360 On the PROGRESS of HEAT 



preceding equation, will exhibit the relation between the tem- 

 perature and the diftance, in the way of all others leaft fubject 

 to mifapprehenfion. 



Let the circle (Plate X. fig. 3.) defcribed with the radius 

 AB, reprefent the globe of the earth ; and the circle defcribed 

 with the radius A H an ignited mafs at the centre. Let H K, 

 perpendicular to A B, be the temperature at H, the furface of 

 the ignited mafs ', and let F D be the temperature at any point 

 whatever, in the interior of the earth, B M reprefenting that at 

 the furface. Then A B being z= R in the preceding equation, 

 AH-r, HK = H, BM = T; AF = *, and FD = /;, thefe 

 two laft being variable quantities , fince 



(u RT — rH\ Rr(H-T) u , ;_'. 



\ R_ r -J x = k=7 — we have, ( takin S A E 



nr — p — , and drawing E L parallel to A B, meeting H K 

 in N, and F D in O,) ODxOEz BA.AH(HK-BMX 

 which is a given quantity. 



Therefore D is in a rectangular hyperbola, of which the centre 

 is E, the allymptotes E G and E L, and the redangle of the co- 

 ordinates, equal to BA.AH X ^-^ , or, which amounts 



B H 



to the fame, to K N . N E. 



It is evident from this, that if the fphere were indefinitely 

 extended, the temperature at the point B and all other things 

 remaining the fame, the temperature at its fuperfices would not 



"D •y it 



be lefs than A E, or than the quantity - — . 



K — r 



The 



