AT THE MABRAS OBSERVATORY, 



•SOS 



Places. 



Equator, 



Porto Bcllo, 



Pondiclierry, 



Madras, 



Manilla, 



Paris, 



Loudon, 



Itruys I'sTafid'Spitz-Bcrg,-' 



Laiitudct 



0: 0: 



9: 33: 30 

 11:55: 10 

 13: 4: ^2 

 14': 33: 36 

 48: 50: 16 

 5i:l0: 40 

 6(3:48: 3 6 

 79:50: 



Bijje 



Length of 

 Pendulum. 



9:33:30 



2:22:10 



2: 8:32 



1:29:24 



34:40: 39 



■■ 2: 40: 2^5 



15: 17:36 



13: 1:44 



Indies. 

 38.9948867 

 39.002878 

 39.011509 

 39.026273 

 39.043620 

 3t). 1272012 

 39.1280000 

 39.1813700 

 39.200034 



Diffc 



Parts of Inches. 



0.008011 

 0.008SG31 

 0.01476 4 

 0.017347 

 0,0.835812 

 0.0007988 Gralmm 



Authors;. 



Bouguer. 



Rouguer. 



Le Gentil. 



Present Expts. 



Le Gentil. 



V'a-rin and des Hayes. 



0.053370 

 0^0 18661 



I SHALL now consider what the computed length of the pendulum at 

 the equator will prove, by combining any two of the lengths given here 

 Trora ekperimeW "in different latitudes fa^ then compare these results 

 ^ii'hMr."']^ou'GtJERV actual determination.^ ' '/' 



34. Proceeding on,.the h^ypothesis that the length of the pendulum 

 decreases in the ratio of the square of the sines of the latitudes,; if / be 



,the length of the simple pendulum at the equator; L, that at the pole ; 



.k'ii:\ ■ . ■■ ■ ■ ^•' ' ■ 



V, the lensrth in the latitude whose sine is s; 'L that in the latitude v/hose 



sine is S, then we have. the foUowintr formula, for the lenr^th of the simple 



pendulum at the pole,, an4 at the equator. ... 



I — ^'^'t- ^^'^ At the^ Equator 



s' ' + r^-0 At the Pole 



' ■ r"!^- -I'/ni g'uiooi 

 Example i. 



Let the lengtli c)f -itit^ ^tki6^i\ii'iA ki' I^nd\}n 6^ . . _- 

 That at Madras, w..,. --'-,>t..„r^:.^. j^^.^^j^4. 





The sine of the latitude of Lo)iddn '..-.. .":,'- - -'- (5 1* SO' 40") 9 . 8936 113=^ 

 The sine of tlrtila|iMe;.trf iWarf/?ds.^--i.l;--.v.-ltl3 4 12) 9.354:3T<)9 = s'Jcrr 

 Then >ve have S^ 7 23.9100000 



}»'L— 2.00 100 13 



A 



S- =0.6126(544 

 i»== 0.0511399 



S-7— s*I>i= 2 1.9089987- 

 Divick'd by 



S^- — 5^=0.5615245 0.5C1524: 



Pcniluluni at the equator / = 39.01693 



