjected .

TO sh o w how the sun after go in g belo w the h o ri z on

n n o d l t and h n o co ti ues t give reﬂecte igh , e ce , pr duces twilight .

o is ‘ co m bsed The m o lecules o f which the atm sphere p ,

’ r ro sun and b the reﬂect the light they eceive f m the , y l s o r Ob ects a re n in n Of ight eﬂected, j see the abse ce direct

n l The a o le Of hu i n s u ight. tm sphere is capab t s reﬂect g LUNAR TELLURIAN MANUAL . 3 1

“ r o f rea t light a mea n distance Of 1 8 deg ees a g circle . ’ Call the pupils atte ntio n to the fact that the su n gives direct light fro m the p o i nt where he is ve rtical to the

Da and i r and n o r r y N ght Ci cle B , that the i direct eﬂected n to the and the n light exte ds circle C , that space betwee

ili ht elt n these ci rcles is called the Tw g B . He ce the ’ earth s su rface as regards light is divided i nto three sec A o n 1 A di rect . 2 . 1 8 ti s : . hemisphere Of light belt

f r o r . re degrees wide o eﬂected light twilight 3 . The

n ith u t i ht mai i ng p o rti o n w o l g .

T ll tr te t wi li h t on th e 2 oth o a rch o I u s a he T g f M .

B ri n n r n to 20th g the cale da i dex the Of March . Call ’ the pupil s attentio n to the fact that there are two twi n n and o rn n n n lights , Eve i g M i g that the eve i g twilight

n n o r n t he o rn n r deepe s i t da k ess , while m i g twilight b ight

n n o n n o o i e s i t su shi e . R tate the gl be up o n ts axis and ’ ask to r u o n the the pupils Obse ve that places p , earth s s u rface must cro ss the twilight belt twice in every 24

o r o o o o n h u s . R tate the gl be sl wly up its axis and ask the pupils to Observe that all places up o n the s a me me ridian fro m p o le to p o le pass i n to eveni ng twilight at

s a me n n o o n r the i sta t , but that th se places l cated ea the

o a o u t w rs t and equat r p ss Of t ilightﬁ , that the higher the t o n o n n lati ude the l ger the twilight c ti ues . This varia tio n is due Sr

l t TO s . the fact that at the equato r the earth ro tates

a s ter n o n o fo r r f tha it d es ear the p les , the same easo n that the o uter part Of a wago n wheel turns faster when the o n in o o n n h b wag is m ti , tha the u .

d r 2 . This va iatio n is partially due to the fact that places near the equato r are carried acro ss the twilight 32 LUNAR TELLURIAN MANUAL .

in n and r i ht a n les to belt a straight li e , at g g it while n ear the p o les places e nter the twilight at right angles

and o not in r n with the ﬁrst circle cr ss the belt a di ect li e , but travel o n an arc of a circle pass i ng o bliquely ac ross

s econd the circle .

Fro m this we see that places in the higher latitudes

a rther to o and must travel f cr ss the twilight belt , at the o n o n a same time , much sl wer tha th se places situated e r o the equat r .

‘ Lo cate up o n the map o f the gl o be the place where

o u are o o o n and y situated , r tate the gl be up its axis ask the pupils to no te carefully the manner this place is

aro bélt T twi carried c ss the twilight . his illustrates the

l o n 20th Of fo r . ights the March , that place

To I llu s tra te th e Twi ligh ts o n th e 2 1 s t of J u n e.

“ Bri ng the calendar i ndex to the 21 st Of Ju ne and ask the pupils to Observe

(a ) That the twilight belt n o l o nge r co nfo rms to the n and no two o n meridia s , that places up the same meri dian e nter the eveni ng o r emerge fro m the m o rni ng

o n twilight at the same m me t .

(6) Th o se places that in March cro ss the twilight belt

r i ht a n les to n ow ro ohli u e so at g g it , c ss it q ly, that the i twilights fo r these places must be l o nger in Ju ne than n

r Ma ch .

leas t o and in (c) That the o bliquity is at the equat r , n creasi ng as the latitude i creases .

Locate upo n the map o f the gl obe the place where

’ ou are o a o o o n and y l c ted , r tate the gl be up its axis ask

34 LUNAR TELLURIAN MANUAL .

o f n l n o o n o n 20th o f a ju e , a d m re bliquely tha the , M rch

and 2 3d o f S r. n n t n eptembe He ce , a mea twilight be wee o t o the ther w .

d o 3 . N w ask the pupils to no tice that o n the 22d Of

D sun r a to o u 2 3 and ecember the is ve tic l s uth latit de A, o n 2 l st o f n no o n n the Ju e , rth latitude C seque tly the su n sustai ns the same relati o n in every pa rticular to t he S o n r o r o uther Hemisphe e at the f rme date , that it d es

to o r rn n th at the latter date the N the . He ce , all e facts o bserved regarding the twilight o n the 2 l st o f jun e in ' n o rthern latitudes apply o n the 22d bf December to co r r o n n o rn n Ob esp di g s uthe latitudes . He ce , all the facts se rved on the 22d o f December in n o rthe rn latitudes may

o n o n 2 t o f n in o n be f u d the l s Ju e the s uther latitudes .

’ S u n s D ec li n a ti on .

’ S u n s Declinatio n n n o o r o The . is his dista ce rth s uth n r n o f the equato r (as i dicated by the ve tical ray). Whe thesun is n orth Of the equato r he is said to have a n orth ern declinati on when s ou th Of the equato r he is said to n have a s outhern decli atio n . ‘ The greatest no rthern declinati o n (2 3 % degrees) o c r On 2 l st Of n and o n cu s the Ju e , the greatest s uther de

D r h in io de rees o ccu rs 22d. A t t e c l at n (2 3 % g ) . ecembe the e u inox es 20 and S 2 3d time Of q (March eptember ), n o n n the su n has decli ati o .

’ To Fi n d the S u n s Decli n a ti o n f o r a n y Da y.

" ' B ri ng the c alendar i ndex to the g1ven day, ro tate the gl obe up on its axi s u ntil the meridian having the degrees ' o o o L ' x n Up n it is br ught u nder the p inter . E te d the LU N AR TELLURIAN MANUAL . 35

o n L o o o f n p i ter t the gl be . The degree latitude u der n t he p o inter is the requi red Decli ati o n .

To Fi n d th e Lo n gi tu de of a n y P la ce.

t o o n n the h l is R ota e. the gl be up its axis u til give p ace u n r o n r o n o de the p i te H , the degree the equat r at the

end o n r on Of the p i te H is the l gitude required . The l o ngitude is east o r west acc o rding as the place is east or

o f r n west the Prime Me idia .

E XAMPL E S .

n o f N e " o 1 . What is the l o gitude w rk

o n o f u 2 . What is the l gitude Calc tta

o n o 3 . What is the l gitude Of "uit

o n S t. 4. What is the l gitude Of Petersburg

o n u o n o 5 . What is the l git de Of H lul u P

To Fi n d th e La titu de of a n y P la c e.

R otate the gl o be upo n its axis u ntil the given place IS b o n r o n o on r ught u de the p i ter H , ab ve the place the

o n r r r o f o r n p i te ead the deg ee latitude required ; , bri g

the n n r o f r r give place u de the edge ci cle B , ma k the c r r o r n ro o n i cle di ectly ve the give place , tate the gl be u til the me ridian havi ng the deg rees marked up o n it is b ro ught

n r . U n r o n r o n u der the ci cle de the p i t ma ked , read up

the mr n r d r . e idia , the deg ee Of latitu e requi ed If the

n o r o f o no o place is th the equat r it is rth latitude , if s uth o f so t : it, uth la itude E EXAMPL S . What is the latitude o f N ew " o rk ' What is th e latitude Of Calcutta P ‘ What is the latitude o f "uito o f St r What is the latitude . Petersbu g What is the latitude Of H o no lulu What is the latitude o f S antiago P UNAR TE URIAN MANUA L LL L .

CUT No . 2 .

o and n r in o Rem ve the day ight ci cle , as the ab ve cut .

A s no w n L n n o to see , the u ar Telluria sh uld be used

n o f o o n o n o f explai the phases the m , eclipses , equati o n of no time , precessi equi xes , etc .

36 LUNAR TELLURIAN MANUAL . 37

i i Long tude and T me.

Lon n r o w in . gitude is dista ce , measu ed h ever degrees ,

n o n o r Of i n er n mi utes and sec ds , east west a g ve m idia

' r r d n r r called the P ime Me i ia . Obse ve that the deg ees ' r u On o at' e hato r and are ma ked p the gl be the q , east west

o f r n — r r n from the me ridian G ee wich the P ime Me idia . O n page (9) we learned ~ that every ci rcle is divided i n o 360 r r r t equal parts called deg ees , eve y deg ee is sub d n o 60 r n and ivided i t equal pa ts called mi utes , every

n o a r o n m i nute is subdivided i t 60 equ l pa ts called sec ds .

The earth in its relati o n to the s u n tu rn s o nce o n its ‘

360 r 24 o an d n n axis ( deg ees) every h urs , must tur as ma y degrees eve ry h o ur as 24 is c o ntai ned ti mes in 360 o r 1 5

d r in o n e r rn d r . S n rn 1 5 s o to eg ees i ce it tu s eg ee h u , tu

' o n e degree it will requi re 1 - 1 5 Of an h o ur o r 4 mi nutes f o time .

" R o tate the gl o be fro m west to east u ntil the p o i nte r L is o ve r the p rime me ridian n o o n no wtakes place up o n

at r n ro o to o r th me idia f m p le p le . Obse ve that all places

' eas t o f this - m eridian hav e passed the sun and that their

' no o n o to wes t have not has passed , while th se places the et n ro to su n and their noon no y bee b ught the , will t yet n have take place .

EXAM P L E 1 .

‘ ’ n no o n 1 2 o o r n Whe it is ( cl ck) at G ee wich , what is the

i h - r 1 0 o f n time Hambu g , say degrees east Gree wich Hamburg bei ng eas t o f G reenwich the time islater by

r to rn 1 0 r S n the time required by the ea th tu deg ees . i ce the r rn o ne in 4 n to n 1 ea th tu s degree mi utes , tur 0 de r r 1 0 4 n o r 40 n g ees will requi e times mi utes mi utes .

ff n in r o 40 n and n The di ere ce time is the ef re mi utes , si ce ’ 1 2 o o r n 40 n r 1 it is cl ck at G ee wich , it is mi utes afte 2 at Ha o r 2 n P 0 to 1 . . mburg, mi utes M 1 “ 8 LiJ N A R T N 3 ELLURIAN MA UAL .

X E E AMPL 2 .

' When it is no o n at G ree nwich what is the time at Rio

n o B z 52 Ja eir , ra il , degrees west 6

Rio n o n wes t r r Ja eir bei g , the time is ea lie by the time

r to rn 52 r S n the required by the ea th tu deg ees . i ce

r rn r in n ea th tu s 1 deg ee 4 mi utes , to tu rn 52 degrees will r 52 4 n o r 208 n requi e times mi utes , mi utes . Reduced 3 h o u rs 2 8 mi nutes the time befo re n o o n at Ri o janei ro ’ ’ 1 2 o o o o n m n o mi n 3 28 i . 8 o 32 n . cl ck less h . cl ck

Rio n ro . A . M . the time at Ja ei

E 3 EXAMPL . ’

n o o . r the Whe it is 1 1 cl ck A M . at Hambu g what is

r o n S . C . 80 w r o n time at Cha lest , , degrees est Cha lest

n ea rlier r o n 80 r bei g west the time is . Cha lest is deg ees

r n and 1 0 r west Of G ee wich Hamburg deg ees east , the distance betwee n Cha rlesto n and Hambu rg is the refo re

de i r r m n . 80 deg ees 1 0deg ees 90 degrees 1 g. 4

90 . 90 X 4 360 n s e 6 o . deg . mi ute , reduc d , h urs ’ ’ 2 1 1 o o A . M. 6 . 5 o o . . cl ck , less hrs cl ck A M

E EXAMPL 4.

