in SPHERICAL BODIES: $67 



18. Hence, by reafoning as in § 6. the momentary incre- 

 ment of the temperature, or fenfible heat, of any flratum, is as 



a x 



— j dire&ly, and its capacity for heat, or mb x inverfely, 



a x v h* a* b* x 



that is, h = — -^zi X b^ __ 



m 



3* — smx 



Let I =y, then - t* =,, & that __, = .__, and 



therefore b = -y^ * Hence 3 = C + 3 J hogb b* = 



c+ — f-i i*'- 



19. To determine C, if T be the temperature of the air at 



a b 

 the furface, when x = r, T = C -f 3OTrLog ^ and C = 



a* & 

 T — 



^mrhogb 



r 



a % b a b 



Hence = T — nm T ^ » -r 



* 



T — 



^mrLogb ' 3 mr Log b 



a* (J, — b L *) 

 3 m r Log Z> 



This formula, when x =z r gives b zz T, and when # is in- 



finite, it gives ^ = T — * rLogfl* ln a11 intermediat€ 



cafes j 



