Electric Waves along Spiral Wires. 425 
diminishes as the turns per centimetre diminish. Hence, if 
we suppose such a helix gradually pulled out into a straight 
wire whilst being traversed by electric waves of constant 
frequency, the wave-velocity would graduaily increase up to 
the velocity of radiation, viz., to 3x10! cms./sec., which 
value it would reach when the helix was stretched out into a 
straight wire, In the case, however, of a closely-wound 
helix, the velocity of electric waves along it in the direction 
of the axis is much less than the velocity of free waves in 
space. 
The simple analysis above given is inadequate to deal with 
the more difficult problem of a very open spiral. If a close- 
wound spiral were gradually stretched out, the velocity of the 
wave along it would increase, and at some pitch would reach 
that of radiation. The precise pitch of the spiral at which 
this would happen is of mathematical interest, but no doubt 
difficult to predetermine. 
The next step was to measure the wave-lengths for various 
frequencies. 
The inductance in the jar circuit was first adjusted to 
produce the fundamental oscillation of the long helix and 
establish a stationary wave on the spiral with a loop or 
antinode of potential at the free end ; and then subsequently 
adjusted to produce the series of odd harmonics with wave- 
lengths in the ratio of 1/3rd, 1/5th, 1/7th, 1/9th, 1/11th of 
that of the fundamental. The position of the nodes was then 
carefully ascertained by the aid of the Neon vacuum-tube, and 
found to be as shown in the diagram on fig. 3 (Pl. XIIT.), 
where O is the open end of the helix and-E the end at which 
the electromotive force is applied, and the numbers represent 
the distances in centimetres separating the nodes N,, N;, «ce. 
from each other and from the free ends of the helix. 
These observations have been very carefully repeated on 
many occasions, aud the figures given are the means of the 
best results. 
Coincidently with the measurements of the internodal 
distances the inductance inserted in the leyden-jar circuit 
se noted, and also the distance of the earth-wire below the 
elix. 
Observations were made with the earth-wire at various 
distances in the case of the fundamental and 1st harmonic 
oscillations; and the results are given in Tables IV., V., and 
VI. The frequency n of the oscillations in the jar circuit is 
calculated from the values of the inductance and the capacity 
