198 Prof. Moseley's Reply to Mr. Earnshaw's 



centre of gravity is in the vertical passing through the centre 

 of gravity of the mass. In this case the pressure will be 

 equally divided between the points; and this equal division 

 will continue whatever form we suppose the triangle to as- 

 sume, provided only the centre of gravity of the mass alter 

 its position so as continually to satisfy the condition that the 

 vertical through it passes always through the centre of gravity 

 of the triangle. Hence, therefore, it is concluded, as it ap- 

 pears to me, rigidly enough, that this equal division obtains 

 also in the limit when one point passes into the line joining 

 the other two. Mr. Earnshaw thus argues in opposition to 

 this conclusion : " Let A, B, C be the angular points of the 

 triangle in its finite state ; then if we inquire into the cause of 

 the pressure on any one of them (suppose C), we shall find that 

 it arises from the circumstance that the side A B is in a cer- 

 tain respect a, fixed axis, about which the body has a tendency 

 to move, and about which it is only prevented from moving 

 by the pressure of the prop at C : as soon, therefore, as the 

 points of support are brought into one line, A B, in which of 

 course, from the nature of the hypothesis, the centre of gravity 

 is situated, the body ceases to have a tendency to move round 

 A B, and the office of C is abolished, and the case of the tri- 

 angle is not applicable to this." 



Now, assuming Mr. Earnshaw's definition of the office of 

 the point C, and calling K : and K 2 the perpendiculars from 

 the centre of gravity and from C, upon A B, it follows that 



pressure upon C K t 



weight of mass " K 2 * 



If now the centre of gravity and the point C pass both into 

 the line A B, K x and K 2 , both of them vanish, and 



pressure upon C 



weight of mass * 



It matters not whether we suppose one of the quantities K, 

 and K 2 to vanish first, and then the other, or suppose them 

 both, as above, to vanish together; the fraction, in either case, 



assumes the indefinite form — . 



Mr. Earnshaw puts this idea under another form. " Let 

 the body be supported upon three props A, B, C, of which 

 A, B are so situated that the line joining them passes through 

 the centre of gravity, and C is situated without. Then the 

 body will balance upon A B, and there will be no pressure 

 upon C; for if C exerted any pressure, it would overthrow 

 the body by turning it round A B. Let now C come into 