’ o M o n n no n 1 0 o . . 28 Whe it is cl ck A , at C sta ti ple , de

’ “ r e what’ is ’ the in o n K o n 1 1 2 s g e s east, time H g g , degree east P H o ngKo ng being 1 1 2 degrees east and C onstan tino le b n 2 8 r n n m p ei g deg ees east , the dista ce betwee the min 28 de . 84 . 1 de . 4 . 84 is 1 1 2 deg . less g deg ; g ;

" 2 2 min n i r 5 hrs . 36 . deg. 84 X 4 336 mi ; educed

‘ in o n o n n eas t r . ff r n . K di e e ce time H g g bei g , the time the e ’ min. l . la ter n 1 o . 5 hrs . 36 O is tha 0 O cl ck A . M by ; hrs mi o r as o o n hrs . 36 1 36 n: 5 5 hrs . c mm ly read , min 3 . 36 . . hrs . P M LUNAR TELLURIAN MANUAL . 39

E EXAMPL 5 .

n S an r n o 1 2 2 . Whe it is A . M . at F a cisc , deg west,

the o rn A ra 143 de . P what is time at Melb u e , ust lia , g east

i r t r n m n . . s 5 hrs . 1 . O A . 0 A M bse ve tha the g eatest

a wa o n c an 1 80 de . t h l gitude a place have is g , hat is , y y

ro n r r n r o n a u d the earth fro m the p ime me idia . If a pe s start at the prime me ridian and go west he will be in

o n n r 1 80 r n west l gitude u til he eaches deg ees , whe his

o n is it r ro o n l gitude e he east o r west . If he p ceed his

o r ten r his o n 1 80 r c u se deg ees , l gitude is deg ees east , less

1 0 r o r 1 0 . o n o n had o n 0 deg ees , 7 E ast If a c mpa i g e 1 degrees eas t his l o ngitude w o uld be 1 80degrees west less

1 0 r o r 1 0 men n 20 deg ees , 7 West ; the are ma ifestly

r r deg ees apa t .

’ To Fi n d th e Diﬁ er en c e i n Lo n gi tu de B etw een Two

P la c es .

If o are in o n r 1 . b th places the same l gitude eithe east

' o r ro r r n r west , deduct the less f m the g eate a d the esult

1 r ff r n 5 thei di e e ce .

2 . o n e and o r s u m Of If place is east the the west, the

r o n ff r n o o thei l gitudes is the di e e ce , pr vided the sum d es n o t 1 8 r exceed 0 deg ees .

/ . 3. o n e nd o r and If place is east a the the west , the sum o f r o n 1 80 r thei l gitudes exceeds deg ees , deduct the

o n ro 360 r and n r th e ff am u t f m deg ees , the remai de is di er

n o f o n o e ce l gitude s u ght .

S o and Ho w ard leav e r r n upp se j ames the p ime me idia , ‘

‘ Jamesgo i n g west and H o w ard go i n g east when each

r 80 r are 1 60 r r has t aveled deg ees they deg ees apa t , .

r ff r n in lo n d o w r n ea s t which is thei di e e ce gitu e , H a d bei g

o f Let r James . each p o ceed 1 0 degrees farther and 40 LUNAR TELLURIAN MAN UAL .

t are 1 r r o n o r n Ho 80 w . hey deg ees apa t , Opp site me idia s ,

rd n r eas t r e o f Let o n a bei g eithe o w s t James . them c tin u e in thei r c o u rse 1 0 degrees James IS the n 1 00

r and o r r o r deg ees west H wa d 1 00 deg ees east . T gethe

r 200 r and 360 d r are they have t aveled deg ees , as eg ees

r to r 360 200 1 60 n er all the e is t avel , , the umb Of d r n o r n n o w 1 60 r eg ees betwee them , H wa d bei g deg ees w es t Of James .

Let r r o n o rn n o o n us p esume they sta ted their j u eyat , a n d that they carried accu rate time pieces whe n they h ad tra veled 1 5 degrees James w o uld fi nd his watch an

o r to o and to o rr rn h u fast, c ect it he must tu it back , ’ while H o wa rd s watch is fo u n d to be an h o u r to o sl o w and To r e must be set ahead . keep the watches ight , th se

n o n n rn n cha ges must be made c sta tly , James tu i g his

4 n fo r r r r and watch back mi utes eve y deg ee t aveled ,

o r n in ro o r o n H wa d setti g his ahead the same p p ti . When e ach r 80 r o and n o o n has t aveled deg ees as ab ve , it is at ’ r m eridian am es o hr i e 6 s . 40 m n the p im , J watch sh ws .

z in hr m in m s . 2 . r . . 4 2 5 0 A M (80 X 3 0 . subt acted ’ i n ro n o o n hr m n . a d o r f m 1 2 6 s . 40 A . M . ) H wa d s min n r hrs . watch sh o ws 5 20 . P . M . Whe each has t av ’ eled 90 de rees ames 6 o o A . . and o r g , J has cl ck M H wa d ’ o o n n o o n r r n 6 cl ck P . M . whe it is at the p ime me idia . ’ n r 1 79 r w o Whe each has t aveled deg ees , James atch sh ws ’ d o r o hrs min 4 n A M. an 1 1 . 56 . . mi utes . , H wa d s sh ws P M . When they meet at 1 80 degrees thei r watches sho w the

o r 1 2 n . n 1 2 o r same h u , , mid ight James has gai ed h u s by

n o r os 1 2 o r setti g his watch back , while H wa d has l t h u s

n o o n by setti g his ahead . Th ugh b th watches i dicate the ’ l ffer n e in r same h o u r the re is really a day s d e c thei time .

r - rn n We e they quick witted Hibe ia s , we might readily

L ‘ 42 UNAR TELLURIAN MANUAL .

" place is carried acro ss the ‘ twihght belt ; n o te the nu m

" o f o n o r o urn ber degrees the equat the gl be has t ed ,

to and is r o n which reduce time , the resul t the du ati o f w t ilight required .

E S E XAMPL .

1 . en o f w S an r n o What is the l gth t ilight at F a cisc , A ugust 1

' ‘

2 . is the len th o f w B erlin u ne 2 1 What g t ilight at , J

The Sun .

, su n n r f o ur o and ro nd The is the ce te o s lar system , a u him all the planets rev o lv e; and fro m him receive thei r and In r r n light heat . matter he is 750 times g eate tha

the n o n A s o h all pla ets c mbi ed . all b dies attract eac o ther and in pro po rtio n to the a mbu nt Of matter they ’ on n so n r o n 50 r r c tai , the su s att acti must be 7 times g eate

n o n r o n o f n and re tha the c mbi ed att acti all the pla ets , we . they all to u nite they c o uld n o t m o ve him his o w n

r ro r f o r diamete f m the cente o gravity o f o u r s la system .

r S O we may justly regard the s un as the ce n ter o f g avity . The attracti o n Of the su n is so much greate r than the ’ r bo n 5 lbs . o n r o ea th s , that a y weighi g 7 the ea th w uld

o r to n o n u n weigh ve a if placed up the s .

The ancie nts th o ught the sun to be an immense gl o be o f i ro n heated to a white heat. While th 1s 1 8 n o t lite r

r it s o r o f sun n ally t ue , h ws they had a bette idea the tha

o f r o to a t. the ea th , which they th ught beﬂ

The apparent diameter o f the su n is ab o ut a de

r — r r r n o a g ee athe m o e than less . Whe viewed thr ugh p o we rful telesc ope his surface p resen ts a mottled appear

n ro o r o n to o f e a ce , which P fess Newc mb like s a dish ric

r so up with the rice grai ns ﬂ o ati n g up o n the su face . LUNAR . TELLURIAN MANUAL . 433

sun to rro n r r The seems be su u ded by a ve y are , light

o r r n ro n to o in atm sphe e , p i cipally hyd ge heated a gl w , i which ﬂeecy cl o uds seem to ﬁ o at these cl o uds se rv e to

‘ cut off fro m us so me o f the ﬁ e rce l ight and heat o f the

' sun and were it not fo r ro no r , these , ast me s tell us his n light and neat w o uld be i to lerable .

n n on of the s o t The prevaili g Opi i be t auth rities is , tha the su n proper is c o mpo sed of condensed gases un der

and to r n s great pressure , heated a temperatu e ma ytime n f rn greater tha u ace heat .

o r o n o f ro n The s lar Spect um Sh ws the prese ce hyd ge ,

ro n n s o an d o n in su n i , mag e ium , s dium ther eleme ts the

‘ o f su n o o n o r but what the is c mp sed we k wve y little . His extreme b rightn ess re nde rs Observatio ns very dith ‘ su n h cult . If the were placed at t e distance o f the nearest ﬁxed star he wo uld appear no la rger than o ne o f the smaller stars .

Sun o on fo o The has three m ti s , as ll ws

1 . A ro on o n o n in 25 9 o u tati up his axis ce days , 54 h rs .

2 A fevolu io n o . t n n o f . s I ar u d the ce ter gravity Thi o n r m veme t is ve y Slight .

A o on 3 . rev luti aro un d s o me distant and u nkno wn

n r n W 1 th n ce ter, ca ryi g him the e tire s o lar system at a rate of an o and r n miles h ur, t aveli g in an o rbit so

to o n o o o great that make e c mplete rev luti n , requires ab out eighteen million yea rs " This is perhaps the m o st

o n n o f all o no o n and th ast u di g astr mical m veme ts , e " questi o n Whither are we go i ng " may well be askedt i o L T 44 UNAR ELLURIAN MANUAL .

Th e arth E .

o ne Of h r1nC1 al n She The Earth is the eig t p p pla ets . r n in z r in her n ro u n a ks ﬁfth si e , ahd thi d dista ce f m the s .

’ Her n r w n 91 and 94 o n dista ce va ies bet ee milli miles .

She n o o n o o f has at least eight disti ct m ti s , but s me them

n o t o ur ro n to o n r in s o r A o n it is p vi ce c side thi w k . m g the S1 mpler and better u ndersto od o f the number are

o o n U o n h r r 2 o 1 . e r R tati p axis eve y 4 h u s .

2 o o n ro n su n nn l in . Rev luti a u d the a ua ly an Elliptical

o rbit .

o to n o f o r ro n o o 3 . Rev lu i the equat a u d the p le f the

f n o E S ee r o n o . cliptic . ( P ecessi the E qui xes )

’ r n o o and The E arth s su face is divided i t s lid liquid , there bei ng ab o ut 3 - 1 0 of the fo rmer and 7 - 1 0 o f the a n and Th t ol . e la ter . The s id we c ll la d the liquid water c rust and liquid c o veri ng Of the earth as c o mpared with her z ver hin ro n o t h n r si e is y t , p bably a u d ed miles thick , a nd if sh o wn upo n the gl o be the c rust w o uld be reduced t o the thickn ess o f thi n c ardb o ard " This c rust is sup r n r o r po sed to ﬂ o at o n the m o lten ﬁe y i te i r Of the ea th . A m o ng the pro o fs that the i nteri o r o f the ea rth is a sea o f

are o o n ﬁre , the f ll wi g

A s we go d own in to the s o lid crust o f the earth the temperatu re rises at n early the u nifo rmrate o f 1 degree n At n o f n fo r every 50 feet we desce d . a dista ce less tha

o o 1 0 2 miles , water w uld b il ; at a depth Of miles , the

- hot o r 90 to 1 00 crust w o uld be red . Bel w the su face ,

r r o f n to an miles , the tempe atu e w uld be su ﬁcie t melt y

o n s ubstance k no w n t ma . ’ LUNAR TELLURIAN MANUAL . 45

’ ' In r o r o f r f ﬁ nd 2 . va i us pa ts the ea th s sur ace we ' ’ n s o f ho t r o n u o u t o f r Spri g wate b ili g p the earth s c ust, andwe k no w o f no way the water co uld be heated ex cept

n rn r o f ar by the i te al ﬁ es the e th .

3 . V o no to ro lca es , that seem act as safety valves , th ugh which the Furies o f the pen t up fi res fi nd relief in sen d m in o r a and . o o g f th fire , g ses lava The latter is c p sed

’ o f - n o n n o and n s well k w substa ces , such as r ck mi eral

to o r melted a liquid f m .

orm o f n o and 4. Thef the earth ﬂatte ed at the p les

o u t o o r in bulged at the equat r, sh ws that the ea th her

o o o childh d (if we may be all wed the term), must have n in o in r o bee a s ft, pliable state , which case the ea th w uld n r o r no ha ro ecessa ily assume the f m she w s . F m what we k n o w o f the i nteri o r o f the ea rth it co uld no t have been in this s o ft plastic state except by the actio n Of heat: l Ge o l o gical fo rmatio ns Sh o w evidences o f great heat at ’ r r o o f r n s o me fo mer pe i d the ea th s existe ce .

