PHYSICS: C. BARUS 
215 
current, corresponding to very different band widths. This is a curious result, 
for it means, virtually, that the magnetic forces and the stresses are in the rela- 
tion of a doubly inflected curve to each other, so that there are three inter- 
sections, two for stable vibratory equilibrium; or else the two harmonic sys- 
tems, the electrical and the mechanical, may vibrate in the same or in opposed 
phases. The cycle in figure 4 indicates the general relation of the band width 
s to the tensions, there being two maxima at m and 
Similarly each current requires its own particular mxaximum tension, which 
increases with the current. The difference is not large, but effective and for 
this reason the fine tension adjustment is essential. 
4. Further observations. — The apparatus was then improved in a variety of 
ways, chiefly by the insertion of a small vibration objective, about 1 cm. in 
diameter, achromatic and with a focal distance of but 5.8 cm. In this case 
the distance a and h, figure 3, could be decreased to 7 cm. and 35 cm. and the 
observer was thus conveniently near the adjusting screw. The slit image was 
white and about a scale-part in width. There would have been no difi&culty 
in using much greater magnification. 
An example of the results (band- width s in scale parts) is given in figure 5. 
The constant of the dynamometer was now C = 10~^ X 0.87 relative to am- 
peres and the total resistance in circuit 710 ohms. The frequency, as before, 
was estimated at about 15 per second. 
The results were a considerable improvement on the preceding and the dis- 
crepancies as a rule lie within 5 X 10~^ ampere. They are much more liable 
to be in the dynamometer than in the vibrator, as the former was not well 
adapted for these small currents. The deflections begin with 3 scale-parts 
(initial slit breadth) and not at zero; but as this appears merely as an initial 
constant, it is not of consequence. 
If we compute the coefficient of induction as 
LW = Air{R + r)2)/Ai2 
(A being a differential symbol) from the first and fifth, second and sixth, etc., 
observations, data for Leo and L follow. 
5. Effect of frequency. — A special mercury interruptor was now made having 
as its distinctive feature contrivances by which the mercury surface was washed 
and thus could always be kept clean and bright. It was furthermore adapted 
to give different frequencies. The apparatus functioned admirably for days, 
frequent washing presupposed. Different frequencies, obtained by a sliding 
weight, were estimated from the moments of inertia sls n = 10, 15, and 20. 
The latter could just be counted in groups of 4 vibrations with a stop-watch. 
Higher frequencies were obtainable by using stiffer springs. 
An example of the results obtained with this apparatus is given in figure 6, 
for the phosphor bronze bifilar differently stretched. All gave evidence of 
the peculiar fact that the sensitiveness increases in marked degree with the 
frequency. 
