Wave-lengths and Velocities of sound in Gases, 429 
_ These related numbers I have projected into the accompany- 
‘Ing curve, whose abscissas are the temperatures, and whose 
ordinates are the wave-lengths. This curve, which is the graph- 
3383/1 us = is evidently a parabola, 
ical expression of y= 
since it has the form y?=aa,; and y will equal 0 when « has 
receded to the point on the axis of abscissas equal to —272-48° 
- Which is “the absolute zero” of temperature 
It is evident that this same curve will give the numerical 
relations between temperatures and the wave-lengths of any 
note, or the velocities of sound in any gas, by merely giving dif- 
ent numerical values to the divisions on the axis of ordi- 
nates 
It only remains to give the simplest formula for determining 
the temperature of the furnace in terms of the observed dis- 
lacements of the resonator serrations, and of the known num- 
r of wave-lengths in the furnace-tube at the temperature 4 
Let t= temp. C. of the air in and around the organ-pipe. 
v= eines “the furnace-tube. 
v= velocity of sound at temp. ¢ 
v’ = “b rz “ v. 
¢= number of wave-lengths in furnace-tube at temp. @ 
d= observed displacement of resonator serrations by an 
elevation of temperature 
Then 7—d will equal the number of wave-lengths in the fur- 
nace-tube (allowance made for elongation of tube by heat) at 
the temp. ¢’. As the velocity of sound in the furnace-tube will 
be inversely as the number of wave-lengths it contains, it fol- 
lows that | 
ek 
v':vii:l:l—d; hence v is but 
(1) v=333/1+ 008674, and 
(2) v'=838/1+ 003677, hence 
(8): wt. 3334/14 00367" 
Reducing equation (8) we obtain 
ed vl 9 ings 
4) t=(syqg aca) ~ 27248: 
which gives ¢ in terms of v, / and d. Combining equations (1) 
and (8) we obtain 
(6) ¢ 
which gives ¢’ in terms of J, d and ¢. But as v has to be calcu- 
_ 972-48 (21—d) d+u 
ie a ; 
— 
