296 PROFESSOR WILLIAM THOMSON ON THE 
Hence the total quantity of heat emitted will be the excess of this above the 
amount previously found to be absorbed when the mechanical effect is all ex- 
ternal; and therefore we have 
1 uw 1 f Yao 
H=-— oh @dv+pu— ru} of — dv : : . 
ral t Tee BS, at ”) 
Whatever changes of temperature there may actually be of the air in or near the 
orifice, this expression will give rigorously the total quantity of heat emitted by 
that portion of tube which contains the orifice and the whole of the second spiral 
during the passage of a volume w through the first spiral, or w’ through any por- 
tion of the second spiral where the temperature is sensibly 7. 
15. To apply this result to the case of a gas fulfilling the gaseous laws, we 
may put 
pu=p w. 
Hence (e) becomes 
i i LT RN 
We @dv=pu log — =p' wu log — Z : 5 (5), 
u oe me 
and, by (3), we have 
qW_ Epu wv ==EW 
are eee an EP Bae 
Hence the expression (7) for the heat emitted becomes 
1 E 
B= {5-sayE} ab Madacowlae puree 
16. Lastly, if Mayerr’s hypothesis be fulfilled for the gas used in the experi- 
ment, the coefficient of W vanishes, by (I.), and therefore 
=O cred tae! Pe bere y ie 
17. From equation (II1.) it follows that, if MayvEr’s hypothesis be true, there 
is neither emission nor absorption of heat, on the whole, required to reduce the 
temperature of the air after passing through the orifice, to its primitive value, ¢. 
Hence, although no doubt those portions of the air in the intermediate neighbour- 
hood of the orifice, which are communicating, by their expansion, vis viva to those 
contiguous to them, will be becoming colder, and those which are the means of 
occasioning the portions contiguous to them to lose vs viva, through fluid fric- 
tion, will be becoming warmer at each instant ; yet very near the orifice on each 
side, where the motion of the air is uniform, the temperature would be con- 
stantly equal to 7. Hence the simplest conceivable test of the truth of Mayer’s 
hypothesis would be to try whether the temperature of the air is exactly the same 
on the two sides of the orifice. This might be done by very delicate thermo- 
meters adjusted in the tube at sufficient distances on each side of the orifice to be 
quite out of the 7wsh which there is of air in the immediate neighbourhood of the 
orifice ; but it might be done in a still more refined manner by means of a deli- 


