of the glass = t / μ, where t is the thickness of the glass, and μ is the index of refraction.
We must also remember that if the line of suspension does not pass through the point of reflexion, the position of M will alter with θ. Hence, when it is possible, it is advisable to make the centre of the mirror coincide with the line of suspension.
It is also advisable, especially when large angular motions have to be observed, to make the scale in the form of a concave cylindric surface, whose axis is the line of suspension. The angles are then observed at once in circular measure without reference to a table of tangents. The scale should be carefully adjusted, so that the axis of the cylinder coincides with the suspension fibre. The numbers on the scale should always run from the one end to the other in the same direction so as to avoid negative readings. Fig. 15
Fig. 15.
represents the middle portion of a scale to be used with a mirror and an inverting telescope.
This method of observation is the best when the motions are slow. The observer sits at the telescope and sees the image of the scale moving to right or to left past the vertical wire of the telescope. With a clock beside him he can note the instant at which a given division of the scale passes the wire, or the division of the scale which is passing at a given tick of the clock, and he can also record the extreme limits of each oscillation.
When the motion is more rapid it becomes impossible to read the divisions of the scale except at the instants of rest at the extremities of an oscillation. A conspicuous mark may be placed at a known division of the scale, and the instant of transit of this mark may be noted.
When the apparatus is very light, and the forces variable, the motion is so prompt and swift that observation through a telescope
