724 



x = et, + .r' cos cf^ -|- y cos f/-, | 

 y = ^0 + «' sin y', + ,i/' ">i y, i 



When we re[)ieseiit llie length of F„b\ and F,Fj by /, and /,, 

 then we maj' write for (17) 



.... (18) 



.V-^o = J + I 



Now we shall express the composition of the phase F in that of 

 the three coniposants: F, F, and F,. We find. 



quantity of F, : quantity of {F^ -{- F,) = F.i ■ FF, 

 or: quantity of F,: quantity of {F, + /'', + F,) = Fs -. F^.i 



When we put the total quantity of F ^ F, -\- F, + F, equal to 

 zero, and when we beai' in mind that: 



Fs : h\s = Fr: F,F, = ,/ : I, 



v' 



then follows: quantity of jf^, = ^ . 



x' 

 In a similar way we find : quantity of F^ = j- . 



Consequently there are wanted for forming the unit of quantity of the 



x' _, y' 



phase F: — quant, of F^ and '— quant, of -F, and consequently also 



x' y' 

 1 — '-j- quantities of F^. We may write, therefore; 



^=^^'^?:^'K^-^-9^* 



(19) 



X y 



When we put — = ??i and "— = m then (18) and (19) pass into 

 (, (, 



(15) en (16). 



Hence it appears a.o. that ni and 7i do not represent the coordinates 

 x' and y' of the phase F, but they are functions of them ; when 

 m and n are known, then also .c' and y' are known and reversally. 

 For this reason we may call m and ?i yet also coordinates. 



The coordinates of the composant 



F^ are x' = y' = consequently 7ji = and ii = 

 F, ,, x' = /j y' = ,, m = 1 „ n = 



F, „ x=0 y' = l, „ m = „ n = i 



