288 DR. LOUIS VESSOT KING ON THE PROPAGATION OF SOUND IN THE FREE 
(ii.) On the Measurement of Temperatures. 
The construction of the resistance thermometers employed in measuring the fall of air temperatures 
passing through the-diaphone is briefly described in §12. Although an attempt was made to make the 
high-pressure thermometer (of resistance R 0 at 0° C.) of exactly the same resistance as the low-pressure 
instrument (of resistance So at 0° C.) it was found on making a careful measurement that 
Ro = 85’044 ohms, S 0 = 82-095 ohms. 
The temperature coefficient of the iron wire employed as determined by Mr. A. A. Scott* was 
a = O'004964. The thermometers R 0 and S 0 were connected by leads of heavy copper wire, of resistances 
0T5 and 0'25 ohms respectively, so as to form two arms of a Wheatstone bridge. The ratio coils o£ the 
bridge were of resistances 100'84 and 100 81 ohms, sufficiently close together in value as to be considered 
equal. In series with S 0 was inserted a magnanin resistance box subdivided into tenths of an ohm. A 
portable Weston galvanometer of 217 ohms resistance and sensitivity of 10~ a amperes was employed to 
determine the balance of the Wheatstone bridge. In talcing readings of temperature differences with the 
diaphone sounding and silent, a rough balance was obtained by adjusting the resistance box to the nearest 
tenth ohm and interpolating from the galvanometer deflection. If SO be the temperature difference between 
the thermometer wires when the diaphone is sounding, and S6' that when the diaphone is silent, 
corresponding to resistances s and s' required to balance the bridge in each case, we easily prove that 
SO - SO' = - (*0- S o> (0 1 - e\) + .(viii.) 
bo CCSo 
Oj and 0\ being the temperatures of the thermometer R 0 when sounding and silent respectively. The 
first term represents the small correction arising from the inequality of resistance of the two thermometers. 
As the series of observations with the diaphone sounding and silent were taken immediately following one 
another, 6 1 and 6\ are assumed to be so nearly equal that this correction term may be neglected. We thus 
calculate the difference of the temperature differences of the two thermometer's under conditions 
“ sounding ” and “ silent ” from the formula 
O 
SO — SO' 
s- s' 
82-095 x0-004964 
2-46 (s - s'). 
(ix.) 
From formula (44) we may calculate the acoustic output of the diaphone from the formula 
w = JC„M (0i-0) 
_ (pi ~p'i) V (0i - ©) / x ) 
t y- 1 0i 
We have seen from the'discussion of § 12 that to a tolerable order of accuracy we may identify the 
actual temperature drop (0i - 0) in the diaphone when sounding with the observed difference of temperature 
differences of the thermometer wires (SO-SO’), (following the notation of (viii.) above). Inserting 
numerical values in (x.) we may thus write for purposes of computation, taking 0! = 288° A., 
w = 
17-8 x (p l -p\) 
( 80 - 80 ') 
288° 
H.P 
(xi) 
In the diaphone actually tested the exhaust from the “ driving head” passed into the resonator so that the 
estimate (xi.) includes the work required to operate the diaphone piston. This includes not only the work 
required to overcome friction but also a small portion of energy converted into sound. The former is 
* Scott, A. A., “ A Study of Iron Wire for Elec! rieal Resistance Thermometers,” 
Third Series, 1913. 
‘ Trans, Roy. Soc. of Canada,’ vol. VII., 
