Prof. Challis on Rectilinear Fluid Motion. 97 
Some time after, viz. in August 1839, Daguerre published the 
account of his perfected process, which reaching us during the 
meeting of the British Association, gave rise to an animated 
discussion in Section A, and I took the opportunity to lay be- 
fore the Section the facts which I had myself ascertained in 
metallic photography, and from the report which was given in 
the Athenzeum of that communication I have taken the above 
extracts. On reading them over, I perceive a discrepancy in 
the result of my experiment on mercury exposed to iodine va- 
pour from that given by Dr. Waller (p. 434), for which I can- 
not at present satisfactorily account. 
London, 21st December, 1842. H. F. Tarzor. 
XVI. A further investigation of the Analytical Conditions of 
Rectilinear Fluid Motion. By the Rev. J. CHALLIS, M.A., 
Plumian Professor of Astronomy in the University of Cam- 
bridge*. 
(THE questions in the analytical theory of fluid motion, 
which I have recently discussed in various communica- 
tions to this Journal, are of a fundamental character, and so 
long as any doubt remains as to the answers they should re- 
ceive, the particular applications of the general theory will be 
involved in uncertainty. Trusting that this will be considered 
a sufficient apology for so often recurring to the subject, I 
proceed to inquire further respecting the analytical conditions 
of the rectilinear motion of fluids, being aware that my com- 
munication on this question to the December Number (S. 3. 
vol. xxi. p. 423.) stands in need of additional explanation.° 
It has been intimated to me that in the proof of rectilinear 
motion which I have deduced from the equation «da + vdy 
+wdz=V dr, I assume, without assigning any reason, that 
V is a function of a line 7 drawn always in the direction of the 
motion. It is true that when the equation is taken by itself, 
it does not necessarily follow that V is such a function be- 
cause the left-hand side is integrable. The reason for the 
assumption is founded on the general equations of fluid motion, 
as I now proceed to show. I am ready to admit that the 
omission of the argument which follows is a defect in the 
former proof. The nature of the argument will be under- 
stood by referring first to the general equations of fluid eguz- 
librium. If p be the pressure and ¢ the density at any point 
zy z, and X, Y, Z be the impressed forces in the directions of 
* Communicated by the Author. 
Phil. Mag. S. 3, Vol. 22. No. 143. Feb, 1843, H 
