424- Prof, Moseley in Answer to Mr. Earnshaw's Remarks 



this, that each such point being supposed capable of resisting 

 in every possible direction, the circumstances under which one 

 point resists do not differ from those under which another 

 resists otherwise than as it respects the positions of the points. 

 Or thus: it being supposed that the resistances are functions 

 of their points of application and their directions, — also their 

 directions being subject in each case to the condition of a mi- 

 nimum resistance, — we may from these data obtain equations 

 from which the resistances themselves will be eliminated and 

 the directions obtained in terms of the coordinates : the di- 

 rections being then functions of the coordinates, the resist- 

 ances are also functions of these. 



I now come to the case of a body supported upon three 

 props. In reference to this case I have reasoned from a 

 finite state of the triangle formed by joining the points of sup- 

 port, to its evanescent state; and so has Mr. Earnshaw, and we 

 have arrived at different conclusions, the reason of which ap- 

 pears to me evident enough. Neither Mr. Earnshaw nor 

 myself can know anything of the relative pressures upon C 

 and G when they have actually passed into the line A B, 

 by reason of the evanescence of the triangles by which a 

 comparison is established between them. All that we can know 

 of their ratio when in that position, must be obtained by ob- 

 serving the limit to which it approximates as they pass into it. 

 Now Mr. Earnshaw, by bringing, first, one of the two points 

 into the line AB, and then the other, has rendered this obser- 

 vation of the limit towards which the ratio of the triangles, 

 and therefore of the forces*, continually approaches altogether 

 impossible. By bringing C into the line AB, he has at once 

 pluno-ed one of the triangles into its state of evanescence, and 

 seeincr no more of it he proceeds to thrust the other also out 

 of his sight. How he should imagine that in this way he can 

 have made any comparison between them applicable to their 

 state of actual evanescence, is to me quite unintelligible. 



On the contrary, I have traced the ratio of the triangles 

 up to the limits of evanescence ; and knowing the forces to 

 have the ratio of the triangles, I know that I have thus traced 

 the ratio of the forces up to the very point of their coincidence 

 with the line AB. 



My only hypothesis has been that when the triangles pass 

 from this exceedingly small but finite state into the evane- 

 scent state, and the forces, from the nearest possible approxi- 

 mation to the line AB, actually into that line, these retain 

 that identity of their ratios which they have up to that point 



* The forces G and C are demonstratively proportional to the triangle* 

 AGB and ACB, so long as the latter definite. 



