426 Dr. Waller's Experiments on the 



tion, which I am desirous of adverting to. In my former 

 communication I inferred from the writings of Poisson that 

 he did not accede to a proposition which occurs in the Me- 

 canique Analytique, viz. that udx+ vdy + wdz is an exact 

 differential whenever the motion is small. But I am not 

 aware that any general reason has been given for concluding 

 that this proposition is untrue. By putting g for the density 

 of the fluid, and P for h . Nap. log. g, and neglecting powers 

 of u 9 v, and w above the first, we have the known equations, 



dP du dj? dv_ dV^ dw _ 



~dlf + dt ~ ' dy + dt ' dz + dt ~ 0; 

 the impressed forces for shortness' sake being omitted. Hence 

 approximately, 



du dv du duo dv dta 

 dy dx 9 d z " dx f dz dy ' 



and it might be argued from these equations that udx+vdy 

 + 1KJ d z is an exact differential for small motions, whether they 

 are rectilinear or not. But the answer is, that the condition 

 of integrability requires that those equations should be identi- 

 cally true, which they cannot be said to be, because powers 

 of u, v,id above the first have been omitted. 



The same answer applies in another instance. If fluid issues 

 at a constant rate from an orifice in a vessel of indefinitely 

 large dimensions, it may be shown that the conditions of in- 

 tegrability of udx + v dy + isodz are satisfied if the motion 

 at parts infinitely distant from the orifice be neglected. Those 

 equations are, therefore, numerically satisfied ; but as a state 

 of motion differs from a state of rest however large the vessel 

 may be, it follows that they are not identically satisfied, and 

 it cannot therefore be concluded that u d x + v dy + 10 d is is 

 in this instance an exact differential. 



Cambridge Observatory, Oct. 22, 1842. 



LXXVI. Experiments on the coloured Films formed by Iodine, 

 Bromine, and Chlorine upon various Metals. By Augustus 

 Waller, M.D.* 



IN a paper presented by me to the Academy of Sciences of 

 Paris, an extract from which may be seen in the Comptes 

 Rendus for October 5, 1840, I first demonstrated the error 

 committed in ascribing to the iodide of silver alone the power 

 of fixing the vapours of mercury, after it had been exposed 



* Communicated by the Author. 



