340 White — Specific Heats of Silicates and Platinum. 



Before this equation can be applied, m l must *be determined, 

 which can be done with entirely sufficient accuracy as follows : 

 If f (0) is the total heat required to raise the body from 

 to'0, 



^-^ is the mean heat from to 0, and a * a ( 2 ) 



2 1 



is the observed mean heat, M . If now 2 = 0, this reduces to 



} * ? that is, to m r If, therefore, the observed mean heats 



are plotted and the curve extrapolated to 0, the value of m x 

 is obtained.* 



For reducing the upper limit to a round number, an equation 

 like (1) is not so easily applied, since the quantity correspond- 

 ing to m^ is here unknown, but if the interval of reduction is 

 small, as it always was in the present work, it is possible to 

 write 



M, = M 9 + A M and A M = -^ (®,-0 Q ) 



by means of which the correction is easily made, taking ^ 



from the tangent to the plotted curve. 



The relation of the true to the mean heat may be expressed 

 in two ways : (1) If the true heat is given by the polynomial 

 A + B0 + C0 2 4-... the total heat from to any temperature 

 is the integral of this, or A + 2 B <9 2 + 3 C 3 + ... and the 

 mean heat isA + 2B# + 3C# 2 + ...f If, then, the mean heat 

 is expressed as a polynomial, the method of getting the true 

 heat is obvious. (2) Unfortunately 3 the specific heat curves 

 thus far obtained are not well represented even by polynomials* 

 with four constants, hence the following mothod, which may 

 be applied graphically, was actually used. If the total heat 



is/ (6) and the mean heat '* -, f (0) is the true specific heat. 



But if the mean heat is differentiated aDd then multiplied by 



0, giving/" (0)- ^p and to this is added the value of the 



* The approximations here made are easily seen, but as just stated, were 

 not practically important in the present work. A more rigorous correction 

 can be obtained by expressing the mean heat as a polynomial, that is, as 

 equal to 



A + B (0 2 - 0x) + C (0 2 2 + 6, 6 2 + 6S) + ... (3) 



and thus determining A, B, C, 



A + B 6, + 6 2 2 + . . . (4) 



is then the corrected mean heat. Both these expressions of course involve 

 the error incidental to representing almost any actual physical function 

 mathematically, but their difference will give very accurately the small 

 correction required to reduce the lower limit to 0. Or (4) can be used to 

 give mi and (1) then applied. 



f Behn has already given a similar treatment, Drud. Ann., i, 263, 1900. 



