Invariable Pendulum, during a Russian Scientiftc Voyage. 423 



to y, we multiply each etjuation by the co-efficient of y in this 

 equation; which gives the following results: viz. 



— 0-3398532 + .rxO-00S7O8O + 3/ X 0-0000758 



— 2-1083632 + XX 0-0540157 +j/X 0029177 



— 2-9359321 + x X 0075204:5 + j/ X 0-0056557 



— 8-0912268 + a: X 0-2070967 + ?/ X 0-0428890 



— 11-6I694-68 + jrxO-2972962 + 3/ X 0-0883850 

 -23-9844280 + jrx 0-6127966 + 3/ X 3755198 



— 24-9792400 + .rXO-6380657 + j/ x 0-4071279 



— 27-5740089 + J7XO-7041567 + J/ X 0-4958368 

 —29-3427299 + xx 0-7491220 + j/X 0-561 1894 



— 14-5525254 + xX 0-3718291 + j/X 0-2199552 = 0. 

 The sum, divided by 9, is the equation of the minimum 



with respect to y. Eliminating between these two equations, 



we have x = 39-02422, y = 0-091787, and -^-^ =0-00865052 



1 



267-7 



= the compression. 



If we substitute these values of x and y in each of the equa- 

 tions, we shall have the respective values of E', E", E'" &c., 

 or the difference of each partial result from that which corre- 

 sponds to the mean of all the experiments, as they stand in 

 the followiniT table. 



The greatest differences fall on Valparaiso and the Bonine 

 islands. Fortunately these two stations are amongst those 

 where the experiments were the most satisfactory : so that 

 there can be no question about tiie errors of observation, in 

 .seeking ibr the cause of the difference; which must therefore 

 be allnbuled to the anomalies of local attraction. 



If, for the purpose of confining our remarks to the Northern 

 hemi.spherc, we exclude Valparaiso, as the only station situated 



