FORMULAS FOR AREA Rectangle-base X altitude. * * Parallelogram-base X altitude. Triangk-Y2 base X altitude. Trapezoid- Y2 sum of parallel si des X a ltitude. Par'8bola-% base X altitude. Ellipse-product of major and minor diameters X 0.7854. Regular polygon- Y2 sum of sides X perpendicular distance from center to sides. Lateral area of right cylinder = perimeter of base X altitude. o o Total a rea = lateral area + areas of ends. Lateral arca of right pyramid or cone = Y2 perimeter of base X slant height. Total area = lateral area + area of base. Lateral area of fru stum of a regular right py~amid or cone = Y2 sum of perimeters of bases X slant height. Surface area of sphere = square of diameter X 3. 141 6. o ! o o I o FORMULAS FOR VOLUME 1 Right or oblique prism-area of base X altitude. Cylinder-area of base X altitude. P yramid or cone-~ area of base X altitude. Sphere-cube of diameter X 0.5236. Frustum of pyramid or cone-add the areas of the two bases and add t o this the square root of the product (;f the areas of the bases; multiply by ~ of the height: V ~ h (B + b + ~B X b). IMPORT ANT CONSTANTS 7. = 3.1416. 'lt 2 = 9.8696. ~7( = 17724 1+7t = 0.3183. Base of natural logarithms = e = 2.71828. !vi = log!. e = 0.43429. 1 + M = loge 10 = 2.3026. Loge N = 2.3026 X loglo N. Number of degrees in I radian = ISO + -:t 57.2958. Number of radians in I d"grec = 7. + ISO 0.01745. WEIGHTS AND MEASURES Avoirdupois Weight Long Measure Dry Measure iVa? = = 27 grs. I dram 12 inches = I foot 2 pints I quart 16 drams = 1 ounce 3 feet = I yard 8 quarts = I peck 16 ounces = I pound 5:1 yards = I rod 4 pecks = I bushel 36 = I 25 pounds = 1 quar: ~ r 40 rods = I furlong bushels chaldron 4 quarters = I cwt. 8 furlongs = I stat. mile Liquid Measure 2,000 Ibs . = 1 short ton 3 miles = 1 league 2,240 lbs. = 1 long ton 4 gills = I pint 2 pints = I quart Mariners' Measure Square Measure 4 quarts =1 gallon " feet = I fathom 31 J1 gallons = I barrel BY !LO fathoms = I cable 144 sq. in.,:. = I sq. ft. 2 barrels = I hogshead length 9 sq. ft. - 1 sq. yd. ROSS R. MIDDLEMISS 7:1 cable lengths = I mile 30~ sq. yds. = I sq. rod Surveyors' Measure 5,280 ft. = I stat. mile 40 sq. rods = I rood 7.92 inches = 1 link Associate Professor of Applied Mathematics 6,08.\ ft. = I naut. mile 4 rvods = 1 2~re 25 links = I rod WASHINGTON UNIVERSITY Troy Weight 640 acres = I sq. mile. 4 rods = I chain 24 grains = I pwt. 10 sq. chains or 160 sq. Technical Consultant To rods = I acre 20 pwt. = I ounce Cubic Measure 12 ounces = I pound 640 acres = I sq. mile Used for weighing gold, 1, 72S cu. in = I cu. ie. 3(' sq. miles (6 miles sq.) silver and jewels. 128 cu. ft. = I cord wood = I township 1 27 cu. ft. = I cu. yd. Miscellaneous Apothecaries' 40 cu. ft. = I ton (shpg.) Weight" 2,150.42 cu. inches 1 3 inches I palm 20 grains = I scruple standard bushel 4 inches = I hand 3 scruples = J dram 23 I cubic inches = 1 6 inches = 1 span 8 drams = I ounce standard gallon 18 inches = I cubit 12 ounces = I pound 21.8 = I Bible cubit *The ounces and pound in this I cubic foot = about four­ are the same as in Troy weight. fifths of a bushel 2Y2 ft. = I military pace 14 * * o o o o o o GENERAL DESCRIPTION This slide rule combines the convenience of the 5-inch pocket size rule with the ac­ curacy of the standard IO-inch rule. On the FRONT FACE ALONE it has all of the standard 5-inch scales-A. B. C , D, S, T, K; and DJ. The arrangement is more convenient than on other 5-inch rules be­ cause all of these scales are on the same side: it is not necessary to turn the rule over to read sines and tangents: triangles can be solved with a single setting of the slide. o K o A B 5 T C o D o D I P"'I" IIIIIIII'"II"IIIII I '1"1'1"111" I I I ' I I I III 'I Q'l II' I'I 'I'I'IIIII'I' II " I q '1'P i ' I' l ' !! I I' I ' ) ' I' , I 11II 11I"IllIlIpll l 11 11 111 11 1111 q II' rI l l f ' I I I . I ' 1 9 e 7 6 5 4 I 3 ' } o o Fig.l On the back face there is a standard to-inch CoD scale combination folded at ",TO: The two parts of C are called C, and C t , and the corresponding patts of D are called D, and D2 This combination gives the same accuracy as the standard to-inch rule for all problems in multiplication and division, percentage, proportion, etc. There is also an L scale which gives logarithms with to-inch accuracy and a 5-inch D scale. This scale, used with D, and D" gives squares and square roots with iO-inch accuracy. 