296 PEOCEEDINGS OF THE AMERICAN ACADEMY. 



appears a less intense irregular loop due to the intermittent primary 

 discharges. 



Plate 1, cuts d and e, and a and h of Plate 2 are photographs of a 

 few of the patterns obtained by the above described method. The 

 second secondary circuit was a wave meter with its coil parallel to the 

 primary deflecting coil, from which it received its impulses. An ex- 

 amination of the primary loop is often instructive in giving the relation 

 of the primary discharge to the secondary oscillation. It is seen that 

 the regular Lissajou's figure may or may not be complete according to 

 the value of the I. C. F. In h of Plate 2 the ratio of frequencies 

 is 3 : 1, and the I. C. F. is 3, so that the primary discharges occur once 

 for every journey of the spot over the pattern, thereby distorting a 

 part of the Lissajou's figure. 



Cuts h-f of Plate 2 are due simply to the deflections of the two 

 secondary oscillations, the second secondary circuit receiving its im- 

 pulses from the same primary coil which excited the first secondary 

 circuit. Some of the photographs shown were purposely taken with a 

 slight diflierence in phase to show the double line. Cut e of Plate 1 

 represents the same ratio of frequencies as that of cut a of Plate 2 but 

 with a considerable shift in phase. 



A consideration of cuts d-f of Plate 2 shows that, although the 

 coupling was close, the secondary currents do not depart from the 

 sinusoidal form even while the primary impulse occurs. A possible 

 rough explanation of this non-departure from the sinusoidal form can 

 be had from a consideration of the shape of the primary wave form 

 shown in Figure 14. The primary impulse I\ of Figure 14 is seen to be 

 approximately a cosine curve, of the same period as the free secondary 

 oscillation, plus a constant, until the maximum current is attained, 

 when the current decreases in a straight line. But by substitution in 

 the diflerential equation for an oscillatory circuit, one finds that a 

 cosine wave plus a constant or linear function of the time satisfies 

 the conditions of a sine secondary oscillation. The proof of this 

 proposition is not given here. 



The shape of the primary wave form, which has just been considered, 

 is determined principally by the changes in resistance which take 

 place in the gap. If there were no change in resistance, and the influ- 

 ence of the secondary current were negligible, the form of the primary 

 current rush would be given by the familiar equation 





