REG: HER DEPARTMENT OF COMMERCE Letter 1 1-3 BUREAU OF STANDARDS Circular WASHINGTON LC 3^7 (October Jl., 1932) Prepared by R. E. Gould, Chief, Time Section ^ . fA SUNDIALS \0> e o> Contents Page I. Introduction „ 2 II. Corrections to be applied 2 1. Equation of time 3 III. Construction 4 1. Materials and foundation 4 2. Graphical construction for a horizontal sundial 4 3. Gnomon . 5 4. Mathematical construction ........ 6 5,. Illustrations Fig. 1. Layout of a dial 7 Fig. 2. Suggested forms g IV. Setting up the dial 9 V. Mottoes q VI. Bibliography -10 . , 2 I. Introduction One of the earliest methods of determining time was by observing the position of the shadow cast by an object placed in the sunshine. As the day advances the shadow changes and its position at any instant gives an indication of the time. The relative length of the shadow at midday can also be used to indicate the season of the year. It is thought that one of the purposes of the great pyramids of Egypt was to indicate the time of day and the progress of the seasons. Although the origin of the sundial is very obscure, it is known to have been used in very early times in ancient Babylonia. One of the earliest recorded is the Dial of Ahaz 0th Century, B. C. mentioned in the Bible, II Kings XX: 0-11. , The Greeks used sundials in the 4th Century B. C. and one was set up in Rome in 233 B. C. Today sundials are used largely for decorative purposes in gardens or on lawns, and many inquiries have reached the Bureau of Standards regarding the construction and erection of such dials. This paper has been prepared to give in a brief form information which will be useful in the construc- tion of sundials. II. Corrections to be applied The sundial, in its usual form, consists of two essential parts, a straight edged indicator or gnomon, for casting a shadow, and a suitably graduated dial on which the shadow is cast Sundials indicate true local sun time which differs from mean solar time by varying amounts throughout the year. It is therefore necessary to apply to indications of a sundial a variable correction known as the equation of time. (See Table on page 3). It is usually necessary to apply a further ccrrec tion because of the fact that in most localities standard time rather than local time, is used and few places are located exactly on the standard meridian. This correction is constant and depends upon the difference in time, or longitude, of the standard meridian of the time zone in which the sundial is to be located and that of the particular place of location. This correction can be calculated on the basis of 15 ° longitude difference being equivalent to a time difference of one hour. For positions to the West of the standard meridian the correc- tion must be added to the sundial reading and to the East it must be subtracted. The standard meridians of