432 Prof. Thomson on the Dynamical Theory of Heat. 

 Hence {e) becomes 



/^**' w' 7) 



W= / tsdv=pu\o^—=p^i^\ogi- . . (5), 

 «y u up 



and, by (3), we have 



dW _ ^pu u' _ EW 

 dt ~1+Bt ^^u ~l-{-Et' 

 Hence the expression (/) for the heat emitted becomes 



«={T-i:(iTw}'' • ■ ■ • '«>• 



76. Lastly, if Mayei*'s hypothesis be fulfilled for the gas used 

 in the experiment, the coefficient of W vanishes by (I.), and 

 therefore 



H=:0 . (III). 



77. From equation (III) it follows, that if Mayer's hypothesis 

 be tnie, there is neither emission nor absorption of heat, on the 

 whole, requii'ed to reduce the temperature of the air after passing 

 through the orifice to its primitive value, t. Hence, although 

 no doubt those portions of the air in the intermediate neighbour- 

 hood of the orifice which are comuumicating, by their expansion, 

 vis viva to those contiguous to them will be becoming colder, 

 and those which are the means of occasioning the portions con- 

 tiguous to them to lose vis viva, through fluid friction, wiU be 

 becoming warmer at each instant ; yet very near the orifice on 

 each side, where the motion of the air is imiform, the tempera- 

 ture would be constantly equal to t. Hence the simplest con- 

 ceivable test of the truth of Mayer's hypothesis would be, to tiy 

 whether the temperature of the air is exactly the same on the 

 two sides of the orifice. Tliis might be done by very delicate 

 thermometers adjusted in the tube at sufficient distances on each 

 side of the orifice to be quite out of the rusk which there is of 

 air in the immediate neighboiirhood of the orifice ; but it might 

 be done in a still more refined manner by means of a delicate 

 galvanometer, and a small thermo-electric batteiy arranged so 

 that one set of the solderings might be within the tube on the 

 side of the entering cuiTcnt of air, and the other set within the 

 tube on the side of the cuiTcnt from the orifice. The tube on 

 each side of the orifice Mould need to be bent so as to bring two 

 parts of it, at small distances from the orifice on each side, near 

 enough one another to admit of the battery being so placed. 

 The only difficulty I can perceive in the way of makmg the ne- 

 cessary arrangements is what might be experienced in fitting 

 the two ends of the batteiy air-tight into the two parts of the 

 tube. It first occurred to me that the little battery itself might 

 be placed entirely within the tube, and the difference of pressure 



