on the Principle of Least Pressure. 423 



system A ; an hypothesis never made by me. He goes on to 

 state, that he considers me to have erred in my argument on 

 this point in two particulars. 



1. In assuming that each of the forces C can be divided* 

 (not resolved) into two parts, one of which is solely employed 

 in sustaining the pressures propagated by the system A, and 

 the other in sustaining the pressure mutually propagated by 

 the system C. 



2. In supposing that these latter forces can be removed by 

 the principle of the superposition of equilibrium. 



Mr. Earnshaw has not informed me wherein I have erred 

 in these particulars. 



His next objection is couched in the following terms : 

 " 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." For his inability to perceive the ground 

 on which this assumption rests, he assigns no reason in his 

 first paper; but perhaps, feeling from my answer to that paper 

 (of which answer, however, he has taken only this notice,) that 

 some reason was necessary, he thus satisfactorily supplies it. 

 "I will now give my reason for saying that, &c. It is this : 

 I believe that only the directions, and not theyb?^^ themselves, 

 when there are more than three, are functions of the coordi- 

 nates." Now, let us try this general principle, his belief in 

 which Mr. Earnshaw assigns as his reason for disbelieving the 

 resistances to be functions of their coordinates, by applying it 

 to a particular case, a method of verification the use of which 

 has the sanction of Mr. Earnshaw's own authority. Let there 

 be a perfectly smooth surface, on which let a heavy mass be 

 placed supported upon any number of points ; a table, for 

 instance, on four legs. 



Now according to Mr. Earnshaw's hypothesis, if we alter 

 the relative positions of these legs in any way, leaving the 

 weight of the table the same, we shall not in the least alter 

 the amount of pressure upon each, but only its direction; so 

 that we shall get four equal pressures in different oblique di- 

 rections. Now let these be resolved horizontally and verti- 

 cally. 



The sum of the vertical pressures must equal the weight of 

 the table, and result, indeed, from it ; but where do the hori- 

 zontal forces come from ? And this, which is at best but an hy- 

 pothesis, and an hypothesis involving, it seems, an absurdity, 

 Mr. Earnshaw calls a reason ! 



My assumption that the several resistances are functions of 

 the coordinates of the points of application is grounded on 



* I have nowhere used the term divided. 



