1 62 Mr. W. Galbraith's Remarks on the Experiments 



thods of the latter may be liable, going upon the generally 

 received principle, that to remove all sources of error, how- 

 ever minute, is preferable to trusting to their correction. 



We believe that the results obtained by the French philo- 

 sophers merit great confidence, from the ingenious devices to 

 which they, in their researches on the determination of the 

 length of the pendulum, had recourse; though we cannot help 

 thinking that the method of Captain Kater, generally speak- 

 ing, is, both on account of its simplicity and accuracy, justly to 

 be preferred. If Captain Kater's apparatus, which may still 

 perhaps be susceptible of improvement, be more delicate than 

 that used by M. Biot, from the irregularities in the density of 

 the materials constituting the exterior crust of the earth, its 

 results may be expected, in particular cases, to be less con- 

 sistent with each other, and with the generally received theory 

 of the oblateness of the spheroidal figure of the earth. 



When however observations are made on a considerable 

 number of points in an extensive arc of the meridian, it may 

 be naturally expected that these small irregularities will tend 

 to correct one another, so that an excess in one direction may 

 be very nearly counterbalanced by a defect in another, and 

 that a mean of the whole being properly obtained, will be 

 very near the truth. For this purpose we have applied the 

 method of minimum squares to the experiments of Kater and 

 Biot, as best calculated to give a true mean result. 



It is demonstrated by the theory of attraction that the 

 length of the pendulum is augmented from the equator to the 

 pole proportionally to the square of the sine of the latitude, 

 in such a manner that, if the length of the pendulum at the 

 equator is represented by z, and its absolute variation from 

 the equator to the pole by y, /, its length in any other lati- 

 tude A, will be represented by the following equation : 



I = z + y sin 2 A ( 1 ) 



If we have two equations of this form, in which I and A 

 are determined by observation, we can obtain the values of % 

 and y, I = z + y sin 2 A 



V == 2 + y sin 2 a' 

 l'—l=y sin 2 A'— y sin 2 A = y (sin 2 A' — sin 2 A). 



Hence y = . . . , . . . . — -r (2) 



J sin (x'+x)sin(a/— \) v ' 



and z — I —y sin 2 A (3) 



At the equator A=0, and therefore l = z as already observed; 

 consequently 4 expresses the diminution of gravity from the 



pole to the equator. 



Now, 