the various time zones of the United States are as follows: - eastern, 75th; central, 90th; mountain, 105th; Pacific, 120th. The longitude and time cor- rection for any given locality can be obtained from maps or tables or from authentic records. I i 1 ii II I 1 I I I I I <D Lft Lft ^ P 1 -P ft LftLftO LftLftO Olft O O LftO O O O LftLft Lft Lft Lftlft i LftlftLftLft Lft Lft.Lft Q Eh CVI ft ft LftCVJ CVJ CVJ ' ft P cti O 03 LftiLftP-P" O POP P" Lft Lft Lft OJ LftCVJ Lft OJ O LftO Lft O Lft O Cti P 0 ft 0 Lft Tsoft-r"- VO VO i i cti (ft crvoo LftLTVp ft” LftLftOJ OJ li I ft Op ooooaon — —IOQ vdOi— — CV10J Lft , . I I I I I I I I I I ft p M O ft ft ft I I I I 1 I ! 1 I I IPPPPPPPij O CQ ft 1 1 I Cti <H ft ft 6 o 3 3 ft P O cti o o o o o o LftO mo LftO OOOOOOLftO LftO LftLftO O O O O O CVI CVI CVJ i li CVJ O 0 O ft > CQ CVJ CVI CVI — —IOO LftLTVp Lft ft O Lft Lft CVJ O Lft Lft P OP” CJ OPCVI i i— pH® o CD VO VO VO Vo' VO Lft p" cti •H CQ S3 VO VO VO VO VO Lft Lft LftLft Lft Lftp" vp -P" Lft Lft Lft LftCVJ OJ CVJ i—I P I I I I I I I I 1 I I I I i I i i CQ CD I I I I I I I fti li li Ii Ii Ii Ii Ii Ii Ii Ii Ii ft p — — — — — — — — — — — — — — — — — — — — — — — — —Ii—Ii—I Pi— CD I I I I I I I I I th O CO i I I 1 1 ! I I 1 1 I p P CD CVI p rH ,3 co cti P CQ • LftlftLft O O O LftO O LTV O LftO LftO O Lft Lft Lft Lft Lft Lft Lft LftO LftLftO OLftO i > Cti CQ P CQ ft LftLftft LftlftOCVJ-p- Lft rH CVJjp Lft —I CVJ Lftp LftO P OJ Lftp” LftLftO P P P CVJ 0) ~ rjj 0 ft <D >>,3 d O OOOPPftCVlCVlCVICvl LOIftftftP'PPPP Lft Lft Lft Lft Lft LftLftVO VO VO VO VO I I I I i li i I, I I I I I ll ll ll ll ll Ii Ii Ii Ii Ii I rH rH Ii li li Ii Ii li -p hDP O — — — — — — — — — — — — — — —Ir — — — — — — — — —li—I i— —IP cti cti I I I I I 1 I ! I I I I I I I I I I p O 1 I 1 1 f I 1 1 I ! Ill P P S O 0 P CQ > cti CQ P O O LftLftLftLftlftO O O O O O Lft Lft Lft lft O O O O Lft Lft LftlftLftLft Lft Lftlft I i i cti CVI CVlJp cvjpp CVJ I hD ft cti O ft O LftLftft ftLOCVJp O O O LftP Lft Lftp Lftlft — Lftlft —I Lftft I P H 0 H (DP >, CO ooooftftftojajp ftLftPPP Lft Lft LftVO VO VO r^-r''-ft--&cn50 0G gv CJV0V ! I I I I ! I I I I I I I I I I 1 I I I 1 I I ft H O ft P 1 I ! I 1 I ! ! cti cti cti 0 P CQ ft . u 0 ft O LftO LftLftO O Lftlft Lft Lft Lft LftLft Lft O O LftO LftO LftO LftO O ft LftO ! <H O O CVJ cti 4» hO ft ft O O Lftp-.p- LftCVJ ft O LftP" LftCVJ P O Lft Lft O LftLftCVJ o LftLftP Lftp" CVJ I 0 cti ft cti CQ P : CQ VQVOVQVO LftlftLftLft Lftlft IftCVJ CVJ CVJ CVJ i I i I i ft! Tti — — —i ooo -P CQ P3 0 + + + + + + + PPPPPPPPPP PP+ pppppppp pp + ! CQ O P O P U •H +» o •H ft ft ft LftLftO O O O O O O O Lft Lft O O LftO LftO LftO Lftfto o o o o o o ftft; o ft ft P P CQ lftp” O ft CVI Lftp- LftO ft P CVJ Lftp” -p" Lft LftO O P PPCVJCVJCVJCVICVJCVICVJPPJ >> 0 O i— P : CQ r J Lft Lft Lft Lft Lft Lft LftVO VO VO VO VO VO VOVOVO VO vb* 1 rH 0 0 cti ft) % ’+ VO VO VO +^' ; I ft ft p ?