708 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



orthogonal projection of a certain radius corresponding thereto in a 

 logarithmic spiral E 1' 2' o', etc. At successive distances of eight kil- 

 ometers, the phases at any instant would be the same. Moreover, by 

 rotating the entire spiral system of Figure 3 counter-clockwise about 

 0, with angular velocity w, the amplitude and phase of the wave stream 

 at any point on the line could be determined, for any moment, by the 

 orthogonal instantaneous projection of the proper radius in the spiral. 



Figure 3. — Diagram of relative matjnitudes and phases of outgoing wave 

 over the line of Figure 2, for the tirst ten kilometers. 



By combining Figures 2 and 3, a mechanical model might be pre- 

 pared to illustrate the first run of an electromagnetic wave over a cir- 

 cuit. Into a cylindrical wooden shaft, of the length 0', Figure 2, 

 metal pins or wire nails are driven at intervals, corresponding, say, to 

 each quarter kilometer. The radial length of the pin from the axis of 

 the cyHnder must conform to the logarithmic curve A B C D, Figure 2, 

 and its angular position about the axis must conform to Figure 3, for 

 the particular line considered, or thirty-two pins to 360°. A shutter 

 S S, Figure 4, movable in a plane parallel to the shaft, like the sliding 

 lid of a box, should start from A and admit vertically-falling light rays 

 L L, on to the spiral, at a moment when the shaft is rotated by the 

 handle H at uniform angular velocity w, and when the first pin at A 



