426 Prof. Moseley in Answer to Mr. Earnshaw. 



the same straight line, and x is the distance from one of them 

 of a certain point, about which the moments of the resistance 

 are shown by the principle of least pressure to be equal. 



Now, if the positions of the points of resistance be supposed 

 to vary so that 3a — b — c may continually diminish, it is evi- 

 dent that to satisfy this equation the value of x must continu- 

 ally increase, and that when 3a — b—c becomes infinitely small, 

 x must be, and is, infinitely great. No ! says Mr. Earn- 

 shaw ; "when 3a— b—c is infinitely small, the first term va- 

 nishes as compared with the rest, and the value of x is 



\ab c 



which is not infinite." 



ab + a c — be 



Now, I will venture to suggest to Mr. Earnshaw that some- 

 what more of attention than he seems to have bestowed upon 

 this objection was due to the controversy between us. Had 

 he not very hastily and cursorily considered the subject, I arn 

 sure he would have perceived that the first term x 2 [3a — b — c) 

 being made up of two factors, it does not by any means follow 

 that we diminish the whole term as we diminish one of its 

 factors, or that the whole term enters upon the infinitesimal 

 state when one of its factors becomes an infinitesimal. Pro- 

 vided the other factor increase as this factor diminishes and 

 become exceedingly great when it becomes exceedingly small, 

 the term itself may retain throughout njinite value. Now this 

 is precisely the case in the equation in question. It is not, 

 therefore, true that when 3a — b — c is exceedingly small, the 

 first term vanishes as compared with the rest. 



If Mr. Earnshaw objects that I have here reasoned of the 

 exceedingly small value of the factor 3a— b—c, and not of its 

 state of absolute evanescence, I answer that neither he nor my- 

 self can know anything of what actually obtains in that state of 

 evanescence. We can only reason of the circumstances which 

 attend its continual approach to that state. 



I have thus shown demonstratively that when the points 

 take up positions differing the least possible from those as- 

 signed to them in my former paper, the pressures upon them 

 are equal ; and I have shown this to result both from a for- 

 mula dependent upon the principle of least pressure, and 

 from a separate and independent investigation. 



I leave Mr. Earnshaw to speculate upon the changes which 

 can take place in the relation of the resistances during the 

 motion of their points of application from the positions in 

 which I have left them through the infinitesimal spaces which 

 intervene between these positions and their uUimalc positions. 



