determining the Thermal Conductibility of Bodies, 133 



To show the application of this formula (4) , let T = 24', and 

 assume that the bar is heated during half this time, and cooled 

 during the other half, and this process continued so long that 

 the changes become regular. If now for each minute during one 

 or more of these periods the temperature of the bar at a given 

 point is observed, for which it can be assumed that x = 0, these 

 observations, calculated according to the method of least squares, 

 must be expressed by the following formula : — 



u n - m x + Ai sin (15°n + /3) + B^sin (30° n + /3') 



+ C 1 sin(45°;i + /3") + (5) 



For an analogous point of the bar, corresponding to #=1, an 

 entirely analogous formula is obtained : — 



u n =m 2 + A 2 sin (15°^ + ^) + B 2 sin (SOPn + fiJ 



+ C 2 sin(45°7i + /3'' l ) + (6) 



The constants m^ A 2 , /3j, &c. have other values than in the formula 

 (5), but stand to the constants of these formulae in a definite 

 ratio expressed by the formula (4). Hence we have 



^ = ^=/and/3-/3'=y/; 



and if we make gl=u, and g'l= a', 



ux'=gg'l 2 = I r~^ H 2 . H 2 



K 2 T 2 + 4K 2 + 2K 



that is, 



K A / 7T 2 H 2 _H_ 2 



V V K 2 T 2+ 4K 2 2K ' 



KT' 



aa '= tTTt^ • ( 7 ) 



a result remarkable for its simplicity. If in formula (7) the 

 value of the magnitude K is substituted, we finally obtain the 

 conducting power 



k = cS.^ (8) 



It is then seen that H entirely disappears from the expression 

 for aa!, so that the value of k is obtained expressed in the specific 

 heat of the body, reduced to the unit of volume, and indepen- 

 dent of the numerous changes to which the radiating power is 

 subject. 



As now the specific heat is one of the elements most accurately 

 known, and which may be determined with the greatest accuracy, 

 there is a possibility of obtaining the absolute value of k. 



The coefficients B lt B 2 , (3 1} /3 2 , &c. may be treated in the same 



