100 Prof. Moseley on the Principle of Least Pressure. 



dx dy 



1u"^ +u'^- + P.R" = 

 dx dy 



.% eliminating^ and -^ - from these equations 



_ M '/V + tt 'V'-?/^ + R'= 

 dy 



_2«"V-w'V'h-z/^ + R" = 



Between which equations if x be eliminated we shall obtain a 

 differential equation of the form 



d-y t F * = ° 



where Fy is a known function of y. 



.'. Y = C — fY y dy = v[/j/ is known 

 .-. log e P + S = $y 



.-. P = £ (^" s ) 



The values of P, cos a, cos /3, cos y, being thus found in 

 terms of x y z, and Pj P 2 , &c, cos « n cos a 2 , cos /3 15 cos /3 2 ... 

 cos y 1} cos y 2 , being all supposed to be similar functions of 

 their corresponding coordinates, by substitution in equations 

 (1.) and (2.), we shall obtain six equations determining the 

 values of the six constants A x A 2 A 3 , JS X B 2 B 3 , and thus the 

 solution will be complete. 



The coefficients of 8 a, S /3, S y may be written thus : 



{a . T> -o 1 d COS OL 



Ai + B^-B^-f^cosaj^ . -j— 



{a r> ™ „1 d cos B 



Aa-B! x+B 3 z+ p. cos/3 J--^- 



-|a 3 + B 3 x- B 3 y + p. cosy X . -^~ 



The equations (6.) will therefore be satisfied by any values 

 ofa/3y which are independent of xyz. That is, they will 

 be satisfied, provided the inclinations of the resistances to the 

 axes of xy z be the same for all the points of resistance ; that 

 is, provided the resistances be parallel to one another, and 

 therefore to the resultant of the other forces impressed upon 

 the system. 



