Thermal Conductivity with Temperature. 519 



and that 



2 



o a a etmii + m + n 



(2 - 7 ) (m + n) + (1 + y)(*mn + ) 



(41) 



39. There ought now to be no difficulty in calculating the 

 constant m from observed corresponding values of 6 and x. 

 The following method has occurred to me ; but there may be 

 better ones. Let five temperatures, 6 , 1} 2 , 3 , 4 , be ob- 

 served along the rod at distances from the origin x, <£ + £, 

 A' + 2f, .# + 3f, and #4-4|f. Let the quantity which goes in 

 geometrical progression, see equations (40) or [19 ; ], be written 



Hi 



m 



and for shortness call the numerator (f)(0) and the denominator 

 ty(0). Then of course 



0i 03 _ / <f> 



whence 



Similarlv 



Therefore 



®- 



0103 — 02 ^ ^1^3 — ^2 

 0004-02 ^M^-^a' 



which, being interpreted, is 



1 + I 1 4. ,'_L l\ 



6, 6 3 g, + * Ug, fl j/ = (*i + 0,- 20 2 )m + 6 A-6 1 

 1 . I_2 . /J _1\ (6»o + # 4 -2tf t )»> + ^«-^' 



*o + *« rW< W 



• • • • (42) 

 the form of which we may abridge into 



«i + ?•&! mcj + di 



