344 BABCOCK. 



tain the value of the constant quantity k {Ra + X), we make use of the 

 fact that the initial and final lines are sensibly straight, which amounts 

 to saying that the change in R of Equation 9 for short intervals of 



time, is not enough to change the slope, —-^. Giving R its mean 



at 



DID 



value for the initial line which is, , where i?o is the first point 



on that line and i?i the last. Equation 9 becomes 



^ = ^F^' = (/'-^^ + X) - ^ (/?, + /?o) (10) 



at ti — to 2 



DID 



and giving R its mean value for the final line, ; -, where R2 



is the value of the resistance obtained by projecting back the final 

 line to the time ordinate through the point at which the heater was cut 

 off, and i?3 is the last point on the final line, Equation 9 becomes 



dR^ ^ R^j^ ^ ^^.^^ + X) - ^ (/?3 + R.) (11) 



at ts — ^2 •" 



(10) gives us the value of {kRa + X) and eliminating {kRa + X) 

 between (10) and (11) gives us the value of k, as follows 



{kRa + X) = ^^^^ + I {Ri + Ro) (12) 



'1 — to I 



R\ — -Ro Rz — Rfi 



k _ ti-to ~ fg - t2 (13) 



2 ~ (i?3 + R2) - {Ri + R.) 



Integrating equation (9) from ti to ^2 to obtain the cooling correction 

 to be applied to the observed temperature change, and substituting 

 (12) in the expression, 



j% dR. ^j^ ^ R^-^ ^^ _^^^^k ^^^ ^ ^^^ ^^^ _ ^^^ _ ^. ^2^^^^ ( j4) 

 Jti at ti — to 2 Jti 



The mean value of R between Ri and Ro may be called Rm so 



^^-Rdt = R,n{t2-tl) (15) 



tl 



Jti 



and substituting this in (14) 



