Di Bella 



This means that, instead of the two masses which are symmetrical every 

 moment in respect to the y axis, a single mass M may be adopted which moves 

 with a well-timed back-and-forth motion along the y axis. The quantities of 

 motion and their derivatives are: 



Qx = Qx = 



Q =MRsinf? Q = MR (cos 6'co2+ sin 0e) 



'■- n '■ .■ \/i ■ " • 



Q, = Q. = . 



The energy of the system is: ' ' -' i 



E = — m,v 2 + - m„v„2 + - ]co^ = const. 



Continuing these calculations, using h = J/MR^, we obtain 



E = MR2 [sin2 fei + 2 ( 1 + cos 0) + h] a;2 , (8) 



and thus, 



CO = 1/R (E/M)i'2 [sin2 + 2 (1 + cos ^) + h]"i/2 , d^/dt . (9) 



From this expression, it follows 



dt = R (-) [sin20 + 2 (1+ cos 0) + h] 1/2 d^ =^ • (10) 



With this expression we can obtain E. By substituting in Eq. (9), E is obtained, 

 and thus by deriving from Eq. (8), we have 



sin 0(1- cos d) E2 



[sin2 + 2 (1 + cos 5) + h] 



The expression of Q becomes therefore: 



1 + (2 + h) cos e + cos^ d 

 Q„ = MRE2 (11) 



^ [sin^e + 2 (1 + cos 0) + h]2 



If we plot Q against t , we obtain a graph of the type indicated in Fig. 8. 



RESULTS OF THE TESTS 



The described devices were submitted to a long series of tests to establish 

 what concrete results could be obtained for propulsive purposes by a mass 



1380 



