• THE 



PHILOSOPHICAL MAGAZINE 



AND 



ANNALS OF PHILOSOPHY. 



[NEW SERIES.] 



APRIL 1828. 



XXXIX. A Letter to the Editors relating to the Ellipticity of 

 the Earth as deduced from Experiments with the Pendulum. 

 By J. Ivory, M.A. F.R.S. 



Gentlemen, 

 T N examining the calculations in the articles relative to the 

 «■ ellipticity of the earth, inserted in the last Number of this 

 Journal, I have detected a small arithmetical error, which, al- 

 though of little moment, it may be proper to correct. The 

 equation at the bottom of p. 1 70, viz. 



2-973 t= --00061, 

 should be, 2*973 t = — -00033: 



consequently, t = — -00011, s == -f 00005, 



/=-2056, A= -01335; 



and the formula for the length of the pendulum, 



I = 39-01335 + -2056 sin 2 A. 

 But the error just corrected is so small as not to affect either 

 the reasoning deduced from the formula at the top of p. 171, 

 or any of the results obtained by it. 



It is directed in p. 207, that the two approximate quantities 

 a and b, be so taken as to satisfy equation (A) : but it is ob- 

 vious that, although this be convenient, it is not necessary in 

 the method of computation I have followed. Nothing more 

 is required than that a and b nearly satisfy equation (A) ; in 

 which case the right-hand side of equation (B), will not be 

 equal to zero, but to a small known quantity positive or ne- 

 gative, — a circumstance which makes no essential difference in 

 finding the corrections 5 and t. 



From the calculations which have been made, we may infer 

 New Series. Vol. 3. No. 16. April 1828. 2 I that 



