414 AUGUST WITKOWSKI ON EFFECTS OF STRAIN 
and bearing on its free end a lever D, whose ends are the points of application 
of twisting forces, produced by weights and transmitted by a system of cords 
and pulleys, sufficiently indicated in the diagram. The amount of twist is 
measured by means of a telescope, and a scale reflected in the mirror Z. An 
electric current, produced by a single DANIELL’s cell of several square meters . 
surface, and therefore very small internal resistance, is conducted along the 
tube. Within the tube there is suspended at the end of a brass rod MN, resting 
on the fork-shaped supports F, one of Sir WiLL1AM THomsovn’s well known gal- 
vanometer mirrors, with magnets on the back. The magnets are perpendicular 
to the axis of the tube, and the stream lines being parallel to it, the current has 
no tendency to deflect the magnet. When the tube is twisted a directing force 
is found to be experienced by the magnet, the direction being that of a force 
exerted by helical stream lines, following the lines of greatest compression of 
the twisted material.* 
The remaining parts of the apparatus, to be presently described, are intended 
to measure the intensity of this force. C is a stout copper strip, bent so as to 
form a circular arc of nearly 360 degrees. Its ends are insulated from one 
another by a piece of vulcanite; and slide over two brass rods which transmit 
the current. The circle C is supported by suitable means, so as to remain 
always in a plane perpendicular to the axis of the tube, the axis passing through 
the centre of the tube. The circle thus forms part of the circuit and exerts a 
force on the magnet. Another nearly circular coil S on the opposite side of the 
magnet, arranged so as to have its diameter easily altered, carries the current 
in such a direction as to compensate the force exerted on M by the coil C, when 
placed at a convenient distance from the magnet. This distance must be 
altered, of course, when the tube is twisted, and from the amount of shifting 
the intensity of the magnetic force exerted by the helical stream lines may be 
calculated. | 
Now, the explanation given by Sir W1LLIAm THomson of the phenomenon 
above described is this—When the tube is twisted, the material forming it is 
compressed in one direction and pulled out in another, the lines of greatest 
compression and pull being inclined at angles of 45° to the axis of the tube, in 
a plane tangential to a coaxial cylinder, passing through the point in question. 
Denote by iD the components (equal of course) of the current ¢, per unit area, 
along these directions in the unstrained state. Then we shall have 
es (1+e) and ye (1—e) 
V2 we 
* In making the experiments described below, it was found necessary to reduce the earth’s 
magnetic force nearly to nothing by means of steel magnets properly arranged for the purpose. 
—e eee 
