178 
MR. C. V. BOYS ON THE RADIO-MICROMETER. 
Owing to the fact that, with increase in the breadth of the cu’cuit, the cross piece 
becomes increasingly mischievous, both on account of its moment of inertia and of its 
resistance, it is clear that the circuit cannot be too nairow until the increased length 
becomes such that it is inconvenient to provide a magnet and pole pieces which will 
enclose so great a length. In another wa,y the thick wire which the narrow circuit 
recpiires is advantageous, as will appear shortly. 
Having thus found the best relations between the variable copper and the arbitrary 
junction and mirror, it remains to see how these may be modified with advantage. 
As, with the narrow form of circuit, the smallest galvanometer mirror has a moment 
of inertia many times as great as that of the active bars, and since the copper must 
have a moment of inertia equal to their sum, it is evident that it will be advantageous 
to reduce the dimensions of the mirror until it again becomes small in comparison. 
By this reduction the defining power of the mirror, supposed optically perfect, is also 
reduced, and thus there must be a limit at which as much is lost by the increasing 
want of definition as is gained by the diminishing moment of inertia. 
The defining power of a perfect mirror—and the smaller the mirror the more likely 
it is to be perfect—varies with its diameter, while the moment of inertia is propor¬ 
tional to the fourth power of the diameter when the thickness is constant, or to the 
fifth power if the thickness is also proportional to the diameter. To find the best 
diameter it is necessary to remember that the fixed moment of inertia K is the sum of 
the moment of inertia of the junction and of the mirror Thus, the accuracy 
of observing a deflection = K„7''y2 (K,„ -fi Kj), where n = 4 or 5 as the case may be. 
The best size of mirror then will be such that 
; k = -5' = 4K„„ when n = 4, 
O O 
or that 
Tr i'i-i 7 5K; 1 
Ix;m= ; A- = = 5K.„„ when n = 5. 
Using the thinnest microscope cover glass, about H mm. thick, it wdll be found that 
the size of mirror which gives the best result when the antimony-bismuth bars have 
the dimensions which will be assigned to them hereafter is one having a diameter of 
2| mm. 
I have picked out a number of discs sufiiciently thin, silvei'ed them, cut pieces of 
the proper size, and then examined them by reflection. With mirrors as small as this, 
the eye itself takes the place of the usual telescope, and it is easy to choose those 
which allow the eye to see by reflection fine distant lines as clearly as if the light 
came direct. The only difficulty I have had in attaching these mirrors to the stem 
arises from the bending of the glass under the action of even the smallest quantity of 
cement. If sealing-wax is used—and this is tlie least magnetic of all the cements I 
have examined—a speck less than 1 mm. in diameter will, by its capillarity wdien 
