Vibrations: Both Masses and Periods Unequal. 37 



•separate pendulums were equal : (2) when either the masses 

 of the bobs or the separate periods were unequal. The 

 present paper deals with the cases where the masses of the 

 bobs and the periods of! the separate vibrations are both 

 •unequal. 



This mechanical case may be regarded as somewhat 

 analogous to the electrical case of coupled circuits in which 

 the inductions and periods are both unequal. 



A series of photographs was taken from sand traces 

 obtained when the masses were 20 : 1 and the length of 

 the pendulum with the heavier bob as 4 : 3 of that with the 

 lighter bob. The ratio of the frequencies then slightly 

 exceeds 8:7, i.e., to put the matter in acoustical terms, 

 the pendulums are out of tune by 248 logarithmic cents 

 or approximately a tone and a quarter. 



Other photographs were taken with masses 20 : 1 and 

 pendulum lengths as 9:8, the lighter bob still being on 

 the shorter pendulum. The ratio of the frequencies slightly 

 exceeds 21 : 20, i. e., the pendulums are out of tune by 

 102 logarithmic cents or approximately an equal-tempered 

 semitone. 



In both cases it was noticeable for small couplings that 

 very little of the energy of the heavy bob was required to 

 build up in the lesser bob an amplitude nearly equal to that 

 •of the heavier bob. Further, that for couplings about 

 30 per cent, the curves obtained were almost identical in 

 the two cases and almost indistinguishable from that of 

 30 per cent, coupling shown in Paper II. for masses 20 : 1 

 and lengths equal. 



The pendulum with the heavy bob was altered in length 

 until it was 3 : 4 times as long as that with the light bob, 

 the masses remaining as 20 : 1. The results of theory and 

 experiment were rather striking. The ratio of the fre- 

 quencies of the separate pendulums slightly exceeds 8 : 7. 

 As the coupling was increased from one to about six per cent, 

 the ratio of the frequencies diminished to about 13 : 12, and 

 the two pendulums had greater action and reaction on one 

 another. When the coupling was further increased, the 

 ratio increased to 2 :1 at coupling about 30 per cent, as in 

 the other cases. 



Quenched Spark.—Proi. J. A. Fleming has pointed out 

 that by means of a rapidly damped spark discharge in a 

 primary circuit a slowly damped electrical vibration may 

 be produced in the secondary or antenna. In this paper a 

 photograph of a mechanical analogue of such a discharge 

 is reproduced from a sand trace. 



