Wire Transmitting Electric Waves. 67 



Now it is possible that the proximity of the wire to the 

 oscillator may have the effect of virtually increasing the size 

 of the oscillator, and if such is the case all the quarter-wave- 

 lengths so determined are too great. According to Poincare's* 

 deduction from the homogeneity of the fundamental equations, 

 the wave length of an oscillator or resonator varies directly 

 with its linear dimensions. In fig. 12 the points A, B, C have 

 abscissae proportional to the dimensions of the three larger 

 oscillators and ordinates proportional to the quarter-wave- 

 lengths given above. It is seen that they lie very approxi- 

 mately on a straight line, but this line does not pass through 

 the origin. Let us now draw a line parallel to it and passing 

 through the origin. The ordinate B'N of this line, correspond- 

 ing to the 40 cm oscillator, has a length of approximately 103 cms . 

 Thus if the principle of direct proportionality, stated by Poin- 

 care, held without limit to its application, the arrangement of 

 the wire as in the experiments should be equivalent to adding 

 44 cms to the quarter-wave-length of each of the three larger 

 oscillators. On the other hand, the fact that varying the 

 length of the wire from 3 m to 8*6 m had no effect on the posi- 

 tion of the minimum, seems to show that the wire did not act 

 in the manner referred to. In other words, the quarter-wave- 

 lengths given are proper to the oscillators. 



Experiments with the first and second Hertzian oscillators, 

 referred to above, gave the following values for the quarter- 

 wave-length : 



For 40 cm plates, straight connection 70 cms I54'4 cms 



30 spheres, " " " 153*9 



These are practically identical. 



For all wires of three meters and upwards in length there is 

 a well-defined minimum between 10 and 15 cms from the end 

 next the oscillator. In figs. 9, 10 is shown a portion of 

 each curve near the oscillator in continuous line, and also in 

 broken line. In this neighborhood the oscillator exerted a 

 strong action directly on the detector. In order to allow for 

 this, readings were first taken as usual (shown by continuous 

 line) ; then the wire was removed and readings taken at 

 exactly the same points. These latter were then subtracted 

 from the former, and the broken line shows the result. Here 

 it is assumed that the action of the oscillator and of the wire 

 singly are equivalent to the two together. To examine this 

 minimum more closely readings were taken at intervals of one 

 centimeter. There is no doubt of its existence ; it is about 

 10 cms from the end for the smaller oscillators and slightly 



* Poincare, Les Oscillations Electriques, Art. 53. 