Moon Th e .

h o on ’s o rm i z e a n d P h s i c a l Co n di ti T e M F , S y on .

oo n r r n r o n . The m , like the ea th , is ve y ea ly r u d Her

r and o 1s o t 1 - 49 diamete is miles , her v lume ab u the

z o f r and o n ‘ z o f si e the ea th“ ly t vmtimum times the si e l sun . o o n to a ea rs n ear r the The m , us , pp y as la ge as un o 400 n the s . This is because she is ab ut times earer to A ro n h in air r n us . ball th w hig the seems smalle tha

n o r whe t ssed up but a few feet . Thus we see the appa

‘ ent si z e o f b odies depends largely up o n their distancé

o fr m us . L 46 UNAR TELLURIAN MANUAL .

The ' m o o n n ro o r n , as see th ugh a telesc pe , p ese ts a very

n n - and o n r o n r o n u eve br ke su face , sh wi g ve y high m u

n and- r r o f n o n o tai s , deep valleys , the c ate s imme se v lca es n o n o o r o a r o w exti ct . The cl uded m ttled ppea ance f its " r o man in o o n and su face s metimes called The the m ,

n no r n o n to n an d t r which ma y ig a t pe ple thi k be la d wa e , is really due to the differe n ce in the reﬂecti ng p ow er o f ’ r o u o r o n o f o o n r the va i s p ti s the m s su face . The higher p o rti o ns o f her su rface seem to be c o mp o sed o f lighter

o o r r n o r ‘ and o e c l ed mate ial tha the l we , they will theref r reflect m o re light than the darke r c o l o red and l o wer su r

If n ro o or face . exami ed th ugh a small telesc pe ﬁeld

are to o S o o n glass , we able see s me p ts the lighter sec ti o ns b righte r than the su rro u nding su rface these are the o f o n n o ro n n n summits m u tai s , the m st p mi e t bei g

r o f o n o o r o r o n o f c rate s v lca es . The m st ca eful bse vati s

e o o n o an o r c an t h m fail t sh ow y atm sphere . The e be ’ n o r fo r the n r n o n lu narida s wate , su s heat du i g the l g y (ab o ut a m o nth l o ng) w o uld evapo rate it and p roduce a c l o ud - like ﬁlm aro u n d the m o o n that co uld readily be n see .

The res u lts o f o bservati o ns upo n the physical c o ndi ti o n s o f the m o o n are such that we must co n clude that it o e o d n n o f is a c ld , lifel ss b y, the esse tial eleme ts life , a ir and r n o t n o n wate , bei g f u d .

’ Th o o o ti e M n s M on s .

The mo o n r o o o n has th ee p sitive m ti s .

A revolu tion on b er ax is once in 2 9 da s . 1 . % y Thus w e see the lu n ar day is 2 9% times l o nge r than the terres

r To an obs erv er o n o o n n o r t . ial t , the m ear its equat , the s un w o uld rise in the east and set in the west but the ’ L TE LLU RLAN . , UNAR A MANUAL pe riod of time betwee n su n rise and su nset w o uld be equal to n r 1 5 o f o u r rr and n sun ea ly te estrial days , whe the

n o r fo r a r o Ho r h ad set it wo uld t ise n equal pe i d . w g eat m ust be the extremes o f temperature ' " The lu n ar day must be hﬁtter tha n anythi ng experie nced upo n the

r h r n the n r n g r t r ea t while , du i g lu a i ht the tempe a u e must fall to a degree u nk n o w n save in the p o lar latitudes o f

To an o er r o n t e o on r o o u r r . ea th bs ve h m , the ea th w uld

lik e o o n 1 r t n oo n l o o k .a huge m 3 times large ha the m

. r to u o r n h o f o o n appea s i s . It w uld p ese t the p ases the m

o n a ra n r . O n to as we see them , but g de scale 3 wi g the ’ ' m o o n o ro t o n er o n o t ar to s sl w axial ta i , the a th w uld appe r o ro n " r n and o r ev lve a u d it , but me ely swi g back f th t ro f h ugh a ew degrees .

A o o n r I 2 . o n r o n in .27 . rev luti a u d , the ea th ce /é days

A ol o n r ro n u n 3 . rev uti with the ea th a u d the s n an u a r o f tw o o o n lly . The esult the last m ti s makes the

of m o o h r e r The o n actual path the ve y p culia . sec d mo

o n n o n o f s o rr o o n ro ti me ti ed , it elf, w uld ca y the m a u nd

r so - o u an e wh the ea th that its path w ld be llipse , ile

o r h o n o n o n n o h weve , t is m veme t is g i g , the last me ti ned

o n N o o in r . 3 a o n and o 30 m veme t , ( ) is ls Ope ati is ab ut r or r o n times as apid as the f me (N . maki g the actual

an i rre u la r r e o e o and o path g cu v , s metim s utside s me ’ n r o r a lwa s cu r ves times i side ,the ea th s bit ; but its path y ’ t o the su n : The m o o n s o rbital vel o city is ab o ut

o fo o r in her miles per h ur , while she ll ws the ea th great — o rbital j o u rney at the rate o f miles an h o ur over

a llz ou s a ml miles a s econ d.

“ If the earth were at rest in her o rbit the path o f the m o o n wo i t o N o . 1 uld be sim lar cut , (E the earth, M 48 LUNAR TELLURIAN - MANUAL .

o o n rro o n the the m , the a ws sh wi g ’ di recti on o f the m o o n s revo lu o n : S n r no t r ti ) i ce the ea th is at est , ' o 1 sho w s the relative and not cut N .

r f o n the t u e path o the m o .

CUT No .

Let A in 2 r r n of cut ep ese t part ‘

o r o f and B F the bit the earth , E will sh o w the tru e path o f the m o o n fro m her last to her ﬁ rst r r o r r n fro rri qua te , while t aveli g

O to o n in 1 . P , as sh w cut The m o o n makes this path because she is carried fo rward with the earth aro un d the sun fro m F toE while she is rev o lvi ng aro u nd the

ro O to 1 . earth f m P , cut If the ’ m o o n s path fro m F to E were o n n G o n the li e H , she w uld either

c r to n o r ro su n u ve f m the , but be travelihg o n a straight li n e and at

n o him i r right a gles t . If th s we e

r o n o t ue , at the p i t j , she w uld be o ve r miles fro m the earth ’ n o o n the at I , but as the m s dist

n o ta ce is ab ut miles , she

K n o f n must be at i stead ". He ce , ’ the m oo n s path must be o n the

n 13: B F w hic h o n to li e , is c cave , o r r n o r u n A cu vi g t wa ds the s . fter ' ’ passing the p o i n t E the m o on s

o r r i n and in 1 4 bit cu ves sharply ,

50 LUNAR TELLURIAN MAN UAL .

and o f o r o n an r n ea rl days), c u se must travel ave age y a

o o n o o degree a day . The m makes a c mplete rev lutio n

ro the n in 2 7 o r o 1 3 r th ugh heave s days , ab ut deg ees

d and in o n s un r n aily , the same directi that the appa e tly

Le o n . t o su n m o n a d to travels us Supp se the , the a star V 'b e in n o n n o n da o o n ob li e a give day the y f ll wi g, if

r sun n o 1 o f se ved , the will be see ab ut degree east the

ar and o o n n o 1 3 r o f st , the m will be see ab ut deg ees east

r and o f u n o o n the sta 1 2 degrees east the s . The f ll wi g day the su n will be ab o ut 2 degrees east o f the star and the m o o n W l ll be ab o ut 26 degrees east o f the star and 2 4 r o the su n O r deg ees fr m . bse ve that at this rate the m o o n will be 2 7 % days iri passi ng aro u nd the e arth and

n n n o n r o n agai getti g i t li e with the sta , thus c mpleti g the

r o n sun in the n ' side real ev o luti . The mea time has passed

o o 2 r o f and fo r o o n to t ab ut 7 deg ees east the star, the m

o r r r o 2 1 - 6 o n ve take him will equi e ab ut days additi al ,

n o o n in 2 thus c o mpleti g the sy n odical rev luti 9% days . The chan ge o f the m o o n depends upo n its relati o nto the

n an n o t to r so ro o n e new o o n to n o r s u d a sta , , f m m a the

is 29% days (ab o ut) .

o th e o o n Th e P h a s es f M .

n n r The m o o n shi es by reﬂected su light like the ea th ,

- r n sun and one half o f her su face is illumi ated by the , when any part o f the light hemisphe re is tu rn ed t o ward s ee o o n r n and the earth , we that p rti b ightly illumi ated , o n o o n the light it gives us we call m o light . The m acts ’ as a g reat heave n ly mirro r reﬂecti ng the su n s light afte r o f o o n of o he is g o n e . The bright side the m is c urse n always toward the su .

n Th e Da rk Mo o .

Ask the pupils to notice that when the m oon is be ‘ ’ 1 LUNAR TELLURIAN MANUAL . 5

a and sun h o f : tween the e rth , the lig t hemisphere the

r A s tronomica l w e m o o n must be hid fro m the ea th . ly say the mo on and sun are in co nju n cti o n as o rdi n arily

r W e sa the D r o f oon o r No exp essed , y it is a k the M " o o n o n rat . M . Dem st e this by the apparatus

M o ve the glo be fo rwa rd in the o rbit u ntil the m oon has passed two o r three i nches to the east o f the p o i nter

L A sk l to o r o o n no t no w . the pupi s bse ve that the m is

w n o and arc S to bet ee the gl be the , but has passed the

r and n o w n ro eastwa d , that the hemisphere see f m the gl o be has a c res ce n t o f lightaro u nd the western part and " that the H o rns o f the M o o n o r the e nds o f the cres * n o n w r . o o n n o w n ew ce t p i t east a d We say the m is ,

a nd n o f n o o n r . bei g but little east the su , sets s afte him A t new m o o n whe n the air is clear we can plai nly see

o n o f d r r n o o n the utli e the a k hemisphe e . Whe the m is situated n early between the earth and sun as at n ew

o o n r o r n r o f r m , the b ight illumi ated hemisphe e the ea th

o r o o n S o w o n r is t wa ds the m . h this up the appa atus ’ m o n in o A n o r r o n N . o o n u ted as cut 1 . bse ve the m s

r r o n o w o da k hemisphe e w uld have , if we may be all wed

r ea rthl ‘ ht in r r o in the te m , ig , cha acter simila , th ugh quantity greater than the light we receive fro m the moo n

n r whe n it is full . The su light eﬂected oy the ea rth to

the m o o n is in a dimi nished quantity re - reﬂected by her to and e the earth , by this light twice reﬂect d we see

* I n f act the moo n the mo men t she pass es between the earth “ " and s un o r reac e co n u nc tio n bec o me n ew t o u she is , h s j , s , h gh

° no t u su a c a ed new u n ti the c re cen t b e . ereafter ih lly ll l s is v isi l H , th wor New an is k Moo n me s Co nju ncti o n . 52 LUNAR TELLURIAN MANUAL .

’ '

o o n r The reaso n . dimly the m s da k hemisphere . why ’ o o n r n r n r h the m s c esce t is b ighter tha the da k hemisp ere ,

o n ro on ce is because the light c mi g f m it is reﬂected but ,

fro m r r t ic that . w e while the da k hemisphe e is reﬂected ,

ff r n in n o n o b the o n the di e e ce brillia cy sh wi g the l ss y, sec d n reﬂecti o .

‘ Whe n new m o o n o ccu rs while the m o o n is ab ove the

e l o n in N o . 1 o o n a oove c iptic , as sh w cut , the m will be

o f su n and her r n as well as east the , c esce t must appear

er n n she o e low tha whe is bel w the ecliptic . Thus we hav and o o n W hat is called the dry wet m .

Fi rs t "u a r ter .

