2. 

 3. 

 4. 

 5. 



6. 

 7. 



of the Pendulum made by Capt. Kater, M. Biot, #c. 167 

 Following here the method pursued at page 164-5: 



1. 39-094187— 2— 0-39034173/=^ 



39-113189— z-0-4932370j/= e 2 



39-1 13002-2— 0-49721 72 y= e 3 



39-118088-2-0-51361173/= e 4 



39-129285-z— 0-5667720 j/= e 5 



39-137700-3-0-6045723 j/= e 6 



39*155442 -2—0-6869300 j/= e, 



8. 39-171776— z— 0-76 13523 y= e 8 



From which is obtained 2=39*129084 — 0-5642543 y. 



Again, 



15-2600913-0-39034172— 0-1523666 y 

 19-2920719-0-4932370 2-0-2432826 y 

 19-4476573 — 0-4972172 2— 0-2472249 j/ 

 20-0915076— 0-51361 17 2-0-2637970 y 

 22-1773831 -0-5667720 2-0-3212304 y 

 23-6615693-0-6045723 2-0-3655077 j/ 

 26-8970478 — 0-6869300 2— 0-4718729 7/ 

 29-8235217—0-7613523 2-0-5796577j/ 

 From these we obtain 2=39-133698 — 0-585937 3/. 

 Equating this and the preceding value of 2, and we have 

 39-129084 - 0-56425433/ = 39-133698 -0-585937 y, from 

 which it follows that 3/ = 0-2 12796, and hence 2 = 39-133698 

 -0-124684 = 39-009014= the length of the pendulum at the 

 equator, and 39-009014 + 0-212796 = 39'221Sl = the length 

 of the pendulum at the pole. 



These determinations differ at the equator by 0-00206 in., 

 and at the pole by 0-00135 in. only, from those of Capt Kater. 

 Whence /=39-009014 + 0-212796 sin 2 A. 



By substituting for sin 2 A their proper values at the different 

 points of observation, we shall have the lengths of the pendu- 

 lum by computation, which compared with those from experi- 

 ment give the differences denoted by <?,, c 3 , c 3 , &c. 



Again, 



