400 On the Principle of Isurrhopic Axes in Statics. 



By calculating the temperatures y anil y■^ of the warmer and 

 colder bars corresponding to the places of contact, we have — 



y- yi- y—y\- 



Ziuc-Iion (not well fitted on~1 ioq - too o i q 



each other) . . . . / ^-^"•^ ^"'^''^ ^'^ 



Iron-Copper do. 68-4 66-1 2'3 



Copper-Iron(separatedbvpaper) 238'5 192'5 46 



Zinc-Bismuth do. * 219 211 8 



These differences do not necessitate the existence of a resist- 

 ance of ])assage. When the conductibility of the united bars at 

 their place of junction is lessened by imperfect contact, or by the 

 insertion of a piece of paper, a considerable decrease of tempe- 

 rature takes place at those points, by which a difference between 

 the temperatures of the two bars at the place of contact could be 

 easily explained. 



LIV. On the Principle of Isorrhopic Axes in Statics. 

 By W. J. Macquorn Ranking, C.E., F.R.SS.L. ^' E.* 



THEOREM. Every equilibrated system of forces applied to 

 a connected system of points, is capable of resolution into 

 three rectangular independently equilibrated systems of parallel 

 forces applied to the same points. 



Demonstration. Assume any set of rectangular axes, to 

 which reduce the forces and the positions of their points of ap- 

 plication ; and let X, Y, Z be the components of the force applied 

 to any point (x, y, z). 

 Let 



2.Xa? = A; S.Yy = B; S.Zr=C; 

 2.Y2'=2.Zy=L; S.Za? = 2.X^ = M; S . X?/=2.Ya: = N. 

 Conceive the surface of the second order whose equation is 

 A^^ + B/ + Cz"' + %hyz -h 2Mzx + 2N^y = constant. 

 Then if the forces and the positions of their points of application 

 be reduced anew to the principal axes of that surface, we shall 

 have 



L=0, M = 0, N=0; 



and consequently each of the three systems of component forces 

 parallel to those three principal axes will be in eqvilibrio, inde- 

 pendently of the other two systems. Q, E. D. 



The above theorem, so far as I am aware, is new. 



Glasgow, Oct. 26, 18.55. 



* Communicated by the Author. 



