in SPHERICAL BODIES. 363 



13. 1. The general conclufions which refult from all this 

 are, that when we fuppofe an ignited nucleus of a given mag- 

 nitude, and a given intenfity of heat, there is in the fphere to 

 which it communicates heat a fixed temperature for each par- 

 ticular flratum, or for each fpherical fhell, at a given diflance 

 from the centre ; and that a great intenfity of heat in the inte- 

 rior, is compatible with a very moderate temperature at the 

 furface. 



2. However great the fphere may be, the heat at its furface 

 cannot be lefs than a given quantity ; R, r, H and T remain- 

 ing the fame. It muft be obferved, that though R is put for 

 the radius of the globe ; it fignifies in fad: nothing, but the dif- 

 tance at which the temperature is T, as r does the diflance at 

 which the temperature is H. 



Therefore were the fphere indefinitely extended, the tem- 

 perature at its fuperficies would not be lefs than the quantity 



R T* — — r T-T 



— ^ , that is, not lefs than 50.5 in the firfl of the pre^ 



ceding examples, than — 44*4 in the fecond, or — 1044.4 in 

 the third. 



14. In all this the fphere is fuppofed homogeneous ; but if it 

 be otherwife, and vary in denfity, in the capacity of the parts 

 for heat, or in their power to conduct heat, providing it do fo 

 as any function of the diflance from the centre, fhe calculus 

 may be inflituted as above. For example, let the denfi- 

 ty be fuppofed to vary as ■ , , then we have as before 



(b — h') (x' 3 — x 3 ) - for the momentary increment of 



heat in a flratum placed at the diflance x from the centre, 



Zz 2 or 



