756 
DR. OLIVER LODGE OR ABERRATIOR PROBLEMS. 
number of reflexions, the interfering rays do not travel identical paths in opposite 
directions, but only parallel paths.^ They enter the square at one point of the semi¬ 
transparent mirror, and they leave it at another point, having meanwhile travelled 
side by side. I therefore designed a compensator, consisting of a plane piece of 
optical glass, with its faces not parallel but inclined at a very small angle ; this was 
mounted in a round cell, and made capable of measured rotation in its own plane. By 
introducing this normally into the beam, and rotating it into the right position, it was 
supposed that accidental inequalities of path could be compensated ; and also that the 
bands could be shifted by a measured amount. Hithej'to, however, no use of the 
compensator has become necessary, and I have some doubts as to whether it would 
act in the way supposed, or whether it would not merely double the number of 
bands in some positions. 
The object of the fourth or front mirror, shown in fig. 8, is to enable the light to go 
more than once round the frame. This mirror has to stand a little forward, in 
advance of the square defined by the planes of the other three, and the amount by 
which it stands forward regulates, at the same time, the width of the beam and the 
number of journeys it makes round the frame. Everything else can be permanently 
set. 
If each beam is of breadth h, and travels n times round the frame ; if the length 
of this fourth mirror is I, and the amount by which it stands forward out of the 
square is d; tlien it is easy to see, by fig. 8, that 
I = [n — 1) y/2 . h, and h = y/2 . d ; 
also that the centre of the effective part of the semi-transparent mirror, i.e. the inter¬ 
section of axes of telescope and collimator, is a fixed distance, viz. behind the 
square. 
Hence the only thing that requires re-adjustment in order to vary the number of 
times light goes round, is d, the setting forward of the front mirror. 
The 45° bevel at the ends of this mirror is to enable the whole of its (silvered) face 
to be utilised, and to allow a beam which just misses it to graze past it unimpeded 
into the telescope. (See Plate 31). 
With the front mirror 4 inches long, and the centre of semi-transparent mirror 2 
inches back from the 38-inch square formed by the other three mirrors, the most frequent 
adjustment has been to set the front mirror 1 .inch forward. A parallel beam incident 
on the centre of semi-transparent mirror, at 45°, must now go three times round 
the frame, rebounding three times from each of the three mirrors, and twice from the 
* This fact makes the bands more susceptible to some kinds of disturbance, e.g., irregularities of 
temperature or density; more stable frii^ges can be obtained by using an even number of reflexions, e.g., 
a triangle instead of a square {cf. ‘Nature,’ vol. 46, p. 500), but then the light will not go more than 
once round. 
