The revolving wheel has its periphery formed by two equal conical surfaces or other surfaces of revolution. The axes of the two conical surfaces are each parallel to the axis of the revolving wheel, at exactly equal distances therefrom, and the three axes lie in the same plane. The vertices of the conical surfaces are at equal distances on opposite sides of the line of sight. In manufacturing, the wheel is first made as a disk of uniform thickness. It is then chucked in a lathe eccentrically, and a straight line motion being given to the cutting or grinding tool, the conical surfaces are generated. The wheel is then rechucked eccentrically on the opposite side, and the other conical surface is generated by the cutting or grinding tool, having the same straight line motion as before. The result is that the periphery of the wheel has its two sides uniformly sloping at equal opposite angles, while the ridge of intersection of the two surfaces crosses and recrosses the axis of vision during each revolution. This wheel is driven with a motion communicated from a suitable motor, either spring, electric, or any form which will produce absolutely regular motion-and at the same time afford means for easily adjusting the speed. In the instrument shown an expansion governor is utilized driven at a carefully arranged ratio speed, but the connexion between the spindle carrying the governor and that carrying the reflecting wheel is not rigid, but effected by means of a coiled spring. The most perfect accuracy of centreing is essential. Outside the box are the remontoir, stopping, and starting lever, and speed adjustment, a spring motor being used.

The peculiar shape of the reflecting-wheel affords means for using it in manners quite impossible in any other form of colour photometer, that is to say, it may, at will, test lights at various angles from the horizontal. Having found the careful cutting of the angles of the wheel so vital it necessarily follows that when lights out of the horizontal are being tested, the box containing the wheel must be just as carefully turned on its axis for preserving the arranged conditions. A double quadrant scale (one scale being numbered at double the actual angle) and a small sighting or view-finding attachment enable the angle formed by the horizontal of the one light and the altitude of the other to be accurately ascertained, and the box to be placed at the correct angle of bisection.

The photometer is made to suit any bar or scale. The standards of dimensions are those of the Lummer-Brodhun apparatus and the ordinary Bunsen disk-box.

XLI. On the Viscosity of Pitch-like Substances. By Prof. F. T. TROUTON, F.R.S., and Mr. E. S. ANDREWS, B.Sc.*

THE

HE various methods which have been proposed for measuring viscosity meet with difficulties when it is attempted to apply them to the measurement of the viscosity of bodies such as pitch. The girder method has been applied to examine the viscosity of ice as well as methods depending on direct extension and compression; but these apparently did not lead readily to a numerical determination of the coefficient of viscosity. The application of Stokes' method, depending on the rate at which a spherical body-say a lead bullet-sinks through the material, seems apparently to have been prevented by the difficulty of knowing exactly its velocity in the middle of the substance, the terminal effects leaving considerable uncertainty. As described later, this particular difficulty was surmounted by the use of Röntgen rays in some experiments made to compare the coefficient obtained by this method and that by the method described in this paper.

To obviate some of the difficulties, a method was proposed involving the torsion of a cylindrical bar. In this method a constant torque was applied to a cylinder of the substance, and the relative motion of the ends observed. From these and the dimensions of the body the viscosity was calculated.

From symmetry we may assume that any two planes in the body, lying at right angles to the axis of the cylinder, move over each other, about the common axis, remaining plane all the while.

Let Sx be the distance apart of the two planes. Then, if u is the coefficient of viscosity of the material of the cylinder (supposed independent of the velocity), and do the relative angular velocity of the planes, we have

where U is the relative angular velocity per centimetre of length of the cylinder, and R is its radius.

The form finally adopted for applying the method consisted in a shaft turning freely on anti-friction wheels with a pulley attached, from which hung a weight for the purpose of *Communicated by the Physical Society: read June 12, 1903.

applying the constant torque (see fig. 1). The shaft carried a square socket for the purpose of gripping the squared end of the cylinder of the substance, which was made to fit exactly. A similar but fixed socket prevented the other end from turning. The rate of rotation was observed by means of a divided circular disk carried on the shaft. With this apparatus the experiments described below were undertaken

to test whether (1) the rate of rotation was proportional to the torque; (2) the rate of rotation of cylinders of the same material was inversely as the fourth power of the radius.

Incidentally two unsuspected effects were at once disclosed by the use of this apparatus. One is that the coefficient of viscosity of bodies such as pitch is a function of the time, observations showing that the velocity of flow for a given stress diminishes with time from its initial value down to a constant quantity. The second is that on removing the stress there is a flow back in the opposite direction, which gradually diminishes to zero with time.

The method lends itself also to the determination of the coefficient of viscosity at different temperatures, as the cylinder can be conveniently surrounded by a jacket and kept at any required temperature. This mainly arises from its not being necessary to have access to the bar while under observation.

In this way the coefficient for soda-glass was determined at temperatures ranging between 500° C. and 700° C., and that of pitch from 0° C. to 15° C,