Remarks on the " Principle of Least Pressure." 20 1 



But in the case we have supposed 

 3a = b + c 

 .-. 3a—b—c = 

 .•. x = infinity. 



Hence, therefore, it follows that the point X, about which 

 the moments of the pressures are equal, is at an infinite distance. 

 The pressures themselves, therefore, are equal, as they should 

 be. . 



It will be observed that there are here obtained precisely the 

 same results, in a somewhat complicated case of resistance, by 

 methods of investigation which are throughout entirely dif- 

 ferent ; and I beg to suggest to Mr. Earnshaw, that he must 

 allow to both methods of investigation, that authority and con- 

 firmation which they mutually derive from this coincidence. 



The theory of the wedge presents an application of the prin- 

 ciple of least pressure under its simplest form, leading to a 

 result which is of some practical importance, and, as I believe, 

 altogether new. 



Let P be the force acting upon the 

 back of the wedge, Q and Q' the re- 

 sistances upon its sides. Now by the 

 principle of least pressure Q and Q' 

 should be the least possible subject 

 to the condition that their resultant 

 shall be P. It is manifest that to sa- 

 tisfy this condition these forces must 

 have a direction parallel to the di- 

 rection of P, or one inclined as little as 

 possible to that direction. 



If, therefore, the surfaces in contact 

 at Q and Q' are such as are capable of 

 supplying resistances at those points 

 parallel to P, then the system will be 

 one of parallel forces, and the points 

 Q and Q' being similarly situated with 

 respect to PA, each will sustain one 

 half of the force P. But if, by reason of the nature of the 

 surfaces in contact at Q and Q', these be incapable of sup- 

 plying resistance in directions parallel to PA*, then will the 



* The following is a principle of statics, of great practical importance, 

 from which the possibility of this supposition will be evident. Let p be 

 a force pressing two surfaces together obliquely, and let 6 be its inclination 

 to the normal at the point of contact ; then p sin 6 and p cos 6 are the re- 

 solved parts of/i, parallel and perpendicular to the surfaces at their common 

 Third Scries. Vol.4. No. 21. March 1834. 2 D 