+ + ?'+ P^ f + + + + + + ++ + + ppppppppp + p tH cti 0 P CQ 0 I o > p •H •H p p 0 ft cti ft P o bfl 0 Lft Lft Lft Lft Lft Lft Lft O O O Lft Lft O O Lft Lft O O LftO O LftLftO OLftO O O ft i p cti pH p CVJ ft O LT\P” LftCVJ ft O Lft LftCVJ HGHCVJp LftO CVJ Lftp- ftp cvi ft, ft o p cvj O ; ft CQ p S3 0 •H p CVJOJCVJi—li—I ft i—li—!i—I o OOOOOOOOPP P P P CVJ CVJ CVI CVJ ft ftft O hO I I I I I I I I I 1 111 ++ + + + + pppppppp pp M I— p p Eh cti cd a 0 0 Lft Lft O Lft Lft O O LftO O Lft lft Lft Lft Lft Lft Lft LftO O LftO LftO LftO ftft o o o ft ft P O ft Sh LTV O ft ft CVJ PPPpp LftLftOJ CVJ P P o lft ftp” ft, 0 CD P P cti g ft 0 Q ft cvj r-ftrft HM-ftrfti'ftr'ft rftr-ft Lft Lft Lft Lft Lft Lft Lft Lft Lft Lft Lft Lft Lft Lft Lft Lft Lft CVJ CVI CVJ CVI ft p p I l I I I I I l I I I I I I I I I I i I I 1 I 1 I I I I 111! cti ft ft 0 0 o ft ft 0 O P O O Lft Lft O O LftLftQ Lft LftO LftO LftO Lft LftO Lft LftO O O O LftLftO o o ft P p !>» O P OP CVJ O Lftr-ftft Lftp- CVJ O Lft LftCVJ O P CVJ LftLftO P ftp- LftO P CVI Lftp- ft ! P cti ft, p- p cti a p ft rftLft LftCVJ cvj cvj ft ft ft HOOOOOOOOP ppppcvjcvjcvjcvicvicvj' Oft cti P PPPPPPPPPP + + + P P I I I I I I I 1 1 I I I 1 I 1 I > 0 o I 0 ft p H p ft p oQ 0 p 0 O O Lft Lft O LftO Lft O Lft O lft O O Lft O O LftLftO O O Lft LftLftO O O Lft Lftlft I i CVJ cti P cti > CQ P Lft CVJ LTVP CVJ ft LfVp CVJ rH Lftp" CVJ O lft Lft —I LftP" CVJ OP” O LftftP Lft Lfti— O I ! 0 p p •H 0 cti i i i ii ft-r-'-VOVOVO £ P cti qO ft cvj cvj cvj — ft — —i o o o O ft CT\ (ft CM50 VOVO ft-ft- LftftLftp-p-Jp i ii I o Pi—I CQ rH —ii—ii—ii—ii—ii— —ii—ii—ii— —Ip pppppppp ppppppppppp rH •H CQ cti PPPPPPPPPP 0 CQ 0 P 0 > p 0 p p p ft ft rH P O O LftO LftO LftO O O LftO OO O LftOftO ft O OftftLftftLftLftft p Cti o ft CQ P" Lft Lft O O i—I i—I CVJ CVJ CVJ CVJCVICVJCV'CVJPPOOLft ftp- LftCVJ P O Lftp- Lft 0 Cti hO 0 > cti 0 > > P O |xj ft rftrftr Lft Lft Lft Lft Lft ft CVJ CVJ CVJ i i i 1 i I i I i i Ii I i •H •H P 0 0 i—ii— ft —ii—ii—li—ii—li—ii— — — P rH — rH P rH p — —Ii— —li—Ii—Ii—Ii—Ii— — 50 P 0 p PPPPPPPPPP PPPPPPPPPP PPP-J—HPPP P • ft Pft Pft 0 CQ 0 n 0 p 0 a ft a o O O Lft Lft O O LftO LftO LftO O Lftlft Lft LftlftLftLft O O LftO LftLftO O O OO -p- i p ft o a p CQ LftO CVJ Lft OJ Lft i I -ft" O Lft LftCVlP" OCVJp” O \lp” O CVJ Lft —I CVI LftLftO P CVJ ft H Eh •H p cti - cti p p ft p p Lftft" ft" ft Lft LftVOVO ft-D— ftVOTSO CftCftOvO OOP P P P CVJ CVJ CVJ CVJ Lft Lft ftft \ > P o o PPPPPPPPPP PPPPP pi I P i—li I i—Ii—Ii—Ii—li—Ii—Ii—Ii—I i—Ii—Ii— ft cti spft P P P P PPPPPPPP PPP 0 H P P O P O 0 ft ft o Eh W ft cti P cti ft P cti p O ft P P H cti P cti cti P p a ft P ft CVJ Lftft" LftVO r—T50 OV O P CVJ Lftp LftVO 0-V0 CftO P CVJ Lftp- LftVO ft-TSO CftOP 0 0 CQ Cti rH cti O ft PPi—iPi—ii—ii—ii—ii—i cvj cvjcvjcvjcvjcviaacuoflcu rftft 3i>>® > <U ft 3 i i J - 4 - III.