M o ve the arm IX fo rward u n til the m oo n ball has

passed o n e- fo urth o f the way aro u nd the gl obe fro m the

To an o o n o r n of arc S . bserver the gl be the c esce t light du ri n g this movement will have i n creased u ntil n o w o n e

‘ o f n r in half the illumi ated hemisphe e is view . The

m o o n is n ow o ne - quarter o f the way aro u nd the earth

f o sun and in ua dratu re. oon no r m the , is q The m is w

r t ua rter in her ﬁ s q .

u ll oon F M .

M ove the arm IX fo rward u ntil the m oon ball has

on e- ha o n o and passed lf the way ar u d the gl be , call the ’ pupil s atte nti o n to the fact that an observer Up o n the earth w o uld see the entire illumi n ated hemisphere o f the

o o n and o o sun m , that as she is alm st directly Opp site the

r o r n n o o n n o w in she must ise at ear su set . The m is

o os ition s u n and ‘u pp with the we have , ill strated , the

o f o n Fu ll Moon phase the m o called the . LUNAR TELLURIAN MANUAL . 53

La s t "u a rter .

i M ove the arm IX fo 1w ard u n til the m o o n ball has

passed three- fou rths o f the way aro u nd the gl obe and ask

“ to o o n n the pupils bserve , as this is d e , that the illumi ated hemisphere o f the m o o n shifts to the eastward s o that

W he n it is b ro ught to the th ree - quarte r p o siti o n o nly o n e

f to an o r r o n o half o it is visible bse ve up the gl be . The

o o n n in r su n and n m is agai quad ature with the , prese ts

r the phase o f the m o o n in her las t q u arte .

n Old Moo .

M ove the arm IX u ntil the m o o n ball is bro ught ab o ut half way between the last quarte r and the dark o f the

m o o n and o r h r n o f n , bse ve t at a c esce t light may be see

a ro n n o f o on o n o f u d the easter side the m , the h r s the " c n o n n to wes t. o o n n o w o ld resce t p i ti g the The m is , fro m which p o sitio n she passes to c o nju ncti o n and the

d oon o n o o n o f ark m , thus c mpleti g the c mm phases the m o n o .

Th e Or bi t o th e oon f M .

o o f m o o n an n The rbit the is ellipse , her least dista ce fro m the earth is miles , while her greatest dis n She o o r ta ce is miles . seld m , h weve , reaches

re r o n ro n these ext me limits , her usual va iati s f m her mea

d n o f n o ista ce miles , bei g ab ut miles each

o o f o o n o o r o f way . The rbit the m cr sses the bit the e an n n 5 r arth at a gle a little greater tha deg ees . This is sho wn (so mewhat exaggerated) by plate E o n the o r o o n in an 1n clin ed o r gl be , which ca ries the m ball bit ’ a o and o o o n n o n b ve bel w the ecliptic . The m s decli ati is an n r o r o I n N o . 1 her dist ce o th s uth of the ecliptic . cut L T 54 UNAR ELLURIAN MANUAL .

' the m o o n is shown abo v e the ecliptic in her greatest no n n o n . I n ou t No 2 rther decli ati . she is sh o wn bel ow

in her r o rn n o n the ecliptic g eatest s uthe decli ati .

Th e o o n ’s N d M o es .

The nodes o f the m o o n are the tw o po ints where her o o r o n o r rbit cuts cr sses the ecliptic . The de whe e the m o o n c rosses the ecliptic co min g n o rth is called her

n n n o and o o ne n n asce di g de , the Opp site the desce di g no de .

’ The pupils sh o uld ﬁ x clearly the m o o n s n o des in their

n o n n n r n n o f mi ds , as up this depe ds the u de sta di g much to o o that is f ll w .

If the sun and m o o n c o uld leave a th read o f light to ’ mark their pathway th ro u gh the heave ns (the su n s ap

r n nn o o r n run pa e t a ual path), we w uld bse ve these li es n in g very near each o the r an d to c ro ss at Oppo site p o i nts o f n s o e f o the heave s , that as view d r m the earth the path o f sun o o o and o s the w uld s metimes be ab ve , s metime

o o f o o n ro n o o n bel w the path the m , c ssi g it at Opp site p i ts ’ n n o o n o f ro n are n the m o o s des . These p i ts c ssi g o t

are o n n n n n to ﬁxed , but c sta tly cha gi g, falli g back the ’ westward o n the ecliptic o rsu n s apparen t path ab o ut 20

r n n . no s o n r n deg ees a ually If the des were tati a y , the the time requi red by the su n to p ass fro mo ne ascendi ng

no to n o r n o r. de a the , ma ifestly , w uld be a yea Because ’ o f the m o o n s n o des rev o lvi ng backward o n the ecliptic

o nn ro n od ab ut 20 degrees a ually , he will app ach her es r Dis ab o ut 1 9 days earlier than he o the wise w o uld .

r n o n 1 365 da s lcss 1 9 ca di g fracti s we have year , y , days 346 days the time required by the su n to pass fro m

l in no n o h A s n n no e o ne ascend g de to a t er . the desce di g d LUNAR TELLURIAN MANUAL . 55

o n tw o n n n o ccurs midway betwee asce di g des , we have 346 days 2 1 73 days as the time fro m the ascendi n g

o n n n o and an r o ro t the desce di g de , equal pe i d f m the

n n n o descendi n g to the asce di g des .

M o ve the arm IX u ntil the m o o n ball is between the

o and arc S rn to r n gl be the , tu the plate E the ight u til the ce nter o f the m o o n ball is Opp o site the p o i nte r L; the

n o o n no n o o o f su n a d m are w at the de . N te the day the

o n n r n n o arm m th u de the cale dar i dex G . M ve the IX fo rward ca rryi ng the gl o be a ro u nd the arc S to its fo rmer

o o n and rn o p siti , at the same time , tu the plate E ab ut

1 - 1 8 ro n in o os ite r o n and o b the way a u d the pp di ecti ,

v sun o f n in o o n ser e the has , because this cha ge the p siti ’ ’ o f the o o n o r as s ed m o o n n o o m s bit , p the s de ab ut 1 9 ’ days earlier than he w o uld have d o ne had the m o o n s o rbit no t changed po sitio n °

Th e Z o di a c a l B elt.

The Zo diacal Belt is a band in the heavens lyi ng 8

d r o n r o f in un eg ees eithe side the ecliptic , which the s ,

o o n and r n n are n to o A ll m the p i cipal pla ets see m ve . the pla nets go aro u nd the su n in the same ge ne ral direc

. o n ro to . o r r ti , f m west east The bit Of the ea th , the

s and ro n n o n ecliptic , is the ba e , f m it the i cli ati s o f the

o r o f v r n are r bits the se e al pla ets measu ed . N o n e o f the o rbits o f p rin cipal planets cro ss the o rbit Of the earth at

an n rea ter n 8 r and o o f ro a gle "g tha deg ees m st them c ss an n o n at a gle c siderably less . If all the planets co uld leave behi nd them a th read o f light to mark thei r

o n o pathway thr ugh the heave s , we w uld see that within

o f n 1 6 r n r a belt the heave s deg ees wide , lyi g 8 deg ees o n i r o f o o e the side the ecliptic , w uld lie the rbits o f all 6 5 LUNAR TELLURIAN MANUAL .

n n and in o n the pri cipal pla ets , this belt they w uld be see to o n o r z o n o f n m ve . This ba d e the heave s is called " Zo The diacal Belt .

Th e Si gn s of th e Z o di a c .

The ancie n t astro n o mers fo r s o me reas o n no t no w well

n o n Zo B elt into r k w , divided the diacal twelve equal pa ts o f r n to n n be thi ty degrees each , givi g each sig a ame , gin n i ng with the vern al equino x o r the equi no ctial co l “ " u re o n n r r and n n n , c u ti g thi ty deg ees east ami g this sig “ " A ries , to the n ext thi rty degrees east they gave the “ " n r so o n n n in o r o n o n ame Tau us , c ti ui g the der sh w up “ o f o n o f the base the gl be . Thus we see that a Sig the " Zo diac is a po rtio n o f the heaven s havi ng a l o ngitude o r length o f 30 degrees and a latitude o r b readth o f 1 6 degrees .

P a s s a ge of th e Mo o n Th r o u gh th e S i gn s of th e

Z o di a c .

We learned up o n the p revi o us page that the m o o n had

" her o o n n Z o and rev luti i the diacal Belt , as she passes c ro n n 360 r in n lear a u d the heave s , deg ees , maki g her

’ o o n s he mus t in sidereal rev luti , that time have passed o S n o f Zo o on nce th ro ugh all the ig s the diac . If the m

ro the 1 2 S n o f Z o in 2 passes th ugh ig s the diac 7 56 days ,

r r o o n o o 2 in (a side eal ev luti ), she will ccupy ab ut % days n ro n n passi g th ugh o e sig . R o tate the gl o be up o n its axis u ntil the ecliptic marked

in h r iz onta l n o u to o n the gl o be lies a o pla e . If y were take a large and wide barrel hO Op and place it aro u nd the e nti re apparatus and h o ld it in such a po siti o n that the plane o f the ecliptic extended to the h o o p it w o uld strike the middle Of the hOOp all the way aro u nd it ; t the

L 58 UNAR TELLURIAN MANUAL .

r on o n o f Z o n of a ve y clear c cepti the diacal Belt , the sig s the Zodiac and theway the m o on passes thro ugh these n sig s .

P a s s a ge of the S u n Th rou gh th e S i gn s of th e Z o di a c )

su n ro n o f Zo in The passes th ugh the sig s the diac a .

nn r r to o o n and r o n . ma er vey simila the m , the illust ati s used to sh o w the passage o f the m o o n thro ugh the s1gns ’ may be used to equal advantage to sh o w the su n s pass

su n a ro n o n age . The p sses th ugh the twelve sig s ce every year and so o ccupies ab o ut o n e m o n th in passi ng n i r N o o i . o n . 1 each s g The p te G , cut , sh ws at all sea s c u s o f the year the sign and the degree o f the sig n

sun . n no x where the is situated Thus , at the ver al equi sun in r r o f n A we see the is the ﬁ st deg ee the sig ries . o o r r to n 2 1 and o r t M ve the arm IX f wa d ju e , bse ve tha in the mean tim e the su n has passed throug h the signs A r and n and n ies , Taurus Gemi i , has reached the sig n Ca cer .

W n w n n z r NOTE . hen stu dyi ng the ch ange o f s eas o s e s aw th at o J u e st the s u n reac e its reate t n ort ern m t 2 e ree n ort o f the e u ato r ro m h d g s h li i 3 % d g s h q , f n i rn u t w ar to w ar h u ato r u w e s ee the s u n whi c h p o si ti o t tu e d s o h d ds t e eq . Th s rn u h m n h r ac e th n a nc r W e er e the w ord tu s s o th at t e mo e t e e h s e sig C e . d iv “ " re io w m n o u rn The w o rd ancer Tro pi c fro m the G reek w o rdt j hi ch ea s t t . C ' o h u when I tu rn u w r n ro m a u n o n f sh o ws the p s ition of t e s n t s s o th a d , a d f i o l “ " T f n r The am ru o f the tu rn m o f the t e e tw o w e et rO ic o a ce . s e is t e g h s g p C , su n no rt w ar o n Dec em er z ad as it reac e th e n a r cornu t ere h d b , h s sig C p i s , h by “ " givi n g u s Tro pi c o f Capri corn .

P a s s a ge of th e Ea rth Th ro u gh the Si gn s of th e

Z odi a c .

The earth is always said to be in the sign di rectly Op

osite o ne r su n . n the p the whe e the is situated Thus , whe sun is in Cancer the earth is said to be in Capric o rnus, ~ LU NAR TE LLU R1 AN MANUAL . 59

’ w here it w o uld be see n by an o bse rver up on the s u n s

r s u face .

Eclipses .