0 o 0 o L C 2 CI (}I 3456789 00 02 .J&"IIIIIIIIIII"'1""I""I"'~ l'I'I'I'I'I'I'I'I'~II'I'I'IIIIIII'I'II~'j1I'1'I'I'I'I'l'lt'll1'i1111'1'i'1'i~111'I11'1'I'I1111~'i'i'l'l'1'l1111111 o 0 1""1"111""""1""1"111'11111111"111""11 '1'1'1'1'1'111111111'1'1'1'1'1'1'1'1'1'1'1'1'1'1'1'1'1'1'1'1'.'1'11'1'11'111"1""1""1""1""1""1"'" 0 1 2 3 4 567891 'Stock SLid~ Fig 2 The names of the various parts of the rule are indicated in Fig 2. They are the BODY or STOCK; the SLIDE which moves in the grooves of the stock: and thB RUNNER, or INDICA TOR, or CURSOR. This cursor is molded of transparent plastic and carries a HAIRLINE or MARKER which is used in making accurate readings and settings. Locating Numbers on the Scales 1. Reading a Slide Rule Scale. Anyone who knows how to read the scale on an ordinary ruler or yardstick can easily learn to read a slide rule scale. The only essential difference lies in the fact that the calibration marks on a slide rule scale are not uniformly spaced (except in the case of L). Fig. 3, which shows only the primary divisions of the D scale, illustrates this important point. It is much farther, for exampk, from I to 2 than it is from 8 to 9. The spacing is called "logarithmic" and it is based on the theory of logarithms. One does not need to understand this in order to use the slide rule-any more than he needs to know the theory of gasoline engines in order to drive an auto­ mobile. 2 o o Fig.3 The part of the 0 scale from 1 to 2 is divided into 10 secondary divisions each repre­ senting IfIO, and each of these is further divided into 5 parts as shown in Fig. 4: each smallest division then represents If. of 1/10 which is 1/ .. or 0.02. ~_O~~ ______D ___ I_II_"_I_"_"_I_I~_I_II_"_11_11_111_11_11_111_11_111_11_111_111_1I1_1_1_1_11_1_lt_I_I_II_I_'I_~_1_':_II_~_jl_I~_jl_I~_jl_jll_II_~._III_1I_1I1_1j1_II_jll_Ij~_II_II_I_II_"_~_11_"_11_1I_17_1I_"1_11_11_~_"_11i_"_1~_'! __ i~ _______~~() ___O-J Between 2 and 5 each primary division is subdivided into 10 parts and each of these is divided into 2 parts; each smallest division then represents Yz of 1/ 10 which is Iho or 0.05. Between 5 and 10 (the right-hand) stands for 10), each primary division is divided into 10 parts so each smallest division represents '/10 or 0.1. When a person becomes familiar with this situation for one scale he can easily read any of them. o (0 l . 1'1 2. Locatin~ a Number on the D Scale. In locating a number on the scale one dis­ o o o o re gards the deci mal poi nt entirely. lnus the same spot on the scale serves [or 1.25 . 0.0 125 . 12 .5.1150. etc. To locate this number one may rega rd the D scale as running ~ from 1 to \0. the ri gh t-hand 1 standing for 10. He may then think of his number as ~ \ .25 regardless of the actual position of the decimal point. 5l[~t&·'1~, ~-::; ~ §lI96'_ZT'lf ...§ V) Since the fir st digit is I, the number is between main d iv isions I and 2 Since the m£~6"'1h § next digit is 2. the number is bet we en \ .2 and 1.3 and is therefore located bctw~cn th~ sl~f::: ~:~il ~ ~ ~cn m06'-",il ~ second and third secondary calibrations. ~ow. each small est division in this interval 519061" %. ....g ~~co SLI'-!I. ..§ repre sents 0.02. so the required point is half-wa y between the second and third of these. 51t6~i'''%. " Figure 4 shows the location of this po int and also shows several others. ;lt~"-n,h ~ ::-1'- SZm:::;!i, :1 ~ O!..§ ~£8961' '1 ~ .