it F r. 



or, by the definition ot 



true ofaaoh atti-.-u-tii!^ parti. !> m: ami there- 

 fore, if N refer to tin- n of the whole attnu 



we shall still have fNdS = Q. But, by Art. 235, .V 

 li proves the proposition. 



-11. If Vbe tlie pof i mass 3/j, am/ /VM/ In- f//r 



portion of M^ contained within a closed surface 6 



CdV , 



r/// ami </S having the same meaning a s in Art. 243, and the 

 integration being extended to the whole surface S. 



Let m be the mass of an attracting particle situated at the 

 point P inside 8. Through P draw a right line //, and pro- 

 duce it indefinitely in one direction. This line will in -mcral 

 cut # in one point; but if S be a re-entrant surtar.-. it n 

 cut by L in three, five, or any odd number of points. About 

 L describe a conical surface containing an infinitrly small 

 angle a, and having its vertex at P, and let the rest of the 

 notation be as in Art. 243. In this case, tin; an;_rl -s O lt 8 ,.... 

 will be alternately obtuse and acute, and we shall have 

 > 



\T ^ n I /I \ m /I 



-\ = - -i cos (TT - 0J = -jj cos C lf 

 r t TI 



A l = ar^ sec (TT - ^) = ar^ sec ^, 

 and therefore N l A l = am. 



Should there be more than one point of section, the terms 

 N t A^ N S A 9 , &c. will destroy each other two and two, 



. Now all angular space round P may be divided 

 into an infinite number of solid angles such as a, and it is 

 rvidnit that the whole surface S will thus be exhausted, 

 it, therefore, 



limit of ^ X* i ]<xw' = 



