62 Trans. Acad. Sci. of St. Louis. 



Ji = ?-5^, (7) 



These equations are all consisteut with each other. For 

 example, as will be at once seen, the value of P^ in (2) is 



/'GO 



where o and g are given in (5) and (8). Also the value of 

 Mq in (3) is 



'P. 



M^ = 4:7r iB^ddB. (10) 



It will be assumed for the purposes of discussion that 



Let the entire mass contract, so that any mass originally 

 •within a sphere of any radius ?'q, shall be within a radius r, 

 .and assume also that 



:?=§=,,. (11) 



This means that the same law of density distribution shall 

 prevail in the second state as in the first. Assume also that 

 the temperature shall remain T^ throughout the mass. 



It is evident that the value of o in (5) is the reciprocal of 

 V, where v is the volume of unit mass and that from (5) and 

 (6) the product 



Pv= PX\=CT^. (12) 







The same equation may also be applied to the entire sphere 

 in its initial condition. Let Vq be its volume. Its average 

 density is three times the density (5) at the surface. Then 



