332 NEWTON S PRINCIPIA. 



or, which is the same thing, 



differentiating, 



=0. 



4 7T // 



Put - - = (f for the sake of brevity. We have now a 



differential equation to find p r. The integral is well 

 known to be 



p r = A sin (q r + B). 



Now because the integral in equation (3.) has r = for its 

 lower limit, it will be found on substitution that this value 

 of p r will not satisfy it unless B = 0. Indeed, if B were 

 not zero, we would have the density infinite at the centre, 

 which is manifestly impossible ; for, no matter how great 

 the pressure may be, it must still be finite. 

 We have then 



. sin q r 

 L 



This gives a density gradually decreasing from the centre, 

 and therefore not contrary to what is a priori probable in 

 the case of the earth. 



The values of A and q have yet to be determined. But 



