276 Wadsworth — Determination of Specific 



2d. Heat taken from air 



= As/* \$ x -p)dx (15) 



and since the heat contained in the water is the same at max- 

 imum point 6 (by assumption) as though all the heat from the 

 body had been communicated to it and no radiation had taken 

 place, we have at the time, a? , of maximum 



(T-0)ics=Asf X \0 x -p)dx * (16) 



or in general at any time, x, from the instant of immersion 



(T-TJw8=(0,-t)(M + W)c + ASr X (0,-p)dx (17) 



To find an approximate value of T X —0 X for substitution in 

 (12) we may neglect the last term as small compared with the 

 others, and write 



(T-T x )ws = (6,-t) (M + W)c 

 whence 



tf.-*) = T f(irWo)-( T (MTf) C + ■ h bT -~ a < 18 > 



Then substituting in (12), we get 



dT 

 dx 

 Integrating we get 



-ios-^ = 2KS 1 (bT x -a) +2KBS 1 (bT x -a) 



25KS7 L g 2KS 1 4-2KBS 1 (6T,-a)J T 



ws . \bT-a l + B(OT -a) MgA 



X ° = 2*KS X l0g 1 W^a ■ l + B(bT-a) (19) 



or 



— Xo flT-a l+B(ftT -a) 

 « - = ST^- 1 +B(CT-a) (20) 



Then solving for T we find 



a 



6T-a 



T °~ 5 + ^Je E [l+B(5T-«)]-B(T-0} 



= + 6{ e K + B(e*-l) (T_*)| ^ 21) 



* It may be observed that the value of the integral in the second member of 

 this equation is not necessarily zero. In other words the conditions (value of /?, 

 etc.), which give the proper value of 6 for use in equation (2) are not such as to 

 make the total loss of heat by radiation zero, as assumed by Rumford. 



