108 Prof. J. H. Cotterill on the Distribution of Energy 



plane. The deflections became now considerably greater, and, 

 besides, corresponded perfectly with those obtained with the 

 magnetometer. 



The two mutually independent methods of investigation have 

 thus conducted us to the same result, that foretold by the theory 

 — namely, that the resistance to galvanic conduction is dimi- 

 nished when the conductor and the current move in the same 

 direction, but is increased when the directions are opposite. 



I will only mention, in conclusion, that I have tried to em- 

 ploy for this investigation a saturated solution of sulphate of 

 copper, with copper poles, and a solution of sulphate of zinc, 

 with amalgamated zinc poles ; but these liquids were quite in- 

 applicable, because 1 could never succeed in rendering the 

 polar plates galvanically so equal that, when the plates dipped 

 into the liquid, a slight current would not arise, which imme- 

 diately varied as soon as the liquid was set in motion. Whence 

 this originated I cannot say. The sulphate-of-zinc solution, 

 however, contained some iron. 



XIV. On the Distribution of Energy in a mass of Liquid in a 

 state of Steady Motion. By James H. Cotterill, M.A., 

 Professor of Applied Mechanics in the Royal Naval College, 

 Greenwich* . 



WHEN a liquid is in a state of steady motion, we know 

 that the total energy of any given particle and of all 

 that follow it in one and the same line of motion is a constant 

 quantity ; or, as we may otherwise express it, the total energy 

 of each elementary stream is uniformly distributed. I am not, 

 however, aware that it has been hitherto noticed that the dis- 

 tribution of energy among the several elementary streams, of 

 which the whole current is supposed to be made up, depends f 

 solely on the molecular rotation at each point of the liquid,) 

 and is uniform when the motion is irrotational. 



For simplicity suppose the motion to be in two dimensions,! 

 and to take place either in a vertical or horizontal plane. Inl 

 the first case the liquid will be under the action of gravityl 

 only; and in the second, which will be included in the first, the 

 effect of gravity need not be considered. In the figure, lei 

 AB, CD be consecutive lines of motion, and P Q a normal 

 to these lines, and let P and Q be particles moving in these 

 lines.] Then, if h be the total head at Q (that is, the total energy 

 of Q per unit of weight), 



*=.+ £ + £ 



w 2g 

 * Communicated by the Author. 



