The 12 maps show both foei to change position from hoiir 

 to hour, and corabiiiing the 12 positions for each focus in 

 a special map, it is obvious that the path for both approaches 

 to a circle, which in both cases seems to be the same circle 

 in which the foei He diametrcially. 



To investigate this, the harmonie formulae representing 

 the four series, resp. for x+, x_ , y-^ and y-, have been 

 computed. 



, ^ I X, =:— 1.1 + 13.5 sin (t+ IS**) -f 2.1 sin 2(t-f 19°) 



-f- focus • + 



[ y^ = — 10.7 + 14.3 sin (t + 14"— 90") + 2.4 sin 2 (t— 2") 



( x_ = — 3.3 + 13.6 sin (t + 24° + 180") + 3.2 sin 2 (t— 15") 

 I y_ = —10.2 -j- 15 7 sin (t + 24" + 90") + 3.0 sin 2 (t— 50") 



The mean vahies of x_^, y^, x_ and y_, viz. the constant 

 terms of these formulae, are nearly the same for both foei, viz. 

 — 1.1 and —3.4 ; —10.7 and —10.2. 



Accordingly both paths have nearly the same central point. 



The terms of the seeond order are small conipared with 

 those of the first order; neglecting them and eonsidering 

 those of the first order only, we see that the moduli are 

 nearly of the same magnitude, and that the amplitudes viz. 



focus 



