35% On the PROGRESS of HEAT 



6. In the fame manner, the heat which goes off from the 

 fecond ftratum in the fame time, is proportional to (h' — //') 

 (x"i — x'^) ; and thefe two quantities, when the temperature of 

 the fecond ftratum becomes conftarit, muft be equal to one 

 another, or {h— ti) (Y 3 — * 3 ) — (// — b") (x" 3 — x' 2 ). 



But becaufe h — b', and x' — x are indefinitely fmall, 

 b — h' — b, and x' 3 — x 3 zz 3 x 2 x y therefore b X 3 x* x =z a 

 given quantity ; which quantity, fince * is given, we may re- 



2 .* 



a x 



prefent by a x \ fo that b zz — ?—. :n — *. or, becaufe b is 

 r J 3 x x $x 



negative in refpect of*, being a deccrement, while the latter is an 



* * 2 



— a, and therefore h zzC4- — . 



3 x 3 X 



increment, b zz 5, and therefore h zz C + 



7. To determine the conflant quantity C, let us fuppofe 



that the temperature at the furface of the internal nucleus of 



ignited matter is = H, and r — radius of that nucleus. Then, 



in the particular cafe, when xzzr and b zz H, the preceding 



2 2 



equation gives H = C -J % fo that C zr H — -— , and confe- 



iiucntly hzz H -\ : or <& :=: H -f — ( - Y 



1 J 3 r 3 x p 3 \# r J 



8. It is evident, from this formula, that for every value of 

 * there is a determinate value of b, or that for every diftance 

 from the centre there is a fixed temperature, which, after a 

 certain time, muft be acquired, and will remain invariable as 



long 



