Reply respecting the Principle of Least Pressure. 273 



cases, it is either altogether rejected or its truth is looked upon 

 as doubtful, until these cases are shown to be excepted in the 

 general demonstration. Now suppose the bod}' acted upon by 

 gravity only, and supported on props acting vertically, then 

 the forces ol the system B are parallel, and their sum is con- 

 stant, being equal to the weight of the body. In this case, 

 then, it is plain the sum of the forces of the system B cannot 

 be either a maximum or a minimum, and, therefore, Mr. 

 Moseley's principle fails. 



As a general objection to the principle of least pressure, 

 I would beg to suggest to Mr. Moseley, that the enunciation 

 of it belongs to the following problem, and does not contain 

 a statical principle at all; viz. To find the ])oi}its of applica- 

 tion of a given number of reactions B, in order that they may 

 sustain a given system of forces A, and have their sum a mi- 

 nimum. If Mr. Moseley disagrees with me on this point, I 

 would ask him, how he would proceed to solve the problem 

 I have enunciated ? 



I will now give my reason for saying that " I am unable to 

 comprehend why we are to consider the forces as functions of 

 the coordinates of the points at which they are applied." 

 It is this. I believe that only the directions, and not the forces 

 themselves (when there are more than three), are functions of 

 the coordinates ; and as Mr. Moseley has put the directions 

 out of the question by saying that we are to take the sum of 

 the forces, I was, and still am, unable to comprehend what the 

 coordinates have to do with the matter. 



With regard to the body supported on three parallel props 

 at the angular points of a triangle, Mr. Moseley, by a certain 

 hypothesis of construction, has shown that the pressure on one 

 prop is £rd of the weight of the body, so long as the triangle 

 is finite; and thence infers that when the triangle passes into 

 an evanescent state, the pressure on that prop undergoes no 

 change. This reasoning is certainly very natural; but, let it 

 be observed, when by a different hypothesis of construction 

 I have shown that the pressure on one prop is zero so long 

 as the triangle remains finite, and come to infer, by the na- 

 tural reasoning before mentioned, that it continues zero when 

 the triangle is evanescent, Mr. Moseley thinks the conclusion 

 not valid. I think, however, there ought candidly to be al- 

 lowed as much validity to one as to the other, for they stand 

 precisely upon the same footing. Mr. Moseley remarks on 

 this head that the pressure on C " is not absolutcli/, but only 

 relatively evanescent." To this I answer, that the pressure 

 on C is as absolutely evanescent as if the prop did not exist, 

 btoanse the moments of the other two props about AB are 



Third Series. Vol.4. No. 22. April 188*. 2 N 



