Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/384

296 attractions towards the whole bodies will be as $$\scriptstyle \frac {A^3}{A^3}$$ and $$\scriptstyle \frac {B^3}{B^3}$$, that is, equal. If the forces decreae in a quadruplicate ratio; the attractions towards the bodies will be as $$\scriptstyle \frac {A^3}{A^4}$$ and $$\scriptstyle \frac {B^3}{B^4}$$; that is, reciprocally as the cubic ides A and B. And o in other caes.

Hence on the other hand, from the forces with which like bodies attract corpucles imilarly ituated, may be collected the ratio of the decreae of the attractive forces of the particles as the attracted corpucle recedes from them; if o be that decreae is directly or inverely in any ratio of the ditances.

If the attractive forces of the equal particles of any body be at the ditance of the places from the particles, the force of the whole body will tend to its centre of gravity; and will be the ame with the force of a globe, coniting of imilar and equal matter; and having its centre in the centre of gravity.

Let the particles A, B, (Pl. 23. Fig. 7.) of the body RSTV attract any corpucle Z with forces which, uppoing the particles to be equal