Prof. Challis on a new Equation in Hydrodynamics. 295 



make T = 0, and suppose the polarization circular, we readily 

 arrive, after some necessary substitutions, at the Astronomer 

 Royal's results. I hope that I am not too rash in adding, 

 that it would seem that those results exclude the idea of there 

 being anything Wke friction between the particles of the lumi- 

 niferous aether and those of the glass. At least they would 

 do so if the equations held for any considerable portion of the 

 path of the ray — if they did not hold they might, it seems to 

 me, be made to furnish a measure of the friction, and so aid 

 us in forming a mechanical theory. 



2 Pump Court, Temple, 

 February 16, 1850. 



XXXVI. On a new Equation in Hydrodynamics^ in Reply to 

 Professor P. Tardy. By the Rev. J. Challis, M.A., F.R.S., 

 F.R.A.S., Plumian Professor of Astronomy in the University 

 of Cambridge *. 



THE observations communicated by Professor P. Tardy 

 of Messina to the March Number of the Philosophical 

 Magazine, on a new equation which I have asserted to be ne- 

 cessary to complete the analytical principles of hydrodynamics, 

 proceed evidently from a mathematician who is well able to 

 iliscuss this difhcult question, and have received from me the 

 most careful consideration. I shall endeavour to reply to 

 them as nearly as possible in the order in which they occur in 

 Professor Tardy's communication. 



In the first place, I fully admit that Professor Tardy has 

 proved that the equation 



may be obtained without making use of my new equation, viz, 



d^ (dV _^dV d^^\ 



I arrived at (1.) after first eliminating A by means of (2.) from 

 the equations 



d-^f d^ d^ 



"='^55' "=''1^' «'=^5;> 



but I did not remark, what indeed the process sufficiently in- 

 dicated, that the result was independent of the value of X em- 

 ployed, and I concluded erroneously that (2.) was necessary 



* Coniniunicated by the Author. 



