Rev. H. Moseley on the Theory of Resistances in Statics. 435 



the points of support, thus dividing the triangle formed by- 

 joining those points into three others, which have its sides for 

 their respective bases ; then the pressure upon any one point 

 of support is to the whole pressure as the triangle upon the 

 side opposite to that point is to the whole triangle. 



Prony, in his work entitled " Lecons de Mecanique 

 Analytique," has applied this theorem to the determination of 

 the pressures upon the three points of support when one of 

 them passes into the stniight line joining the other two, the 

 triangle formed by joining them containing always the inter- 

 section spoken of above, and eventually resolving itself into a 

 straight line. He has remarked, that under these circum- 

 stances the relations of the several pressures to the whole 



pressure will be expressed by fractions of the form ^. To 



determine its value he has supposed the vertical through the 

 centre of gravity of the mass first of all to intersect one of 

 the sides of the triangle formed by the lines joining the points 

 of support : the pressure upon the opposite point of support 

 thus vanishing, he has supposed that point to pass into the 

 line joining the other two points ; and he has thence concluded 

 that the pressure upon this third point, when under any cir- 

 cumstances occupying a position in the line joining the other 

 two, is evanescent. 



It is remarkable that he should not have perceived this 

 case to come under the first, at the instant when the third 

 point comes within an insensibly small distance of the line 

 joining the other two points. 



There is a case in which the value of this fraction ^r may 



be easily determined; and it is valuable as completely over- 

 throwing the strange position, that of a number of points of 

 support, situated precisely alike with regard to a given pres- 

 sure, it is possible that a certain number should sustain no 

 portion of that pressure, — a position which is principally built 

 upon this case of a mass supported upon three points in the 

 same right line, and which, notwithstanding the abundance of 

 absurd conclusions that may readily be shown to flow from 

 it, has yet, under the sanction of respectable names, in some 

 sort fixed itself as a principle in statics. 



Let the vertical through the centre of gravity of the mass 

 pass through the centre of gravity of the triangle formed by 

 joining the points of support. The pressures upon these 

 points will then all manifestly be equal, since the smaller tri- 

 angles, shown by the theorem of Euler to be proportional to 



3 K 2 



