RATIO OF SPECIFIC HEATS. 13 



bolometer from the following three sources : (1) as the result of electric current in 

 the strip (this, as we have already seen, being negligible) ; (2) as due to conduction 

 through the terminals; (;5) as due to direct ?'«^w//2'o?i impinging u[)i>n the strip from 

 the walls of the reeeivei'. 



To treat the srcdiid case first : tlie heat received by the sti'ip from the thick 

 terminals may be a[)[)i'o.\imately computed, — at least with reference to the eiror 

 resulting. We will assume for thi« [tiirpose that the terminals retain their initial tem- 

 perature during the whole interval of expansion. Let the bolometer strip be a thin 

 straight conductor, one end of which is kept permanently at the temperature 3q of 

 the terminals, while the surrounding air is at the temperature i*,. Ijct ,r be the dis- 

 tance of any [)(>iut of the stri[) frum the terminal end at temperatui'e S^Q,and let S be 

 the tem[)erature at this point at the time t. Hence by Foui'ier's equation of the 

 temperature distribution in an infinitely long rod subject to ladiation 



a 5 „ 32 s / \ , s 



l7 = ''-aV^-/^(^-^>) ^'^ 



wlierein 



o Z' , r„ h u 



a- = — , and /- = 



f /( " (• /' (/ 



and i denotes the coefficient of internal heat conduction. 



/i, the coefficient of e.'cternal heat conduction. 



{■, the specific heat of the strip. 



/', its density. 



t/, the area of a right section. 



//■, the circumference of a right section. 



But the thickness, d, of the strip is negligibly small as compared with its 

 breadth : thei'efore 



U _ 2 



q d 



At the close of the expansion the thermal distribution is stationary along the wire 



oft 



as observation has shown. Hence — -- = 0, and ecpiation (3) becomes 



a='f4=/M-^-^,) (4) 



If for X — 0, the temi^erature of the strip, we put s = S^, ;uid for x = oo, we 

 put S = 5,, the integral of equation (4) is 



5-s, = (i»„ -s,).-~ •'"■-^/'' (s) 



where -^ - =-, /XT- 



a \! k d 



The following values may be assumed for the mid<lle or etched part of the 

 platiruim strip : 



