ALONG THE CIRCUMFERENCE OF A CIRCLE. 



455 



in the third column, we take the sum of these, which is the logarithm of cA, 

 and place it in the second column. The sums cA + Ad and log cA + log Ad 

 are next obtained. The half of the latter sum gives log AC, whence AC ; the 

 half of the former sum is CB, whence its logarithm. This very simple compu- 

 tation is repeated until we obtain GI and IH alike as far as our tables enable us 

 to proceed. Log AC — log CB is written in the third column, it is log sin B', 

 whence we obtain B', the maximum value of the angle B, and similarly for the 

 others. The maximum value of H is 90°, that is to say, since this is the angle 

 at the zenith point, the moving body would just describe the whole semicircum- 

 ference from N to Z. We have thus computed all the dimensions of the 

 diagram, fig. 10, on the left hand side of the line cl. 



In order now to find the time in which the arc of 6° from the bottom of the 

 circle would be described, we make cdA = 3°. Adding to the log sine of this 



Ad 

 the logarithm of -r- we obtain log sin Acd, whence Acd = 59° 00' 46". 9 



Ac 



or 



Half the sum of these angles is CAB ; by adding to log sin CAB, log -p 



log sin B 1 , we obtain log sin B, whence B. And thus we proceed until we 

 come to H = 21° 37' 38". 



In the following scheme the calculations are given for the arc 6°, and also 

 for the whole arc 7° : — 



a = 3 oo oo-oo 



c = 59 00 46-90 



8-718 8002 

 1-214 3247 



3 30 00-00 

 90 00 00-00 



8-785 6753 

 1-214 3247 



9-933 1249 



0-000 0000 



A = 31 00 23-45 

 B = 13 52 53-07 



9-711 9215 

 9-668 1324 



46 45 00-00 

 19 49 46-30 



9-862 3526 

 9-668 1324 



9-380 0539 



9-530 4850 



C = 22 26 38'26 

 1) = 20 49 29-60 



9-581 8127 

 9-969 0427 



33 17 53-15 

 30 44 43-40 



9-739 5685 

 9-969 0427 



9-550 8554 



9-708 6112 



E = 21 38 03-93 

 F = 21 37 11-98 



9-566 6532 

 9-999 7242 



9-566 3774 



32 01 18-27 

 31 59 56.40 



9-724 4733 

 9-999 7242 



9-724 1975 



G = 21 37 37-96 



32 00 37-34 



90 



0-167 9689 



90 



= 0-256 3407 



111 37 37-96 

 L. tan 55 48 48-98 - 



Log log tan ( 45 + — j = 



Log nep tan 10 = 

 Colog IH 



122 00 37-34 

 61 00 18-67 = 



9-225 2289 



0-362 2157 

 0-425 6121 



9-408 8176 



0-362 2157 

 0-425 6121 



1-030 520 



0-013 0567 



1-572 698 



0-196 6454 



