as deduced from Experiments made with the Pendulum. 7 



It is only with the latter of these equations that we are to 

 be occupied at present, and for the sake of simplicity we shall 

 write it a little differently. Let, 



17:' - L 5 A o 



M 



T + 



14 



n= •-- 



<? e 



105 

 16 



X — 4r = M sin 2 h — N sin 2 2 A. 



then, 1 + — ^ sin 



I now take the following results of Captain Sabine's experi- 

 ments from the Quarterly Journal of Science, No. 39, p. 103, 

 viz. 



Latitude. 

 , 2° 31' 43" 

 51 31 8 

 63 25 54 

 , 70 4-0 5 

 74 32 19 

 79 49 58 



The first of these places is very near the equator, and the 

 others are so far removed from it that the variation of the 

 pendulum may be supposed very great in proportion to the 

 errors of observation. Putting L for the equatorial pendu- 

 lum, and observing that gravity is proportional to the length 

 of the pendulum, the foregoing formula will give us the fol- 

 lowing equations in numbers, viz. 



Stations. 

 Maranham 

 London 

 Drontheim 

 Hammerfest 

 Greenland 

 Spitzbergen 



Pendulum inches. 

 39-01214 = XV 

 39-13910 = IW 

 39-17456 = Z< 3 > 

 39-19519 = IW 

 39-20335 = l^ 

 39-21468 = l^ 



1-0000168 



1-0053007 



1-0069196 — 



1-0077021 



1-0080351 



1-0083805 - 



;cn 



L 



L 



L 



Z (5) 



L 



,(6) 



•001946 M — 

 •612797 M - 

 ■799954 M — 

 •890112 M — 

 •928930 M - 



■007771 N 

 •949107 N 

 •640110 N 

 •390313 N 

 •264075 N 



•968840 M - -120756 N 



We must next exterminate from these equations, the term 

 containing the unknown quantity L. For this purpose, mul- 



tiply the first equation by 



j(2) 



(2) 



1-0032711 



= -001953 M 



= 1-0032543; then, 

 007796 N; 



and 



