Of GREATEST ATTRACTION. 233 



BD, BM, BM', BD', which make up the whole reda-ngle DM', 

 that its attraction in the direction AB is expounded by the area 

 of the fpherical quadrilateral fubtended by it, and, therefore, 

 that the attraction of the whole rectangle MD', is expounded by 

 the fum of thefe fpherical quadrilaterals, that is, by the whole 

 quadrilateral fubtended by MD'. In the fame manner, if the 

 perpendicular from the attracted particle, were to meet the 

 plane without the rectangle MD', the difference between the 

 fpherical quadrilaterals fubtended by MG and M'C, would give 

 the quadrilateral, fubtended by the rectangle MD', for the va- 

 lue of the attraction of that rectangle. 



Therefore, in general, if a particle A, gravitate to a rec- 

 tangular plane, or to a solid indefinitely thin, contained between 

 two parallel rectangular planes, its gravitation, in the line per- 

 pendicular to those planes, will be equal to the thickness of the 

 solid, multiplied into the area of the spherical quadrilateral sub- 

 tended by either of those planes at the centre A. 



The fame r may be extended to all planes, by whatever figure 

 they be bounded, as they may all be refolved into rectangles of 

 indefinitely fmall breadth, and having their lengths parallel to 

 a ftraight line given in pofition. 



The gravitation of a point toward any plane, in a line per- 

 pendicular to it, is, therefore, equal to n, a quantity that ex- 

 preffes the intenfity of the attraction, multiplied into the area 

 of the fpherical figure, or, as it may be called, the angular 

 fpace fubtended by the given plane. 



Thus, in the cafe of a triangular plane, where the angles 

 fubtended at A, by the fides of the triangle, are a, b and c ; 

 fince Euler has demonftrated * that the area of the fpherical 

 triangle contained by thefe arches, is equal to the rectangle un- 

 der 



* Nov. A&a Petrop. 1792, p. 47. 



