ATMOSPHERE AND THE ACOUSTIC EFFICIENCY OF FOG-SIGNAL MACHINERY. 243 
When the velocity is intermittent we may write for the purpose of the present 
discussion 
U = U 0 (l +e cospt) .(60) 
where U 0 is the average velocity of the air, and | £ | = eU 0 may be taken to represent 
the velocity amplitude in the sound-wave generated by the intermittent flow. From 
(59) and (60) we have for the surface temperature the expression 
0 S = kTJ* (l +W 2 + 2e COS pt + ie 2 COS 2 pt). 
At the surface of the iron thermometer wire (radius of silk insulation = 0'0092 cm., 
radius of wire = 0'0048 cm.) the periodic terms contribute corresponding fluctuations 
of much diminished amplitude, which, however, vanish on averaging with regard to 
the time over a complete period. Thus the average temperature rise due to kinetic 
heating measured by the thermometer wire is given by 
0 ,■ = KU 0 2 (l+!e 2 ).(61) 
Denoting by the suffixes „ and r temperatures of the valve and resonator 
thermometers respectively, we notice that SO of equation (58) is the difference of 
the temperature rises due to kinetic heating, so that we may write 
SO — 0 iv —0 ir — k v \J 0v 2 (l+^e v 2 ) — /c r U 0r 2 (l+|v). 
When the diaphone is silent and the average flow is the same we have, writing 
e„ = 0 and e r = 0 
SO' = /f t ,U 0i; 2 —/c r U 0r 2 , 
and thus 
SO — SO' — ^U 0t ,V-^ r U 0r V.: . . . (62) 
If we take the value of |£ [ obtained in (64) from the measurements of the acoustic 
output of the diaphone, we have | £ ] = 3'02 x 10 3 cm./sec. corresponding to an average 
velocity U 0 = 4'18 x 10 3 cm./sec., and hence = |-|£ ]/U 0r ) 2 = 0*26. 
The term K r TJ 0r 2 represents the kinetic heating effect of a stream of velocity U 0r in 
the resonator. The experiments of Kelvin and Joule already quoted give the 
rise of temperature due to this cause as 1° C. for 180 ft./sec. (5'48 x 10 3 cm./sec.). 
Thus the value of the second term on the right-hand side of (62) is given by 
0'26 x [(4'18)/(5'48 )] 2 x 1° C. = 015° C. As it is probable that the first term on the 
right-hand side of (62) is of a magnitude not very different from that just calculated, 
we are justified in supposing the term (SO —SO') in equation (58) to be small compared 
to the principal term (0 X — 0\). 
Under the assumptions just made, we may write, finally, in terms of the tempera¬ 
ture difference obtained from the readings of the differential resistance thermometers, 
w — JC V M (Qi — O'i) ergs/sec, 
2 K 
VOL. CCXVIII.-A. 
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