412 Formula connected with the Motion of a Free Pendulum. 



It will be obseiTcd, that, rejecting the two results obtained 

 from the oscillation in the direction N.W. and S.E., the mean of 

 the remaining results would be 1'812, — a very close approxima- 

 tion to that calculated from the sine of the angle of latitude. 

 The above, however, are all the experiments that have been mado 

 with this apparatus ; and as the result comes so near to the 

 mathematical solution, and the means of perfecting our experi- 

 ments further are not obtainable without great difficulty in this 

 colony, we consider it would serve no end to multiply our obser- 

 vations further. 



We are, Gentlemen, 



Your obedient Servants, 



Jones Lamprey, ^.J5.,ili.J3., 

 Assistant Surg eon ^ \^th Regt, 

 H. ScHAW, Lieut, R.E. 



LXII. Formula connected with the Motion of a Free Pendulum* 

 By the Rev. A. Thacker. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 



IN your Number for August last, you did me the favour of 

 inserting a short letter on the apsidal motion of a pendulum. 

 I observe, in the formulae there given, two errors of the presSj 

 which I trust you will allow me to correct. The expression for 

 the apsidal angle should be 



lJ\ 4. § ^ M ^ ab(a^'hb^) \ 

 2 l_ 8 * /2 "^ 256 ' Z'* J' 



and for the progression of the apse in one revolution, 



-.o^ro «^/i 9 a^ + b^\ 

 185°x-^(H-g5.-^). 



If the dimensions of the orbit be small compared with the 

 length of the pendulum, the last tenu may be neglected ; and 

 we then have the formula given by the Astronomer Royal, by 

 Messrs. Galbraith and Haughton, and more recently by Mr. 

 Coombe. 



I may add, that by the method I have employed, the approxi- 

 mation may be continued without difficulty ; for instance, the 

 next step gives 



i'^KO^abr.,9 a^ + b^ , 151(^ + &4) + 58fl^^>n 

 for the progression of the apse. The complete formula, as might 



