298 SCHREINEMAKERS art. h 



a-2 = Wb, X = Ws; and x — Xi ^ as, Xo — x = sb. From (2) it 

 follows that 



mi X as = mn X sb. (3) 



If we put (compare Fig. 2) sb = ab — as, or as = ah — sb, then 



nij mi 



as = ; ab, sb = ; ab. (4) 



m.i -\- nii ' mi + m2 



Thus the position of the point s depends upon the ratio rui'.m^. 

 When mi = m2, as = sb, so that point s is situated in the middle 

 of ab; when mi > m2, as < sb, so that s is closer to point a; when 

 mi < nh, s is situated closer to point b. 



If we imagine a mass mi in point a and a mass m2 in point b, 

 then it follows from (3) that point s is the centre of gravity of 

 these masses. If we denote the f 's of the phases A and B by 

 f] and ^2, then the total ^ of system (1) is yriiti + m2^2- If we 

 call the i' of a unit quantity of this system ^s, then we have 



mi Ti + m2 ^2 ,_>, 



ts = T (^) 



m.i + m2 



We now take aa' = fi and bb' = ^2 (see Fig. 2). Then f, = ss'. 

 This can easily be proved. For 



ss' ^ sp + ps' = f 1 + ps\ (6) 



But from the similarity of the triangles a'ps', a'qb' it follows that 



ps' a'p as m2 ,„. 



qb a q ab mi + m2 



and from (7) follows 



m2 , m2 , , 



ps' = — r~ X qb' = — —- X (r2 - ri). 



^ mi + m2 mi + m2 



Substituting this value of ps' in (6), 



mi Ti + ^2 12 ,„x 



ss = , Co; 



mi + m2 



From (5) and (8) we see that f « = 8s' . 



