132 M. A. J. Angstrom on a New Method of 



the lateral faces must influence the results obtained, they could 

 not stand in a simple ratio to the conducting power. 



§2. 



From what has been said, it is clear that a method for the 

 determination of the value of k is needed by which this shall be 

 expressed in known magnitudes, or at any rate in such as are 

 more easily determined than the radiation from the surface. I 

 think I have found such a method by using a general formula 

 for the propagation of heat in a bar of parallelopipedal form, 

 that is, 



du d*u „ ,„* 



* =k ^- Hm > (3) 



where 



K=4andH = ^ 



CO cow 



and c denotes the specific heat of bar, and $ its density. 



If a metal bar be taken so long that, in determining the law 

 of the propagation of heat in it, regard need not be had to its 

 terminal faces, and if it is heated or cooled during fixed periods, its 

 periodical changes of temperature must be transmitted along the 

 entire bar; and hence, in consequence of radiation from the sur- 

 face, not only will the amplitudes diminish, but the maxima and 

 minima will occur later at a greater distance from the points of 

 heating. If we suppose these periodical heatings and coolings 

 sufficiently long continued, so that the periods can develope 

 themselves completely, in which case the mean temperature of a 

 given point of the bar acquires a constant value, equation (3) is 

 satisfied by the assumption 



me 



in which 



+ be'*' 2 ' sin {-rf -V ^2* + ff ) 



-^--gWWx + P"), • (4) 



9 =a / / ^ = ^~ j* 



V V K 2 T 2 + 4K 2 + 2K 



g'=A / /~ 7r ^~ 7W. E. 



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



and T denotes the length of the period. 



