20 The Rev. T. R. Robinson on the Relation between the Temperature of 

 Integrating 



which requires no arbitrary constant, because du vanishes with u. 

 Integrating again, e being the base of the Neperian logarithms, 



_V 1 



\e ■ +e ^ ) 



As y vanishes when x = 0, we have then 



1_ 



m 

 and hence deduce 



^ = ¥x /.> ^ ..N2 . (4) 



which determines the thermic condition of any point x. 



As the pyrometer gives only T, the mean temperature, we must find its 

 expression for any length x: 



rJydx ^ ^f. ( 1 \ 



^ - ^ - ^ + mx "" W<'+"' + ly 



In strictness this should be taken from to the centre of that portion of 

 the wire which is of uniform heat, supposing both supports to cool it equally; but 

 as this part extends close to the upper support, I prefer taking it from to \, 

 the place where the heat declines ; in this instrument \ is five inches. 

 Thence 



It then remains only to determine 6, /u, and e""". 



In (3) the quantity n is the diiference of two quantities ; one the heating 

 power due to the increase of resistance by heat, which, being proportional to p, 

 may be called ip, r being, as we have seen, 0.0015; the other representing the 



