62 Mr. L. F. Menabrea on Cavendish's Experiment. 



the Institution of Civil Engineers (ii. p. 60). I am very glad 

 that this important topic has engaged the attention of so able 

 an inquirer as Mr. Russell, but I believe the foregoing extracts 

 will show that the question has not remained unnoticed until 

 now. I have the honour to remain, Sir, 



your faithful humble servant, 

 4, Clarence Street, Penzance, W. J. Henwood. 



May 6, 1841. 



XII. On Cavendish's Experiment. By L. F. Menabrea*. 



r ■''HE paper before us is a fresh mathematical investigation 

 *■ of the formulas necessary in the application of Cavendish's 

 experiment for determining the mean density of the earth ; 

 and the author seems to have been in some degree incited to 

 the task by hearing of the intended repetition of the experi- 

 ment in England. It is unfortunate, however, that as Mr. 

 Baily's apparatus is not altogether the same in its details as 

 that of Cavendish, the results of this paper are not wholly ap- 

 plicable to the new observations. 



Mr. Menabrea sets out with the well-known equation 



^=fr°-dm=fr$dm, 



where dm is an element of the system which is moved by the 

 attraction of the large balls, and r is the distance of that ele- 

 ment from the axis of the torsion wire. The integral I r §dm 



arises from attraction-forces and torsion-forces. The former 

 are, — 1st, the attraction of the large spheres upon the small 

 ones ; 2nd, the attraction of the large spheres upon the rod 

 which connects the small ones ; 3rd, that of the beam (which 

 supports the large balls) upon the small balls ; (in Mr. Baily's 

 apparatus the large balls are not suspended from a beam, but 

 are supported on a plank;) 4th, the attraction of the box 

 (which contains the small balls) upon these balls. These are 

 all investigated in the paper before us. 



The next step is to calculate the Moment of inertia of the 

 small balls, the connecting rod, and the verniers (in Mr. 

 Baily's apparatus there are no verniers attached to the torsion 

 pendulum). The equation is then integrated, and expressions 

 connecting the earth's density with the data of observation are 

 found. 



Mr. Menabrea next proceeds to examine the effect of the 

 resistance of the air upon the time of vibration. Assuming a 



* This article is a notice of a paper in the Turin Memoirs (Second 

 Series, vol. ii. p. 305). 