A n in n n o ff in o o r in eclipse ge eral , is the cutti g wh le

r n o n r o r o o n . pa t the su light , as it falls up the ea th m A ll the planets are Opaque they abs o rb in part the sun

n and r n r r ab light that falls upo them , the emai de afte

o r o n 1 n o N o s pti s reﬂected back i t space . light passes

ro o n o n th ugh them . They cast shad ws i t space , the exte t o f these shad ows dependi ng up o n the s iz e o f the planet

and dis ta n ce ro s un r n its f m the . The large the pla et the

r r o and r r n ro la ge the shad w , the fa the the pla et is f m the

r To s u n the fa ther the shad o w will extend i nt o space .

r r o n o o o in illust ate this , draw a ci cle the blackb ard a f t

to r r n s u n r r S two diameter ep ese t the , ma k this ci cle

ro r r a m all r n feet f m this ci cle d aw s ci cle , say three i ches

in er to r n r . diamet , mark this circle E rep ese t the ea th Draw a st raight li ne fro m the to p o f ci rcle S to the top

o f r o n n n o o o r o r oe ond ci cle E , c ti ue the li e a f t m e y E n r w n ro o o o f r S to bo t ext , d a a li e f m the b tt m ci cle the ' tom Of r E and o n n r n n ci cle , c ti ue this st aight li e u til it c ro sses the o ther li ne the dista nce fro m whe re these

n ro to r r r n n the li es c ss , the ci cle E , ep ese ts the dista ce

o o f o n Dr no r shad w the earth w uld exte d . aw a ther th ee

n r s a ou r ro c1 rcle S and r i ch ci cle , yf feet away f m , d aw similar straight li n es fro m top to top and b o tto m to bo t to m o f r l n n in o r the ci c es , exte di g them as the the illus ' ' ’ tratio n and to o no , ask the pupils bserve , that w the dis

n o n o he r ta ce fr m the - cro ssi g f the li nes to t ci cle E is g rea ter than in the ﬁ rst i nstance when the circles were o n o cl ser to gether . Thus we see that the earer a b dy o f n z e t r o a give si is o the su n the sho ter will be its shad w , 60 LUNAR TELLURIAN MAN UAL .

and the farther it is fro m the sun the long er will it ex t n Dr a r n ro n o e d . aw st aight li e f m the ce ter f circle S ro n r o f r and n nt th ugh the ce te ci cle E , exte d it u il it

o n o f tw o n o r n o n reaches the cr ssi g the li es bef e me ti ed , and ask the pupils to observe that the li ne last d rawn

r r n and o may ep ese t the ecliptic , that it divides the shad w ,

n o two r o n e ' half o f a ooo e and o ne i t equal pa ts , which is

o S o r n o her o w half bel w it . the ea th i t space casts shad , r o f o n equal pa ts which lie ab ve a d bel o w the ecliptic . Thus we see

a o an n or ( ) That the shad ws cast by y pla et , great ’ i n o f n n o . small , must lie the pla e that pla et s rbit

(6) That the shad o ws cast by the planets are in the o f con e r n to o n o f o n shape a tape i g a p i t , the base the c e

n in to o f n bei g equal diameter the diameter the pla et, the distan ce to the p oi nt o r frustum o f the c o ne depend ~

s n o f n ro he u n ing up o n the di ta ce the pla et f m t s .

o casti ng the shad w .

The co ne - shaped shad ow o f the planet is called its

u mbra and to an r in r s un , Observe situated the umb a the

o is wh o lly o bscured andto him the eclipse is t tal . Place

' the o bserve r just o utside o f the umbra and the sun is not w h o lly obscu red to him ; his situati o n is n o w in pen

ra To o en u méra the r o n u mé . sh w the p take ﬁgu es up

o r to o w r ahd in o n the blackb a d used sh the umb a , additi draw a straight li ne fro m the oottom o f c1rcle S th ro ugh

the top o f ci rcle E and extend it a fo o t o r tw o bey o nd . Draw ano ther straight li n e fro m the top o f ci rcle S

tt m f and n o re thro ugh the oo o o circle E exte d it as bef , LUNAR TELLURIAN MANUAL . 61

the Space beyon d the ci rcle E o n either side o f the umb ra and b etwe en it and the li nes last d rawn sh ows the pen m r o o f n o u b a . The shad ws all heave ly b dies must have

r and n r umb a pe umb a .

Umbra m ns-tota lit and en u mbra a rtialit ea y, p , p y.

T m o h th a n o on ’ m bra he Di en s i on s f t e Ea r d M s U .

" ’ The length o f the earth s umb ra is ab o ut

o r o 3 r n o o n IS ro miles , ab ut % times fa ther tha the m f m

r s a vera e n : in D and the ea th . Thi is the g le gth ecember Jan ua ry (because then near the sun) the umb ra 15 ab o ut

in n and n r miles , while Ju e July (whe fa thest n r away) her umb ra is early miles . The diamete ’ o f the earth s umbra at the distance o f the m o o n is o n an r o n ave age ab ut miles , early three times the ’ oo n r m s diamete .

/ ’ The average length o f t he mo o n s u mbra is

r o r ro to miles . It va ies , h weve , f m miles . ’ Obs erve tha t the a verag e leng th of the moon s u mbra is a li ttle less tha n her a verag e dista nce f rom the ea rth

miles Ther ore i the moon ha vin her a v ) . ef , f g ag e u mbra pa s s between the ea rth a n d s u n a t her a ver a e dis ta n ce rom u s the u mbra would n ot rea ch the g f , ea rth b n ea r miles in this ca s e y ly . The eclipse wou ld be a n n u la r a n n t t ta S ee a n n u la r ecli s es d o o l. ( p page

’ The greatest po ssible diameter o f the m oo n s umb ra U on r o 1 5 and can as it falls p the ea th is ab ut 7 miles , this be o nly when t he m o on is at her greatest distance fro m

su n and the at her least po ssible distan ce fro m the earth . 62 L T UNAR ELLURIAN MANUAL .

no wn o and n and E clipses are k as s lar lu ar, as the terms

n are o f sun and o o n i dicate , they the m .

Partial o r L n r E u a clipses may be ‘ o t tal . o ' Partial , t tal S o lar E clipses may be o nn r a ular.

I / wn a r Eclip s es .

If the m o o n rev o lved aro u nd the earth in the plane gf ’ the ecliptic she w o uld pass th ro ugh the earth s shad o w and r ull moon and o ro be eclipsed at eve y f , w uld th w her o wn o U o n r r n e moon shad w p the ea th at eve y w . Her o o n n to o n rbit is , h wever, i cli ed the ecliptic , as sh w by

o n o ro plate E the gl be . That she may pass th ugh the ’ o and o o n n earth s shad w be eclipsed , the m must , whe

o r n r no o r o full , be at ea her de , the wise she will pass ab ve ’ o r o r o ~ n o t n r bel w the ea th s shad w . It is ecessa y that ’ the m o o n be ex a ctly at her n o de to strike the earth s a o fo r n 1 r o r o r f sh d w , , if withi 0% deg ees either bef e a ter ’ the no n o r o and de , she will pass i t the ea th s shad w be

o o r r o r n to her n rn wh lly pa tially eclipsed , acc di g ea ess “ " to o r dista n ce f rom the n o de when she fulls . This n 1 0 r r o n o dista ce , % deg ees eithe way fr m the de , is called “ " n . the lu ar ecliptic limits Thus we see , that at either no de there is a lunar eclipse limit o f 2 1 degrees i nclud ~ in o no 42 n n g b th des , degrees , withi which limits all lu ar

o r eclipses must ccu .

o o f o o n o on M ve the arm IX the gl be f rward , u til the m " No 2 o o n ro to o n in . ball is b ught full , as sh w cut l se

r o n and n n the the sc ew h ldi g plate E , tur the plate u til

gear - wheel that d rives the m o o n ball rests up o n the o of o n in n l wer part the plate , as sh w cut tighte the 6 LUNAR TELLURIAN MANUAL . 3

to o n o w f o o n s crew , ask the pupils bserve , that the ull m

i o n o n s bel w the ecliptic (the li e J , as marked up the o and o o f o gl be), that the shad w the earth will pass ab ve

o on and no o . the m , eclipse will ccur

ta nt tha t the u ils remember that W l t is impor p p ,

s iz es o the ea rth s u n a nd moon a re while the rela tive f ,

wn it is im oss ible to s ho w their rela ti ve dis ta n ces . s ho , p

I we were to do this the lobe s hou ld be la ced a bou t f , g p moon ba ll a mile a n d a ha lf f rom the a rc S a nd the la ced a bou t 2 0 eet rom the lobe a n d la ced at thes e p f f g , if p

dis ta n ces the moon ba ll mus t be a t or ver n ea r the , y ’ lobe s ecli tic when u ll in order to a ll within the g p f , f s hadow; a little va r ia tion a bo ve or below wou ld ca us e ’ he o e s s ha dow a lto ether the moon ba ll to miss t gl b g .

If full m o o n o ccurs when the m o o n is a few degrees 1 0 o r n n no (say degrees) bef e she reaches her asce di g de , ’ she will pass th ro ugh the lower p o rti o n o f the earth s ’ s o o r n u er r o f mo o n had w , thus c ve i g the pp pa t the s sur

w o n a r o f o o n face ith shad w , givi g pa tial eclipse the m . Sh o uld full m o o n o ccur when the m o o n is 1 0 degrees

n n nOde her lower o r o past her asce di g , limb edge w uld ’ b e i r o r o n o f o w ecl psed by the highe p ti the earth s shad .

Rev o lv e o ne - ro n and the plate E half way a u d , ask the pupils to o bse rve that n o w the m o o n ball is a bove the p and o o . I l ecli tic J , that the shad w must fall bel w it f fu l o o n o n o o n o r r n r no m ccurs whe the m is at ve y ea her de , ’ the e nti re m o on will p ass thro ugh the earth s shad o w

a nd o l S an the eclipse will be t ta . uch eclipse o ccurred

a o n n 1 1 1 881 . b ut mid ight Ju e ,

ol r li s S a Ec pse .

There are but two celestial o bjects that can ever c o me 64 LUNAR TELLURIAN MANUAL .

betwee n us and the su n o f sufﬁcien t si z e to cut Off fro m

o tw o are o o n and V n . us the s lar light . These the m e us ’ o f n V n o n The passage the pla et e us acr ss the su s face,

n r is usually called a transit o f V e us . The last t ansit o f

V o De n c . 9 1 8 4. n e us ccurred , 7 The ext will take place

Dec . 6 1 882 no r n o n n , , after which t a sit will ccur u til Ju e

8, 2004.

r l of o e viz . : o There are th ee c asses s lar eclips s , t tal ,

and nn Let in o partial , a ular . us treat them their rder .

All o f the sun o f eclipses , caused by the passage the

o o n n and sun mu st o r new moon . m betwee us the , ccu at No w n ew o o n o in n o f , if m ccur while she is the vici ity

no an o f o n o r. her de , eclipse s me ki d must ccu If she is ’ a t o r ver n ea r her n o ro n y de , she will pass ac ss the su s

centra ll o r n so and if face y, very early at this time she

n to n ea r en ou h to her r w r happe s be g us , umb a ill each ’ o o o n o f the r and to o n s me p rti ea th s surface , that regi , o O 61 n the eclipse will be t tal . n page we lear ed that ’ the greatest p o ssible diameter o f the m o o n s umb ra at the earth is 1 75 miles ; the usual regi o n o f to tality is very o o f su n much less . Thus we see why t tal eclipses the

’ ’ to so o r o n o f r r are visible small p ti s the ea th s su face , While a lu nar eclips e may be seen fro m any pa rt o f an

o n o f o entire hemisphere . The durati s lar eclipses is

n n n o f o in very much less tha lu ar . The le gth t tality a o r nn o ex ceed 6 o r 7 n and s la eclipse ca t mi utes , is usually

’ r o o n n o ve y much less , while the m may remai t tally

fo r n r tw o o a n z o f eclipsed ea ly h urs . The ppare t si e the su n and o o n are r n r and r r m ve y ea ly the same , it equi es ’ the en tire b o dy o f the m o o n to hide the su n s disc and eclipse him wh olly s o metimesshe is no t able to do even

sho rtl see. this , as we shall y

" 66 LUNAR TELLURIAN MANUAL

’ On page 61 we ﬁ nd the average length o f the m o o n s

and r umbra is miles , her ave age distance fro m

r so o o o n the ea th miles , , sh uld the m pass ac ro ss ’ the sun s face when so situated the umb ra wo uld no t

r o reach the ea th by s me miles . The appare nt siz e o f o o n now n su n and o the m is smaller tha the , she w uld in o o n n to n r o this p siti be u able hide his e ti e face fr m us , and n n n n o r r n whe passi g by his ce ter, a ri g f i ge o f light ' o n ro n o o n A n w uld be see all a u d the m . eclipse o f this n n u la r o r n ki nd is called a . The w d a nular mea ns like a 0 n o r r n rr n to r n o r r ri g i g shaped , refe i g the i g f i nge o f n o n light s e e n aro u d the m o . Thus we see that the m o o n

n re n r n o r must be ea r the earth tha her ave age dista ce , that the su n must be at a greater than his ave rage distance to make it po ssible fo r the m oo n to hide his e nti re face

d o ro o o f sun an t p duce a t tal eclipse the .

o arm fo r r and M ve the IX wa d , ask the pupils to oh

o o on o serve , that the apparatus sh ws the m s metimes

n o r n eare r the earth tha at the s . 0 It is no t necessary that n ew m o o n o ccur exactly at the ’ m o o n s n o des to g1v e ah eclipse o f the sun ; if within

r o f either wa 1 6% deg ees it y, she will eclipse him . Thus we see the s ola r ecliptic limit is 33 degrees at either nod o r in 66 fo r o n o and n e , all , degrees b th des , withi this

o o limit must all s lar eclipses ccur .

r Wh y m o e S o la r tha n Lu n a r Ec lip ses .

