Prof. Challis's second Reply to Mr. Airy. 63 



formula for that resistance, composed of two terms varying 

 as the velocity, and as the square of the velocity, he finds 

 that the isochronism of the torsion pendulum is not sensibly 

 affected for small vibrations. But he does not (as might be 

 supposed) attempt to assign the small constants which enter 

 the law of resistance, nor to make the resistance itself affect 

 the final result. He examines the effect of the resistance of 

 the air upon the results of Cavendish's method of finding the 

 point of repose of the torsion pendulum, and shows that it is 

 insensible when this point of repose remains in the same place. 



The author then examines the manner in which the mean 

 density, obtained from the experiment, combined with the hy- 

 pothesis that the earth is composed of spheroidal layers of 

 variable density, is to be applied to determine the mass of the 

 earth. 



As to the question of mathematics, this paper may be use- 

 ful in pointing out to future investigators a complete mode of 

 taking into account everything that can affect the result of 

 Cavendish's experiment. But the analysis goes somewhat be- 

 yond the practical necessities of the question ; a circumstance 

 which is almost inseparable from any attempt to investigate 

 the conditions of a problem which contains so many unknown 

 disturbing forces as the one of which Mr. Menabrea has 

 treated. 



XIII. Reply to Mr. Airy's additional Remarks on Professor 

 Challis's Investigation of the Resistance of the Air to an 

 Oscillating Sphere. By the Rev. James Challis, M.A., 

 Plumian Professor of Astronomy in the University of Cam- 

 bridge. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 



T^HE communication you did me the favour of inserting in 

 your Number for June, was written under the idea that 

 some further explanation was required from me of my reasons 

 for differing in the solution of a hydro-dynamical pi'oblem from 

 so high an authority as Poisson, and before I was aware that 

 Mr. Airy intended offering any additional remarks on the 

 subject. That communication is consequently not a direct 

 answer to the arguments contained in Mr. Airy's letter in the 

 May Number, and I therefore ask permission to add some- 

 thing in reply. I shall endeavour to be as brief as possible, 

 the discussion having, perhaps, already occupied too much of 

 your valuable space. 



