Rev. H. Moseley on a New Principle in Statics. 285 



case in which the first solid is a sphere of the radius a', be- 

 cause both Lagrange and Ivory have used it to show that the 

 reasonings of Laplace are incorrect. In this case, then, the 

 surface described by the point p" is that of a sphere whose 

 radius is the difference between a and a' ; and the values of 

 V,V',V" and A, are % *a'\ % ira\ f*r(a'-«) 2 , and % va', 

 respectively. 



Substituting these values in the equation V + V'— V r/ = 2a A, 

 and omitting the common factor £tt, the resulting equation 



a /2 + 2 -(a'-a) 2 = 2aa 

 ought to be identical ; — and so it manifestly is. 



L. On a New Principle in Statics, called the Principle of 

 least Pressure. By the Rev. H. Moseley, B.A. Professor 

 of Natural Philosophy in King's College, London*. 



ET there be conceived a system of forces, of which a cer- 

 *^ tain number are given in magnitude and direction, and 

 the rest are supplied by the resistances of as many fixed 

 points. 



Also let the points of application of all the forces of the 

 system be supposed to be given. 



Now to the complete determination of any force in magnitude 

 and direction, its point of application being given, it is neces- 

 sary that we know its resolved parts in the directions of three 

 rectangular axes. 



To ascertain, therefore, completely, the magnitudes and di- 

 rections of the resistances on the different fixed points of the 

 system we have supposed, we must have at least three times 

 as many equations between the resolved parts of the forces and 

 resistances which compose it, as there are points of resistance. 



The known conditions of equilibrium supply, at most, but 

 six such equations. If there be more than two points of re- 

 sistance, these equations are therefore insufficient. And it re- 

 mains to establish some other relation between the resistances, 

 their several points of application, and the other forces of the 

 system, as shall enable us to determine the former, in terms 

 of the others, of which they are manifestly functions. 



The following principle is sufficient for this determination. 

 It is believed to constitute a new principle in statics. If there 

 be any number of forces in equilibrium among which there enters 

 a system of resistances, then are these resistances such, that their 

 sum is a minimum ; each being considered a function of the 



* Communicated by the Author. 



