Dr. Mallet on the production of Sulphuretted Hydrogen. 235 



tA ii 1 TIP U 1 d P ; d P 7 <* P 7 Li 



of the partial differentials - — a x, -7 — d y, — — d z, it is ta- 



ct tV ft y a % 



citly assumed that P is a function of x, y, z, which varies con- 

 tinuously, and not arbitrarily, with the variation of the coor- 

 dinates, and so far as the variation of the function is such, the 

 substitution is legitimate. Now in any instance of fluid mo- 

 tion it is only in the direction of the displacement of the fluid 

 that the variation of the velocity and density at a given time 

 is in any respect necessarily continuous and not altogether de- 

 pendent on the arbitrary displacement. In this direction it 

 depends in part on the propagation of the motion, and on the 

 mutual inclination to each other of the normals to the surface 

 of displacement, in a manner which it is the peculiar province 

 of the integration of a partial differential equation to make 

 known, and so as to leave the particular form of the function 

 expressing the arbitrary displacement indeterminate. But the 

 variation of velocity and density at a given instant from one 

 point to another along a surface of displacement altogether 

 depends on the arbitrary disturbance, and cannot therefore be 

 given by a similar process of integration. With the above- 

 mentioned limitation respecting the direction of variation of 



t j. yi.dP.dP. dP . t i,l 



the coordinates, both ^ — dx 4- 3 — dy -\- 3 — a z, and udx 

 dx dy * dy 



+ vdy + w dz are exact differentials in every instance of 



fluid motion, excepting where the motion is not essentially 



different from that of a solid. 



After this communication I shall not again enter upon the 

 consideration of the problem which has given rise (not, I hope, 

 without some advantage to the cause of science) to so pro- 

 longed a discussion. But the general principle on which my 

 solution rests is too important to be hastily dismissed, and I 

 shall probably take other opportunities of exemplifying it. 



Cambridge Observatory, August 19, 1841. 



XXXIII. Note on the Production of Sulphuretted Hydrogen 

 bythe Action of decomposing Animal Matter upon Sulphates. 

 By Robert Mallet, Ph. Z>., M.U.LA. 



To Richard Phillips, Esq., fyc. $c.' 

 Sir, 

 HPHE valuable communication in the Number of the Phi- 

 "^ losophical Magazine for this month (July) by Mr. Daniell, 

 on the spontaneous evolution of sulphuretted hydrogen in the 

 waters of the African Coast, &c, has ;been read by me with 

 peculiar interest, from its connexion with a subject to which 



