Dr. A. M. Mayer on an Acoustic Pyrometer. 21 



parabola, since it has the form y <2 =ax; and y will equal when 

 x has receded to the point on the axis of abscissae equal to 

 — 272°*48 C, which is " the absolute zero " of temperature. 



It is evident that this 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 different nume- 

 rical values to the divisions on the axis of ordinates. 



It only remains to give the simplest formula for determining 

 the temperature of the furnace in terms of the observed dis- 

 placement of the resonator- serrations, and of the known number 

 of wave-lengths in the furnace-tube at the temperature t. 



Let t = temp. C. of the air in and around the organ-pipe, 

 /' = „ „ the furnace- tube, 



v = velocity of sound at temperature t, 



u — a a )> * i 



I = number of wave-lengths in furnace- tube at temp, t, 

 d = observed displacement of resonator-serrations by an 

 elevation of temperature t ! — t; 



then l—d will equal the number of wave-lengths in the fur- 

 nace-tube (allowance made for elongation of tube by heat) at 

 temperature t'. As the velocity of sound iu the furnace-tube 

 will be inversely as the number of waves it contains, it follows 

 that 



v':v : : I: l—d; 



hence 



but 

 and 

 hence 



, vl 



v== T=d> 



= 333 i/l+ -00367/, (1) 



vl =333 Vl + -00367*'; .... (2) 



vl 



jZZ- d = 333 \/l + -00367? (3) 



Reducing equation (3), we obtain 



Hwith)J- m ' 48 ' ■ ■ ■ ■ (4) 



which gives t' in terms of v } I, and d. Combining equations (1) 

 and (3), we obtain 



,_ 272'4>S{2l-d)d+tP 



l ~ JJZ^f > w 



which gives t 1 in terms of /, d, and t. But as v has to be calcu- 



