32 PROFESSOR C. V. BOYS ON THE 
paper on the radio-micrometer,* I dwelt on the importance of the proper propor- 
tioning of the mirror to the rest of the suspended body. Then I only considered its 
moment of inertia and weight. In the present case these remain important, and 
there is besides the resistance to motion due to the viscosity of the air, which unfor- 
tunately is of the most serious moment. If the usual round mirror is employed, the 
definition, as is well known, is directly proportional to its diameter—that is, if its 
figure is perfect. The advantage of a large mirror is somewhat counterbalanced by 
its weight, which tends to break the fibre, so that lighter balls or a coarser fibre are 
necessary ; by its moment of inertia, which increases the already prolonged period ; 
and by the resistance which it meets with in moving through a viscous atmosphere. 
As it is important to keep the mirror or mirror and balls swinging as long as possible, 
in order to determine their periods accurately, a high decrement is most objectionable. 
By making the mirror in the form of a long bar, I have succeeded in partly reconciling 
the incompatible conditions, for not only may the weight and moment of inertia be 
reduced to less than half of that which would be due to a disc of the same diameter, 
but the definition is decidedly better, as I have proved by experiment, and as is 
shown by optical theory. I should have said that the definition in a direction 
parallel to the length of the har is better, that at right angles being obviously not so 
good. For the purpose of reading the divisions of a horizontal scale, vertical definition 
is of consequence only in so far as it is sufficient for the purpose of reading the figures 
attached. These I had made large with this object. I have already stated that the 
scale is formed by black lines on a luminous ground. By this means I am able to 
obtain a degree of reading power which might seem beyond that which a mirror of the 
size used ought to give. The mirror will form a spurious image of a luminous point 
of an oblong form, the long dimensions being vertical, and bearing the same relation 
to the short as the length of the mirror, which is horizontal, bears to its breadth, 
which is vertical. If the mirror could be made indefinitely long, the image would shrink 
to a vertical line, and horizontal definition would be perfect. Owing to the limited 
length of the mirror (‘9 inch, about) the width of the spurious image subtends an 
angle of about 5”, and this is the limiting separating power in the horizontal direction. 
Now, if the scale were made by very fine white or luminous lines upon a dark ground, 
each line would be seen as a band with shaded edges 5” wide; but, as the angular 
distance which I have been able to employ from one division to the next is only 14”, 
the lines would have appeared half as broad as the spaces. If the lines on the real 
scale were of sensible thickness, then the proportion of apparent line to space would 
have been higher. If, on the other hand, the ground is luminous, the lines are dark 
and are made rather coarse ; the effect of the spreading of the light is to pare off the 
dark edges, and leave the appearance of a finer line, which, though it is not sharp, is 
symmetrical, and, as a recurring phenomenon, allows of definite observation to one- 
tenth of a division, ¢.c., in the actual case to 1:4”. This corresponds to a movement 
* © Phil. Trans.,’ Jan., 1889. 