On page 62 we see the m o o n must be withi n 10% de g rees (eithe r befo re o r afte r) o f her n o de at Full M oo n to n o o n n L n B e ter the earth shad w , c seque tly her u ar elip 1 0 1 0 21 r no or tic limit is 54 % deg ees at either de , ’ a to tal o f 42 degre es o f her o rbit wherein lunar eclipses LUNAR TELLURIAN MANUAL . 67

o In s o n s ola r i may ccur . the last ecti we see the ecl ptic 33 s no o r o o f 66 limit is degree at either de , a t tal degrees i a r o n o o n which s ol eclipses may ccur . The it f ll ws that the p ro po rti o n o f s ola r to lu na r eclipses is the same as

66 bears to 42 o r as 1 1 to 7 .

Sea s o n of Ec lip s es .

We have already learn ed (page 55) that the time fro m o ne no o no new o o n o r de t a ther is 1 73 days . If a m ccu s n r n n nod and su n in 1 3 fol ea asce di g e eclipse the , 7 days

o n o o n o r n r n n n o l wi g, full m will ccu ea the desce di g de ’ and n o o and she will pass i t the earth s shad w be eclipsed . ’ L r 1 881 o o n no o rr o n ast yea , , the m s des ccu ed ab ut Ju e

1 and D r r 1 2 o 1 1 . 88 bo , ecembe This yea , , they ccur a ut

1 9 r r o r o 22 and o 1 1 and days ea lie , ab ut May , N vember , s o o n n ro a to r o n to f n c ti ue f m ye r vea , wi g the alli g back ’ o f o o n no S ee the m s des . ( page

S o r 33 in The la Ecliptic limit degrees , is equal time

S o an o f sun o r to 36 days . eclipse the may ccu 1 8 days ’ e o r o r 1 8 o o n no b f e days after the m s de , which , the past

r 1 881 n ro 23 to n 2 9 yea , exte ded f m May Ju e while the s ola r ecliptic limit fo r the Oppo site node embraces the

o o 1 2 to D 1 time fr m N vember ecember 8 .

L n 2 1 ‘ to 23 The u ar Ecliptic limit degrees , is equal

a an o f o o n an d ys , thus eclipse the m may take place at y o o n o r n 1 1 o r o r nod full m ccu ri g % days bef e after the e . Thu s the Lu na r Ecliptic seaso n is fro m may 30 to Ju n e 22 and fro o 1 9 to D 1 2 of , m N vember ecember , the year

1 881 .

P The eri o d of Eclip s es .

’ By referri ng to the subject o f the m o on s nodes (page 6 8 LUNAR TELLURIAN MANUAL .

54 ﬁ nd n o not x o ) we the des are ﬁ ed , but have a retr grade o n o n n 20 r r m veme t the ecliptic , early deg ees every yea , o r at a rate that will carry them clear aro un d the ecliptic i n o 1 8 5 o n . If r r ab ut years , m ths we ma k ca efully the

o o n o f n o o n . n o w and n o p siti the des , the ecliptic , te the

o fo r 1 8 r 5 o n h and o r eclipses that ccur yea s , m t s , rec d the

and o r no n fo r r o fo l result , bse ve the phe me a a like pe i d o n w e ﬁ nd for latter r o l wi g, , shall the eclipses the pe i d

o n o r K no n the alm st ide tical with th se o f the ﬁ st . wi g this astro no me rs are able to fo retell eclipses to the ve ry day andh o u r a hu nd red years in advance o f their o ccurrence

o These peri o ds are called the Saro s or Pe ri d o f Eclipse .

The Precession of the Eq uinox es .

The p recessi o n o f the equino x es is due to a gyratory ’ m ovement o f the e arth s axis rev o lvmg the po les o f the

o n o o f A s equato r ar u d the p les the ecliptic . the equa to r o r equi no ctial and the ecliptic cut each o ther at an

n o f 2 3 r so . U o n a gle % deg ees , must their axis bisect p

r ao r and o s the gl o be is ma ked the equ t ecliptic . The p le

o n o f x o f o and of the equat r are the e ds the a is the gl be , the p o les o f the ecliptic the p o i n ts where a vertical li n e d rawn th ro ugh the center Of the globe w o uld cut its sur ’ o r o n o f r face . This gyrat y m veme t the ea th s axis is very

o r n o to o o ne r o sl w , requi i g ab ut years c mplete ev l io n ff o f o n to r ut . The e ect the m veme t is car y . the

and o o n o ro n equi n o ctial s lstitial p i ts backward , sl wly , a u d

o f o the ecliptic fro m east to west . The value this m ve ’ n n o n o f . o r ment a ually is sec ds arc The earth s bit,

d nto 360 r r like all circles , is ivided i deg ees , these deg ees

‘ d no n and . n n o on sub ivided i t mi utes the mi utes i t sec ds . LUNAR TELLURIAN MANUAL . 69

* The exact s olar year is the time required bythe earth

to 360 r o f o r o n o r travel deg ees its bit , less sec ds ,

min To r o 359 de . 59 . see. n o g , , illust ate up the gl be

o n o r o r ro r reces s ion o f the precessi , m e p pe ly the the

no ro o o equi xes , p ceed as f ll ws

A r n o o n in ro 1 . 9 ra ge the gl be as sh w cut II , page t ate the gl o be upo n its axis u ntil the ecliptic up o n the n n ’ gl obe lies in a ho ri z o tal pla e .

o arm O o w to o n 2 . M ve the sl ly, the left , c mpleti g a

ro n n r and o r circle a u d the sta da d P , bse ve that as this is do n e the p oles o f the equato r describe ci rcles aro u n d the p o les o f the ecliptic (the no rth p o le o f the ecliptic onthe gl o be being where the 90th me ridian east c ro sses the arc

i r In n n o o f ea rth t c ci cle) . like ma er the p les the de sc ribe ci rcles aro u n d the p o les o f the ecliptic o nce eve ry

r o r . yea s , as bef e stated

3 A o fo r n o t he o . djust the gl be the cale dar m ve gl be

o r r to o r and o r o n s l owly f wa d its bit , bse ve that the p i ter ‘ e ros n o r n I . r “ t ac s the ecliptic , c si g the equat , givi g equi

and S r 2 noxes ab o ut March 20 eptembe 3 .

‘ Mdve arm 0 r o f o n 4. the a pa t the way ar u d the

s n r in 2 o o n e - half o f an n o ta da d P , as ab ve , say i ch ; m ve

o r r to o r and. r no do it f wa d its bit , Obse ve that the equi xes n ot o ccu r at the same po i nts in the o rbit as in the fo rmer

n n ea rlier . o n o n i sta ce , but Repeat the Operati , m vi g the

* g it fr u n h ro " r ar en r O e eq e tly call ed t e T pi cal ear. The e e g e ally recko ned

t ree ear . 1 ereal " ear as the t me re u re the art to m n h y s Sid , i q i d by e h ake o e om e o r a m m n 6 o u t c te t o e e t o r a 6 ur m n e se co n . 2 Th pl bi l v , 3 5 d ys , h s , 9 i s , 9 ds . e ’ o ar o r ro ca " ear as the t me re u red fo r the u n ert ca ra to a S l T pi l , i q i s s v i l y p ss m i ro tro c to trO c and retu rn o r 6 a u r 8 m nu te eco n . f pi p , 3 5 d ys , 5 h o s , 4 i s , 46 s ds

. The " ear o f 6 an d 66 da accor n as the ear a co mmo n o r 3 Civil 3 5 3 ys , di g y is a r l e p yea . 0 L T L 7 UNAR ELLURIAN MANUA .

O and o no arm little by little , bserve the equi ctial po i nts f n in o r arm O o alli g back the bit as the is m ved .

rn i no o r 5 . The ve al equ x ccu s as the s un e nters the

o f n A r o f Zo ﬁrst degree the sig ies the diac . I f these

n r o r n n sig s were ﬁxed as egards the bit , ma ifestly the ext succeedi ng ve rn al equi no x wo uld o ccur 50 1 sec o nds be ore n A r r and so o n n to f the sig ies we e reached , c ti ue

in n ro to . n ho w fall back the sig s f m year year The sig s ,

r f to n o f eve , are shi ted agree with the falli g back the equino xes thus the equino xes will always o ccur in

and n n o w . s i ns ho w the same degree sig as The g , do n ot a ree o n o n ro h ever, g with the c stellati s f m whic r n to they de ive their ames .

tion of Eq ua Time.

S i derea l S o la r a n d ea n Ti m e. , M

n r o n ne o f Time is a measureme t o f du ati . O the ﬁrst objects o f ast ro no mical study was to ﬁ nd a standard fo r

r n o f o n Fo r o a the measu eme t durati . this purp se the p parent diu rn al revo luti o n o f the s un marked the begin nin gs and e ndi ngs o f the standard days while this did n o t r o n n o u n orm r od o f m ma k durati i t if pe i s ti e , it was o n to f n fo r and f u d be su ﬁcie tly accurate the civil , the

su n - crude astro no mical uses o f the earlier days . The dial se rved to mark the subdivisio hs of the day but as the in n o r in o r dial was useless the ight time cl udy weathe , a m o re reliable i ndicato r was s o ught in mechanical de

to o ur o and . vices , similar cl cks watches The makers o f these we re s orely pe rplexed because they co uld no t make their machi nes agree with the su n fo r any co n siderable o f are o r time because this , we t ld , the make s

uff on and n o disre s ered persecuti , their machi es fell int 1 LUNAR TELLURIAN MANUAL . 7

and r and r pute , we e little used whe e used at all , they

r n s u n - r me ely suppleme ted the dial , by which they we e

to regulated fro m time time .

It w as s o o n disc o ve red that the su n days we re no t o f

n o r n and n r r u if m le gth , that the machi es we e the bette

- r r o n time keepe s . The causes Of this va iati will be ex

n o r plai ed bef e we leave the s ubject .

The S iderea l D ay is the peri o d that elapses betwee n two successive transits o f any ﬁxed star this pe ri o d is n n n o f r 24 u varyi g. The le gth the side eal day is sidereal “ " o r o r 2 3 o r 56 n 4 o n o f n . h u s , h u s , mi utes , sec ds mea time

The S ola r D ay is the peri o d that elapses betwee n tw o

ns o f s u n r o r in n successive tra its the this pe i d va ies le gth , bei ng so metimes more and s o metimes les s than 24 mean

r time h o u s . Thus it is that the cl o ck and su n do no t r ag ee .

The 1V ea n D ay o r the rll ea n S ola r Day is the a ver a e n o f o r o f r and o f g le gth all the s la days the yea , is

o r n r n in n and n r c u se u va yi g le gth , is the sta da d civil day

o u r o and are o which cl cks watches made t keep . The mean day is 3 mi nutes 56 seco nds l o nge r than the sid ereal day .

The varyi ng len gths o f the s o lar days depend u po n tw o causes

T 1 . he u nequ al velocity a t which the ea rth tra vels in its orbit .

2 . The in clina tion o the e u ator to the ecli tic f g p . 2 L T 7 UNAR ELLURIAN MANUAL .

