Intelligence and Miscellaneous Articles. 



159 



other. The advantage of using very small arcs in performing these 

 experiments is therefore sufficiently apparent. 



In the following summary I have brought forward the total of 

 the eleven experiments given in my last letter, and added to them 

 thirty others which have been performed since. Four of these ex- 

 tend through a period of nearly twenty- four hours each. 





A few days ago I received an obliging and most interesting letter 

 from the Rev. J, A. Galbraith, of Trinity College, Dublin, containing 

 a formula which he has discovered for calculating the apsidal motion 

 of the ellipses which a pendulum-ball describes. He says, " The value 

 you gave for the correction for each ^^th of an inch, in the June 

 Number, viz. 0°-7, agrees very well with it, the formula giving 

 0°'626." I had there stated, that the mean length of arc in those 

 experiments was '* about 7 feet," This rough estimation I after- 

 wards examined more carefully, and altered it long ago in my minute- 

 book into 7*4 feet. This gives a still better agreement, viz. 0°'66 

 formula, 0° 70 experiment. It does not agree so well (as Mr. Gal- 

 braith observes) with what I gave in the July Number, viz, 0°-43 per 

 hour for a mean arc of 3 feet, the formula giving only 0°'27. The 

 agreement with what I gave in the postscript to that letter is much 

 closer. 11°"60 per hour with -J-*19 inch ellipticity, and lP-39 per 

 hour with — *17 inch, gives 0°-058per hour for each J^^thof an inch 

 ellipticity ; the formula gives 0°-082 per hour. This important for- 

 mula I believe Mr, Galbraith intends communicating to your Maga- 

 zine, together with the calculations from which it is derived, 

 I am, Gentlemen, 



Yours very respectfully, 



Thomas G. Bunt. 



PENDULUM EXPERIMENTS : FORMULA FOR CALCULATING THE 



APSIDAL MOTION. 



To the Editors of the Philosophical Magazine and Journal. 

 Gentlemen, 

 The following formula may be of some use in observations like 

 those of Mr. Bunt on the motion of a pendulum. 



