242 DR. LOUIS VESSOT KING ON THE PROPAGATION OF SOUND IN THE FREE 
for steady flow with f in the case of intermittent flow. If it is ascertained that the 
eddy-motion has entirely disappeared over the regions where the temperatures are 
measured, f and f are steadily converted into heat given up to the gas and are then 
included in the terms of (57) depending on 6 and Of ; the same remark applies to the 
parts of f and f representing thermal energy given up to the diaphone piston. 
The practical realization of this condition would be to place the resonator-thermometer 
sufficiently far from the piston that the escaping air is free from eddies. The 
objection to this procedure lies in the fact that losses of heat into the material of the 
trumpet are liable to be involved, and also that owing to possible propagation losses 
the acoustic output is no longer measured at the source of the sound-waves, but 
becomes a function of the dimensions, shape, &c., of the resonator. It is evident that 
unless f can be identified with f, the value of w calculated from (57) will be an over¬ 
estimate (the case f < t /’is hardly probable). 
The temperature differences calculated from the readings of the resistance ther¬ 
mometers, denoted by and 0\, differ from the true temperature differences 6 and O' 
by amounts SO and SO' respectively, arising from the effect of kinetic heating already 
mentioned. Although this effect is diminished owing to the fact that differential 
readings of temperature are taken, the resonator thermometer registered an excess 
of temperature over the valve thermometer owing to the fact that the former was 
more exposed to air velocity than the latter. Writing 0 X = 0 — S0 and 0\ = O'—SO', 
equation (57) becomes 
w = JC v k(0 l -0' 1 ) + JC v M.[(S0-Se')-{A0-A0')]-(f-f). . . . (58) 
It is not unreasonable to assume that the Joule-Thomson effect is very approximately 
the same for steady as for intermittent flow, so that the term (AO — AO') in (58) may 
be neglected. 
More serious is the kinetic effect due to the air impinging on the wires of the 
resistance thermometers. The term (J$ —tiff) can only be neglected if this effect is 
approximately the same for steady as for intermittent flow. The effect of the silk 
insulation on the wires is in favour of reducing this effect by confining periodic 
temperature changes to the surface in a manner analogous to the well-known skin 
effect in the electrical conduction of alternating currents. A rough estimate ot this 
source of error may be made as follows :— 
According to the experiments of Joule and Thomson* it was found that the rise 
of temperature due to kinetic heating in a steady air current of velocity U was 
proportional to the square of the velocity. In the case of the insulated thermometer 
wires, we may write for the rise of temperature at the surface of the insulation the 
expression 
0. = *tr>.(59) 
* Joule and Thomson, 1 Trans. Roy. Soc.,’ June, 1860 ; Kelvin, ‘ Collected Works,’ vol. I., p. 405. 
