Forced Oscillations of a New Type. 519 



in which it divides up into one, two, or more segments. 

 Since the frequencies of oscillation which a variable spring 

 of given frequency may maintain under suitable circum- 

 stances also form a series, it is evidently possible for more 

 than one mode of vibration to be maintained at one and the 

 same time, each with its own appropriate frequency. In 

 other words, the variable spring may maintain a compound 

 vibration, and as the components of this motion need not 

 both or all be in one and the same principal plane of vibra- 

 tion of the string, we may readily obtain by a little calcu- 

 lation and trial types of maintained motion in which the 

 oscillation in one principal plane is of one frequency and in 

 the perpendicular plane of a different frequency. Under 

 these circumstances, the motion of a point on the string in a 

 plane transverse to it is the appropriate Lissajous figure, and 

 the frequency relation between the component motions is 

 thus rendered evident to inspection in a most striking 

 manner, 



The photographs represent short sections of the string 

 thus maintained in stationary vibration, one point in the 

 middle of the section being brilliantly illuminated. Fig. 1 

 shows the ordinary 1st type of maintenance in which the 

 frequency of the motion is half of that of the fork. Fig. 2 

 shows a compound of the 1st and 2nd types in suitable 

 phase relation, the motion being in a parabolic arc. Fig. 3 

 is a compound of the 1st and 3rd types. Fig. 4 is a com- 

 pound of the 2nd and 3rd types which have frequencies 

 respectively equal to and half as much again as that of the 

 fork. Figs. 5 and 6 are complementary, i. e, relate to the 

 same type of oscillation, fig. 5 showing one part of the 

 string and fig. 6 another part. In these two photographs, 

 the 1st and 3rd types of maintained motion occur together 

 in one principal plane, and the 2nd type by itself in the 

 perpendicular plane. In fig. 5 the 1st and 3rd types are in 

 similar phases, but in fig. 6 they are opposed, hence the very 

 remarkable splits-ring effect in the latter. In fig. 7 we have 

 the 1st and 3rd types again in perpendicular planes, but 

 along with the 3rd type there is a clear addition of the 

 2nd type as well. Figs. 8 and 9 are complementary, and 

 show the 1st type maintained in one plane, and the 2nd and 

 4th tj'pes together in the perpendicular plane. Fig. 10 

 shows a compound of the 2nd and 5th types having fre- 

 quencies respectively equal to and two and a half times that 

 of the fork. Fig, 11 shows the 1st type in one plane and 

 the 2nd and 5th types together in a perpendicular plane. 

 Fi°*s. 12 and 13 are complementary, i. e. show different parts 

 ° 2M2 



