334 APPENDIX A. 



stant, and the effective force is as the number of particles 

 concerned, or simply as d, 



385. Lemma. If the height of a cone be 

 a, the radius of the base 6, and the oblique 

 side c, the mean distance of the base from the 



vertex will be -g. — ^— " 



For, if the fluxion of the radius of the base be d>r, the 

 product of the elementary ring 29r^Ax, into its distance */ 



(a2 + x% will be 27^x^x V (cf + x") ; and since d J (aH x^)i > 



=:|-x2xdar ^J{a^-\-x^\ we have ^ttjc V(a2+jr2)Ar=-— 



(a* + a;2)2, which becomes initially—- a% and when xzilI, 



o 



27r 



-5- c^ and the difference, divided by 7r¥, the area of the 

 o 



(j3 ^3 ^3 ^3 



base, that is, f — — — , or f _ _, will be the mean dis- 



0^ C^ — Or 



tance of the base from the vertex. 



Corollary. For a solid cone, the mean distance be- 

 comes f of that of the base, as in the case of the sphere : 



and the expression becomes, in this case, |-— -. 



386. Theorem. The deficiency of the 

 mutual actions of the superficial particles of a 

 fluid, of hmited extent, deducts from the tension 



-^ of the whole force of a stratum equal in 



thickness to the radius of the sphere of equal 

 action. 



