of Iron and German Silver. 



485 



convenient to deduce from equations (2) the difference of tempe- 

 rature of two points in the bar, one of which has the distance 

 x=\ly and the other the distance x = ^l-j for in this special case 

 all terms in which n is divisible by 2 and 3 vanish from the series 

 which occur in both expressions ; and these hereby take a form 

 so convergent that even the second term becomes vanishingly 

 small in comparison with the first as soon as the time 6 has 

 reached a certain value. When, therefore, a commencement is 

 made with the observations first at the expiration of a certain 

 time 6 reckoned forward from the beginning of each period, only 

 the first term of that series need be taken into consideration. 



Let Dg^ denote the difference of temperature, in an even period, 

 between two points whose distances from the end are a?=J/ and 

 a? = |/, and let D2;it+i denote the same value in an odd period; 

 then, from equations (2), we find : — 



D,, =(!fo+^-u)(A-B)+^^(A + B) 





+ 



87r^\/3 Wo-Wj^^_^^^ 



Here 



1 + e-^'^ 

 4'7r2 



l^ 



k-\-h. 



(4) 



(5) 



A= 



^ (^s/l^Wl) _ (,f^x/l -^V^/\] 



e^ k—s ^ k 



B=- 



^,i^s/l_,-Wl) ^ (,l^x/f ^.-.-x/f ) 



e ^ k —e k 



The first two terms in the above expressions (4) are constant 

 quantities; the same holds for the factor of e-^^; consequently 

 the expressions of J)2fi and D2,a+i have the form 



Da^ = M -Ne-p^. 



;} 



(6) 



