﻿192 ON THE USE OF EQUIVALENT FACTORS 



{Q-|^i")y+(Q'-|'n^+ + ii/_|'L = o, 



to which Ave shall give the following notation : 



Q. y + Q'.z + + il4 = 0, 



(18.) Q',2/ + R, z + + i\; = 0, 



Let w be eliminated from these new equations (18) in the same manner that x was 



Qi 



from the equations (8), multiplying the first by -^ and subtracting it from the second, 

 giving 



(«.-^^'Qg--+ + iv;_Ql'M. = 0, 



with the corresponding notation, 



(190 R.y-- + + N,, = Q. 



For a more complete illustration of the notation, we will collect in one view the 

 equations obtained by the successive eliminations : 



(a) p x + F'y^F' z + + L = 



(i) p ,r + Q y + Q' z + + i»f = 



(c) P"x+Qy-irR z + + iV = 



Final 

 Equations. 



(20.) {h) Q,y+Q',z + + ilf. = . 



(O Q',y4-K^, + + iV, = lEquanonsformedby 



eliminating x. 



(c,j,) i?,j,; -|- + ■ZV,j,= \ Equations formed by 



iminating x and y. 



) Equ 

 J elii: 



Let /i be the probable error of one of the original equations of the unit of weight. 

 The probable errors of the second members of the equations (20) will be, 



Probable error of the equation (a) = /i /^p 



{b) =)^\/q 

 (c) =iJ.^/R 



(21.) « " " {K) =^VQ. 



(O =f\/^ 