1 . To Il lu s tra te th a t th e Un eq u a l V elo ci ty of th e Ea r th i n i ts o rbi t i s a Ca u s e of th e Ex i s ti n g a ri n o V a ti o f th e Len gth s of th e S o la r Da ys .

A r n o o n in 2 36 and r a ge the gl be as sh w cut , page , p ro ceed as fo ll o ws B ri n g the calendar i ndex to the 2l st o f Ju n e ro tate the gl o be up o n its axis u ntil the p rime me ridian is u nde r

the p o i nte r L extend the po i nter L u ntil it is withi n 1 - 1 6

f n o f o o o o r in o an i ch the gl be . M ve the gl be f ward its

o r an n r o n and o o n L bit e ti e revoluti , bserve that the p i ter is by this m o veme nt carried fro m w es t to e ast acro ss the — me ridia ns at a rate that will carry it clear a ro u nd 360

r - in o n e o f 365 o o r deg ees year % days (ab ut), a triﬂe h r n d r o n t e a . n less tha a eg ee a day , ave ge This dista ce

i t e to n o n is equal n im 3 mi utes 56 sec ds .

o o U o n ro wes t to eas t and R tate the gl be p its axis f m , o bserve that this m o vement carries the po i nter L ac ro ss the me ridian s fro m eas t to wes t at a rate that will ca rry it clear a ro u n d in on e day s o it fo llo ws t hat while the ’ da ily ro tati o n is ca rryi ng the su n s ve rtical ray 360 de

ro ea s t to wes t o r o n o f grees f m , the f rwa d m veme t the earth in its o rbit is carrying it back n early a degree

o 59 n o f n ro w es t to eas t. (ab ut mi utes dista ce), f m There fo r r rn more n o n o n to e , the ea th must tu tha ce up its axis

o r o r in c o mplete a s la day . This little m e a year

o n to 360 r fev o lutio n . S o r am u ts deg ees , a , the t uth is apparen t that the earth must tu rn 366 times up o n its axis to c o mplete 365 s o lar days o r 366 sidereal days are

equal to 365 s o lar days . "f the movement of the ea rth in her orbit were u n i

orm da to da throu hou t the ea r the va r iation f y y g y ,

wou ld be u n orm a n d the s ola r da s wou ld be o e ua l if , y f q

LUNAR TELLURIAN MANUAL .

and o o n r o n r east, bserve this m veme t ca ries the p i te L

to r r n no t on n e o f ecli tic back the p ime me idia the li the p , o o in a ra llel o o n but f ll w g the p . Thus the rbital m veme t

r sun o r o n an n and o car ies the f rwa d a gle , the daily r ta ti o n bri ngs it back o n a straight li n e describi ng tw o li nes o f n o f IS o n a tria gle, which the ecliptic the hyp the use , a parallel o f latitude and the prime me ridian bei ng the

r t o o the w sides .

m g to the anglin g m o vement about 1 - 1 2 o f the displacement is los t; the reby sh o rten i ng the so lar day 1 - 1 2 of 3 n 56 o n n o r mi utes sec ds (the average displaceme t), o o n b o o for r to the ab ut 20 sec ds . . M ve the gl be w a d

o o n o o 1 st o f n and o e p siti it ccupies ab ut the Ju e , bserv that fro m this time u ntil ab o ut August l st the m o vemen t o f the su n o n the ecliptic is n ea rer in the di rectio n o f

n A o r o n o o n n i . the r tati tha March ls , that a deg ee the ecliptic is greater than a degree upo n the parallels to

sun o n and which the is , at this seas , vertical , the daily * - o o n o . O i n to o 1 1 2 o f s r tati is sl wer w g this , ab ut thi

n a i n ed n n n o r displaceme t is g , thereby le gthe i g the s la

1 - 1 2 o f 3 n 56 o n o r o 20 s o n . day mi utes sec ds , ab ut ec ds

The Ti des .

The S u bjoi n ed Ex p la n a ti on of th e Ma th em a ti cs

m en ts i s b P r o . . Co lb er t of th e Ti da l Mo ve y f E , th e w ell k n own As tro n om er of th e Ch i ca go

Tri bu n e.

n are in o o n r n The waters o f the o cea ceaseless m ti , isi g in n r o r o 25 and falli ng twice each lu a day , ab ut every

* in i s urna moti o n The su rface o f the earth at the equ ator travels faster t di l h u r t the the tro c e n near 2 0 m e a rther rom the th an t e s face a pi s , b i g ly 5 il s f f ’ earth s ax is '

. E L R 1 LUNAR T LU AN MANUAL . 75

o r r n o f w r ow o r h u s . The isi g the ate s is called the ﬂ flood and n o f ebb tide tide , the falli g the same the . The height to which the wate rs rise th ro ugh a number of n n o t n o r n succeedi g tides is u if m , as will be explai ed here aft r r S n n . a d e The g eater are called pri g, the lesser

s in o n to o ne Neap tides . The water act bedie ce that

n s o f r u iver al law gravity , which may be exp essed as fo llo ws

A ll bodies a ttra ct all other bodies throughou t space di rectly in p roportion to thegu a n tityof matter they con ta in a nd invers e a s the s u a res the dis ta n ce be , ly q qf t en them o r o we . We may further add that the f ce f at traction is exerted in the directi o n o f a st raight li ne j o in in n o f r o n x g their ce ters g avity . The subj i ed e ample x n o n o f l will e plai the applicati this aw .

Let two o ten of b dies be placed feet apart , the weight A to be 2 to ns and that o f B 1 to n thei r attractio n for o r o r 2 to 1 each ther is di ectly as their matter , as is .

Let 1 0 equal the power o f attractio n o f A fo r B and

ower o f o n fo r A S r e 5 equal the p attracti o f B . epa at the bodies 20 feet they n o w attract each o ther in the

r o i e o n o er Th . . 2 t 1 w e same ati , , but with dimi ished p . o f r n 1 1 1 1 square the ﬁ st dista ce ( 0 feet) is 0 X 0 00. The square o f the sec o nd distance (20 feet) 1 5 20 X 20 A o r n to n 400. cc di g the law abo ve give the attract in o o f A and tw o o o n 18 i n vers el g p wer B m the p siti s y, 1 00 to 400 o r dir ect 400 to 1 00 o r 4 to 1 as is , ly, as is , as in n o f and the respective dista ces 1 0 20 feet . Thus we 1 0 r o fo r see that at feet the att active p wer is u . times

n 20 . e n greater tha it is at feet If, as stat d ; the attracti g

' o r o f A fo r 1 0 2 2 - it 2 4 p we B at feet is , at 0 feet is 76 LUNAR TELLURIAN MANUAL .

o r Fo r 1 0 o 1 2 f B at feet the p wer is , at 0 eet it is 1 4

The ave rage tide pro ducmg i nﬂuence o f the m o o n as

o r o f su n n r 2 to c mpa ed with that the is ea ly as % is 1 . in n o n do no t to 5 The tides Ope cea rise exceed % feet , while in the breake rs o f the tidal wave as it reaches a

o n n n r m r In c ti e t the wate rises very uch highe . the

o f n r o n earl 1 00 Bay Fu dy , the wate s s metimes rise v feet .

A t o o n tide is o B st the usually lab ut 1 4 feet . '

The tides o f o ur o ceans are due to the dif erence be tween the attractive fo rce exerted by the m o o n and sun on o and o n r her the earth as a wh le , the wate s at sur

o o n n o n o f o o f face . The f ll wi g expla ati the the ry the tides on ly applies strictly to such parts o f the o cean sur face as are n o t near to considerable masses o f land sur f o n o f the in o n ace . The retardati tidal wave m vi g

o o n in o n thr ugh shall w water , with the cha ges its directi ,

d and o o n n n and n spee , v lume , caused by c ti e ts isla ds , are matters which belo ng m o re to physical ge o graphy than to rono to n o o r ast my. It may be well te , h weve , that n in r o f the eve the deep wate s mid Paciﬁc , the tidal wave is retarded by the same cause that makes it t ravel behind — the m o o n i nstead o f keeping di rectly u nder her fric

o n that athers o n rn o f ti . The tide wave g the easte side O the Pacific Ocean fo ll o ws ab o ut tw o h o u rs behi nd the o o n and o o 40 o r in n ro n to m , ccupies ab ut h u s passi g u d o ur Atlantic co ast - 1ess than a cerc umference o f the gl obe .

Let M represent the p o siti o n o f the m o o n A D the A o r D and . we earth , E its center If take E , E , the LUNAR TELLURIAN MANUAL . 77

’ a n n fo r a o e rth s radius , as u ity , the , the le st p ssible dis tance o f the m o o n ; MA 55 ME 56 and MD 5 n r 7 ea ly .

’ Let m denote the measure o f the moon s attractive fo rce at the u nit o f distance ; it equals abo ut

n n o n A feet . The the disturbi g f rce o the water at will be measured by m m

feet .

’ Similarly the m o o n s distu rbi ng fo rce on the water at D is measu red by m m

(my; feet . 2 m a We mav also calculate that which is

n o f o r and n the mea the ab ve esults , is the mea tide due

o o o n t the m n acti g at her least p o ssible distance . The

o n o r fo r n r o o n calculati gives m e the tide u de the m , and 0 1 1 fo r o ff r n are less the Opp site tide . The di e e ces really much less than this ; o wi n g to the fact that the crests o f the tw o tides are at a and d i nstead Of o n the

n A D In n a li e . the Ope o cean they l g ab o ut 43 degrees

’ n o f o o n and o and behi d the place the m , its Opp site are

l o r r s stil m re eta ded when theymeet with land masse . 78 LUNAR TELLURIAN MANUAL .

' The greatest possible dis tance o f the m oo n fro m the ’ ’ earth s center is ab o ut 64 times the earth s equato rial u n o radius . Calc lati g as bef re , we have

m 772

Di rect tide feet . m m

o Opp site tide feet .

2 m

Mean tide feet .

In in o r 2m this case , as the the , the tide equals divided by the cube o f the relative distance fro m the ’ r n and n a sm all n All ea th s ce ter, plus mi us qua tity . pertu rbati o ns due to the fo rce Of att ractio n vary i nversely

a s o f n o r n the cube the relative dista ce, plus mi us a c o rrecti o n which dec reases with an i n crease in the rela n t ive dista ce .

The least and greatest distan ces o f the m o o n in her r o r are o 57 and o ( ave age) bit , ab ut These c rre

s o nd to and f . P feet , eet respectively Half the

o f tw o o r sum these is feet, which is ab ut the ave age

o f r o f n r in n o n height c est the lu a tide wave the Ope cea .

u n o Our s n ro The s als causes a tide . di ta ce f m him

' when in Pe riheli o n is and whe n in Apheli o n ’ t o r imes the earth s equat ial radius . The value Of

m fo r o n o f n o f s u n , these assumpti s dista ce the , is

n r n o f ea ly . The resulti g values the

o r are and r s la tide feet ave age feet .

The lu n ar and the s o lar tides m o ve afte r the place o f

t r in n r rn heir espective causes the heave s , as the ea th tu s

ro n n r A t the o f N e an u d u de them . times w d Full

Mo o n two fo r o n and n the ces c i cide , the u ited tide is equal LUNAR TELLURIAN MANUAL . 79

in magn itude to the sum o f the tw o bei ng

n r n r to sun and o o n feet , whe the ea th is ea est m

a nd n o are feet , whe b th at their

r n n o n i o r g eatest dista ce . Whe the m o is n her ﬁrst third

r r r o n su n o n qua te s , the dep essi caused by the c i cides with the elevati o n caused by the m o o n and the tide varies

o 2 n o on in fr m feet , whe the m is ‘ r and r in o n to pe igee the ea th apheli ,

n mo o n in a o and r in feet , whe the is p gee the ea th peri h eli o n .

