638 Prof. Pollock: Comparison of Periods of 
being 1:065. Drude concludes from this experiment that 
“the half natural wave-length of a nearly closed thin wire 
circle is 6°5 per cent. greater than its length.” This value I 
believe to be far too small. 
With the circuits used, the present experiments give for 
the ratio of the perimeters of rectangles 30 cms. in width to 
the lengths of open circular circuits, when both have the same 
period of vibration, values varying from 2°38 for a rectangle 
with a perimeter of 760 cms., to 2°28 for one whose perimeter 
is 1050 cms., the gaps in the circles being about 15 cms. 
long to avoid any appreciable capacity effect due to the 
pr oximity of the ends of the circuit. 
Comparing this result with that given just above for 
straight wires, 1t is found that the electrical vibration con- 
nected with a wire bent into the form of a circle, with a 
considerable gap in its circumference, has a shorter period 
than that associated with a straight wire of the same length. 
The actual result obtained is that a copper wire 0°33 cm. in 
diameter, if bent into the form of a circular are, with its ends 
separ ated by a distance of about 15 cms., requires to be 3°2 
per cent. longer than a straight wire of the same gauge 
310 cms. long to give a radiation of the same wave- length, 
and 3°4 per cent. longer than a straight wire 445 cms. in 
jength. This result is to be expected when the ends of the 
circular are are not brought too closely together, as the 
inductance of the wire is less in the circular form than when 
straight and the capacity is practically unaltered (see Thomson, 
‘Recent Researches,’ § 385). 
A further decrease of inductance without appreciable 
change of capacity can be made by bending the wire forming 
the open circle into the shape of a narrow "rectangle with an 
open end. One would expect, therefore, the period of vibra- 
tion in such a circuit to be somewhat less than that in an 
open circle of the same perimeter. That the periods of 
electrical vibration connected with such circuits are, at least, 
nearly equal when the perimeters are the same, is shown by 
a result obtained by Sarasin & De la Rive* in connexion 
with their experiments with waves along wires. In these 
experiments it was found that the distance from the free ends 
of the wires to the first node was nearly equal to half the 
circumference of the resonator, and in such a case of parallel 
wires with free ends, the end section may be considered to 
correspond with an open rectangle. Macdonald, ‘ Electric 
Waves,’ p. 121, in giving the distance to the first node from 
the end of the wire as 0°1922, makes the ratio of wave-length 
* Sarasin & De la Rive, C. #. vol. cx. 1890. 
