6i Trans. Acad. Sci. of St. Louis. 



superposed layers exert upon the sphere will now be deter- 

 mined. 



That pressure is 



/-> GO 



(18) 



As both g and d have bj the shrinkage been multiplied by 

 /?, it follows that P in (6) must have been multiplied by p"^. 

 Putting in the values ofg and d from (16) and (17) the 

 pressure due to gravitation, of these superposed layers, is on 

 integration 



^ ~ 2irkE'' ^^^^ 



It is therefore evident that, on account of skrinkage due 

 to gravitation, the gravitating pressure exerted radially inward 

 across any and every concentric spherical surface has be- 

 come p times as great as the internal mass can support, 

 unless the temperature has increased. When he comes to 

 deal with the subject of contraction, Woodward seems to 

 have omitted from his analysis the work done in compressing 

 unit mass, due to increase in weight of superposed layers. 

 At any fixed point in space, the weight of a gramme increases 

 as shrinkage proceeds, because the mass of matter internal to 

 it is increasing. The v^ov^ pdv done on unit mass in the case 

 discussed by him, does not all come from the action of gravi- 

 tation upon the unit mass itself. As a result Woodward not 

 only rejects the work of See, but Lane's law as well. 



For the initial conditions the equation for a perfect gas gives, 



P, 



/ = CT,. (20) 



Evidently in the second condition of equilibrium 



?^ = CpT,= CT. (21) 



where 



r T 



T = ^^- (22) 