The c rest o f each direct tide is the o retically 40 to 45

d r o r o 2 o r 50 n la te o n r eg ees ab ut h u s mi utes , the pa allel o f latitude co rrespo ndi ng to the decli n ati o n Of b o dy caus

in if o o n in 20 r no g the tide . That is , the m be deg ees rth

d n o n r n r in 20 r o f ecli ati , the di ect lu a tide will be deg ees

n o r r o f o o th latitude . The c est the pp site tide is , simi

larl o i o n o n Le n n o o t e . t y, m vi g latitude pp site the d cli ati ’ u den o te the angular distan ce o f any p o i n t o n the earth s su rface fro m the crest o f the lu nar wave at a g1v en mo me nt w its angular distan ce fro m the crest o f the s o lar

n t n A o f n wave at the same i s a t ; , the height the lu ar

r and E o f o r n c est , the height the s lar c est . The the

o f n and height the tide at the desig ated time place , will e qual

A o . c s . 2 u B co s 2 w ( ) . . ( ) rememberi ng that the co si ne o f an angle greater than 90 r and s n 2 0 n deg ees les tha 7 degrees , is esse tially n egative . RE AD THE

OPINION OF CAPABLE JUDGES ‘

’ D" T S I S T C S A S S C T H EA UAR ER LLINOI EA HER O IA ION ,

S P GF D DE C . 2 1 880 RIN IEL , 9, .

A . . A D W S Co . H N RE , “ — Gentle men " o u r n ew Lu nar Tellu ri an Glob e is a Splendid apparatu s fo r cl ass u se in ill u strati ng M athem ati cal

G eo ra hy . The re at o n o f the earth su n and mo o n are g p l i ships , we and ll c learly s ho wn . The Glo be has m o re merit an d fewer defect t an an m ar a aratu w a r n It s h y si il pp s e h v e e v e s ee . is a cred t tothe n entor an d man u fac tu r r " o u r r ctf e . e e u i i v s s sp lly, “ . L. e mo u r o m a n r S f No r U e t B o o m n to n . M y , : l iv si y, l i g ’ . A . a tm an n E G s S u t. S c o o a d P re den t I no Teac er , p h ls , si lli is h s

A ss o c i ati o n .

W n r D . . e two t r nc a o o N o rma S c o o E n e S P o C . h, i ip l C k l h l , gl w o o d ll. , I

" enr L. Bo ltw ood P r nc a Ottaw a Tow n h h S c oo l H y , i ip l s ip H ig h

ttawa Ill. O ,

dr t h bu r Ill A n w u t. S c o o a e . . e S G M s , p Ci y ls , l s g,

I. Le e Lew S u t. S c hp o ls de P ar I I sli is , p , Hy k ,

. P e er e e Ill. J ik , J s yv ill ,

m o n P r n . S c ho o an a Ill. W . . W a a H illi s , i ls , H v , W t e t r Ill R . . a hew e . M s , Ch s ,

mb Ill. G eo . B o u n t S u t. S c o o ac o l , p h ls , M ,

fr m P f. E. OLBERT A ronomer of the hica o Letter o ro C , st C g T i ne r bu .

C G ILL. Ma 2 . 1 88 1 . CHI A O , , y,

W S O . A . A D C H . N RE “ Gentlemen - I ha v e c arefu lly ex am i n ed yo u r Lu n ar d Tell uri an a n d am c harm ed w i th it. The apparatu s may b e u s e to ill u s trate m any o f th e phen o m en a t hat are due to the m o v e

n O f h arth and m o o n w th referen ce to the s u n and c o n m e ts t e e , i ; v eys a m u c h c l earer idea o f th e s am e than has hi therto b een ob ta i n ed by the great m ajo ri ty O f tho s e who ha v e ess ayed to

u n der tand them . SO far a s I n o w it u n e ua ed. s k , i s q l V er re ec tfu y sp lly,

E . C OLBE RT.

— OON The E art e n ar er t an her ate te we can s ee mo re t a n M h b i g l g h s lli , h - 1 Th a her u r ace s av 8 00 . e fferen ce i n eat n the o o n at n oo n a n d h lf s f , 5 di h o M T m n t 00 e ree . he oo n e u s o n 1 as m u c t a s id igh , is 5 d g s M giv s ly h ligh u n The u o f m o o n w o u o u the S . n t e s a t ere a e re sky f ll s ld giv d yligh . Th h v n ee n i c o ere ome n Of atmos r n m n i o ce tly b d s v d s sig s phe e o the oo , t is th u ght .

R —The fo u rth la n et o f the tem h as ar of a o u 68 a MA S . p sys a ye b t 7 d ys ; dis n ro m s u n 1 1 m o n m am r m I has w o moon ta ce e ete e . t t f , 4 illi il s ; di , il s s ; e ame a s o u r o r ta S 00 m r m n u t da a ou t th e e e e e . y b s s ; bi l p d , 9 il s p i —Th ﬁ an h m 80 m n m l UPI TE R . e t et as o o n tan ce o e vo J f h pl , 4 s ; dis , 4 illi il s : o f s u n h m H h s f u r a m 1 t at . a . . 2 05 e a o te te am u e h His d ys , o 55 . s lli s ; di

m e . ear e u a 1 2 o f o u r m m nu eter e o c t 8 e a te . , il s His y q ls s v l i y, 4 3 il s i — n nual r o u t n r h m s u TURN . e o a o u nd t e s u n 2 ear s ta n ce ro n SA A v l i 956 y s di f , n m e am t r m : o u m m a f a D n ~ 88 m l o e e e e 00 t e t t o E rt . e 1 i li il s ; di , il s v l 7 i s h h

n a f n o n w r D i oh . s it le s t a t t o a t er ea e o or e t an ate . a y, s h h y h h v ly b dy , l ss h y,

m 2 s It the mo t remar a e an et o n acco u n t o f its e t and 8 ate tes . 1 4 . 4 is s k bl pl b l s lli —Re o e a ou t he S u n in 8 ar a m r o me tre U RAN Us . v lv s b t 4 ye s ; di ete kil s ; n ro m s u n 1 o ooo m His ar has two n o wn ate te ta t ooo e . e k s lli s is dis f , 77 , , il s y is r 84 o f o u s . — i n f Hi m n a n n ear N E ttle s o w n o t s an et . s ea t ce is NEPTU . Li k hi pl dis ly i o n m e er o c t me 1 6 ear h as 1 mo o n ameter o 3 bill il s ; p i di i , 4 y s ; ; di , kil m e metre o r . s , il s The air ro o fs us o ver a nd retai ni ng the h ea t o f the s u n kee ps u s w arm The ’ n tant orc e s a e o n the eart e u a to tr o n o f en ne su n s co s f di l y d h , is q l 543 illi s gi s

r pwo r n d n n A m n w n 1 0 . o f 400 h orse p o we eac ki g ay a d ight a eighi g 5 lbs

we 6 On u ter . o n earth, ighs 39 J pi

m n r r i u mm r en ce it E arth is il es ea e to s u n n w i n ter th an in s e . H is m r o f th o u rn m r an in th n o r ern s u m r ho tter in the s u m e e s th e he isphe e th e th me . S P ACE h as p ro ba bly n o resisti n g m ediu m its temp erature is abo u t 200 de grees be lo w z ero . m n LI G HT go es iles a s ec o d . Th n e are t fi x e s tar i s 1 6 o n m e tant an d it ta e t ree ear fo r e s d billi il s dis , k s h y s a u s The i e t ee o f a r fle a eet er eco n its light to re ch h gh s sp d i b ll is f p s d . m r Of the a tero are ro m 2 0 o 00 m a o f ll o f The di a ete s s ids f t 4 il es . M ss a - f them pu t togeth er l ess th an o ne q u arter o earth . o i n t e re are a o ut 1 8 m o n co met tra er n ou r tem e A ra g th ks h b illi s v si g sys . Th y tho u ght to be flu id o r vap o r° RS — h ere are a o u t e in the w o e ea en o t n ort n T . a d S A T b visibl h l h v s , b h h r r 2 0 o f the i s t m a n tu e 6 o f the 2 n d 2 00 o f the rd o f So u t . e e a e 00 h Th g i d , , 3 , 4 h f h 6 h %u f h m the th o f t e th O t e t . t o t e i h a n tu e t ere are 4 , s , 7 g i d h 1 000 tar the 8th th e ih In the W a t ere are 1 8 3 s s , 9 Milky y, h m o n ta r a n d en w e c o n er t at w e are o n o n e o f the tar o f the illi s s , wh sid h s s W a ho w w o n er u the wo r o f crea t o n and ho w n n fi c ant re a Milky y, d f l ks i , i sig i , l tiv ely is the eart h School Apparatu s

O f all n a n d er e t u a ty uc as G o e 60 n B ac o ar ki ds , v y b s q li , s h l b s ( ki ds) , l kb ds , u a t n fo r ame O u t n e Ma n ato m c a an d Rea n art N u Liq id Sl i g s , li ps , A i l di g Ch s , ’ m r Fra me n rew a te Dra w n B o o N o e e ate etc . e a l s , A d s Sl i g k , is l ss Sl s ,

Ma and B ac o ar w t an d W t o u t nea ea u re . p l kb d Po int e rs , i h i h Li l M s s

N n m ar w h n w ha. l o Cray o n w e h ave e ver s ee c o p e s i th t e e Alp Dus t ess .

It ma e a c ea n w te ma r n o t rea a n d o e n o t cratc the o ar . I t k s l hi k , is g sy d s s h b d o u a t s ix c a bra o n Th e eman fo r it u n rece en te . am e ent tl s s h lk y s . d d is p d d S pl s s t a r o n c a t o n C er ro s . ro fo r 0 e c he s appli i . 75 p g s 5 g ss $3 5

A N D R E W S ’

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Dustless Blackboard Eraser.

P a ten ted,

And the Be t Ever U s sed . Only Per Doz en .

S am e ent o n r o f 1 pl s ec eipt 50 .

It is e n ou gh to s ay thagteache rs c o n si der this the b es t E ras er fo r the p ri ce th ey h a ve e er tr e a nd the mo t ree ro m u s t v i d , s f f d .

Th e cu t o n the right sh o w s the Globe Case w hic h is s en t wi th a ll 8 an d 1 2 i nc h

o e . I m gl b s t ay be h u n g u p o n the w all i r th e c oo ro o m as o w n in c u t o r c o e s h l sh , l s d a nd o c e at n l k d ight.

O ur n ew co m ete a n d ha n o m , pl ds ely Ill u s tr t d a e Cata logu e O f S c ho o l Me rch a ndise w be ma e an o n e o n rec e t o f 2 0 c ts ill il d y ip . Add ress fo r all p arti cu l ars the

an u ac tu rer M f s ,

A. H . An r d ews 81 Co . ,

1 and 1 Wa as A v 9 e. ca o 5 97 b h , Chi g . l D k s The Triumph S cho o es .

D v e ta il ed a n d Do w e le d th e r B t a ti o na r o To ge . o th S y a n d F l in o d g To p .

e e De o f u c ac now e u er or t in con tru ct o n to a n a n d Th s sks , s h k l dge d s p i i y s i y ll o t er e rece e the e t aw ar at o t the a e a an d ar a h d sks , iv d high s ds b h Phil d lphi P is x o s ition s 1 m eant so methin at the t me an d it mean omet n t p This i , s s hi g s ill E d u cators and Sc h oo l O ﬁi cers w o w ish to kno w the req u isi te s o f a ﬁ rs t a e an d W H" the R U has a n d mu t co nt n u e to ta e the ea cl ss d sk , T I MPH s i k l d: w ill please sen d for o ur Descrip tive Circu l ars o f Desks an d all ki n ds o f Sc hoo l M erc h an dise

w i D k The Ne Foldin g L d es s .

o o he m n mu m The The lid and s eat are fo ldi n g an d redu ce the sp ace t t i i . Two fo r tu o ne fo r wr t n an d on e as w en m o u r o t o n . lid assu es f p si i s s d y, i i g h o x c l o sed an d l o c ked u p o n the boo k b . r the anu actu rer Add ess M f s ,

“ n r ws Co. H. A d e A. ,

1 nd 1 a a A ve . c a o Ill. 95 a 97 W b sh , Chi g ,

THI S B OOK I S DU E ON THE LAST DATE STAMP ED B E LOW

AN I NITIAL FI NE OF 2 5 CE NTS

W ILL B E A S S ES S ED FO R FA ILU RE TO RETU RN S B OO K O N TH DATE DU TH P THI E E . E ENA LT" W ILL I NC REAS E TO 5 0 C ENTS O N THE FO U RTH DA" AN D TO O N THE S EVENTH DA" O ERDU E V .