1903 - 4 .] Mr J. K. Milne on a New Form of Juxtajoositor. 359 
otherwise satisfactory, could not claim to be entirely symmetrical 
as regards absorption with respect to the two beams of light. Of 
course, as regards symmetry, absorption is not the only thing to 
be taken into account : the reflections and refractions of the two 
beams must be the same ; but an examination of the figures will 
show that each of the two beams of light in this apparatus suffers 
two reflections and four refractions ( i.e . into the glass, into and 
out of the cement, and finally out of the glass). This form of juxta- 
positor, as the author originally designed it and had it constructed, 
was arranged in what at first sight appears to be a symmetrical 
manner, and the fallacy involved was not observed till later on. 
£ 
Fig. 3. — The letter 0 cannot be shown in the above diagram, but its 
position is the same as in fig. 2 (a) and (/ 3 ). 
In this older form the upper of the two blocks of glass which 
compose the apparatus was cut through at an angle of 45°, as 
shown by the line GB (fig. 2/3). The triangular corner so detached 
was cemented on again, the cemented junction GB in the path of 
the upper beam being for the purpose of balancing the cemented 
junction DO in the path of the lower beam. The reasoning as 
to the symmetry of this form with regard to the two beams of 
light is as follows : — Each beam is twice reflected at a silvered 
surface. Each beam passes once from air to glass and once from 
glass to air. Each beam passes through the same total amount of 
glass. Each beam passes through one cemented junction. Hence 
the juxtapositor is symmetrical with respect to the two beams. 
In this reasoning, however, we are assuming the effect of a junction 
to be the absorption of the light owing to its cement layer, while 
