6 Ellery W. Davis 



vector and upon the black, of the change in the double vector is 

 precisely such a double harmonic motion as we have been describ- 

 ing, the amplitudes being 2 and 2s/2 times the black vector. 

 The projection, parallel to the black vector and upon the red, of 

 this same change is discontinuous, being infinite for a finite varia- 

 tion in 6. While 6 varies from o to tt/o, the blue point remains 

 at infinity in the direction of the original red vector. As 6 passes 

 71-/0, the blue point flies from infinity in that direction to infinity 

 in the opposite direction, whither the black point went at the 

 start. Fig. 6 is supposed to represent the facts when 6 = 



e~, 



4$ 



e-3/ / 



Fig. 6. 



and when is passing 71-/0. The dotted line midway between 

 the infinite vectors is the projector of the black point. Both the 

 black point and the blue point stay at infinity until 6 passes sr, 

 when the black flies from 00 through the finite position, sym- 

 metrical to its original position with respect to O, on to infinity 

 in the opposite direction. Thither also the blue point flies when 

 6 passes 371-/2. 



When both parts of the double vector are infinite, neither the 

 blue point nor the black will ever come into the finite field. If 



