214 Dr. A. A. Robb : Graphical Solution of Differential 

 Thus since A A n — Bs', we have for the A curve 



* - ij*feK + ifaw^ y^)^-o A »- 



But the right-hand side of this equation is constant, and 

 so for the A curve, the relation (3) holds. 



It is thus evident that the A curve is one whose p and c& 

 equation satisfies the differential equation (2). 



On the other hand, the N curve is one whose polar equation 

 with P as pole satisfies the differential equation (2), and this 

 curve is more convenient than the A curve for giving the 

 relation between p and g> directly. 



In the special case where 



(£(£) = a sin m£, 

 the curve (5) becomes 



r= 9 1 sin co dco, 



a 

 = — r, cos ft) 4- const. 



If the constant of integration be taken as zero, we get the 



simplest curve, which is 



a 

 r= — 9 cos ft). 



This is clearly a circle passing through P and of which 



the diameter is — 9 . 

 m L 



Thus in this particular case, which is one of special 

 importance, the curve (5) is very easily drawn. 



The curve (5) might be drawn with a different pole from 

 P in case we desire that it should not be in too close prox- 

 imity to the N curve. 



The lines on the squared paper parallel to the axis of y 

 would still give the proper direction of the radius vector. 



It will be observed that if the function <j> is zero the 

 points A , A 1? A 2 , .... A n coincide respectively with the 

 points M , M^ M 2 , .... M» and we get the same result as 

 previously obtained, 



In conclusion, I wish to express my best thanks to 

 Mr. E. V. Appleton, who called my attention to the im- 

 portance of this problem. 



Note on the above by E. V. Appleton, M.A. 

 The production of undamped - electrical oscillations is 

 nowadays accomplished in various ways. But in most cases 

 the assembly of the generator may very simply be reduced 



