12 
REPORT ON THE COMPLETION OF 
The points of principal consequence are, well made hardened knife edges, and a 
magnet that will not lose magnetism. The temperature coefficients of well hard- 
ened thin bars, especially of those supplied by Robinson, have been very small ; 
and it would not be difficult for the maker, by a few experiments, to diminish or 
destroy the effect of temperature altogether in the manner suggested afterwards. 
The only subject then remaining for the maker's skill would be the formation of a 
powerful and periiianent magnet with a hard well-made knife-edge. I have 
already shown in other places, than no dependence can be placed on the coeffi- 
cients involving the time of vibration of this needle. 
Mechanical Temperature Compensation. — The difficulties connected with the 
diminution of the temperature coefficients of magnets, for the purposes of the 
bifilar and balance magnetometers, may be, to a great extent, aA^oided by mecha- 
nical compensations. Such compensations, by a little experimentation and previous 
calculation, may be sufficiently complete for most self-registering apparatuses, to 
render considerations of the varying temperature negligible : even for the more de- 
licate apparatuses, however, any incompleteness of the temperature compensation 
may be determined by the process which I have emploj^ed. The following me- 
thod of compensation may be adopted for the bifilar magnet : — Let the upper ex- 
tremities of the suspension wires be attached to the ends of two brass rods, which 
approach each other within an interval equal to the diameter of the lower wheel, 
and let the other ends of the brass rods be fixed to a beam of wood, so that an 
increase of temperature will cause the free ends of the rods to approach each 
other, by an amount equal to the difference of their expansion and that of the 
wooden beam to which they are fixed. Such an approximation will diminish the 
directive force of the wires, and by a proper regulation will compensate for the 
diminution of the magnet's moment. If the suspended wires are silver, and the 
lower wheel is of brass, the coefficient (<?) of contraction of the space betwixt the 
suspension wires at the top will be found from the equation of equilibrium to be 
where q is the temperature coefficient. Thus, in the case of the JMakerstoun 
bifilar = 0*000266, the interval of the wires is nearly 0'5 inch, and, therefore, the 
brass rods would require each to be about 7^ inches long, in order that the in- 
terval be diminished 0-000266 of itself, or 0-000138 inch; the difference of the co- 
efficients of expansion of brass and wood being assumed =0-0000085. ]\[ag- 
nets with a temperature co-efficient of 0-0001 would require brass suspension 
rods of3 inches in length, or less in proportion as the interval of the wires is less 
than 0-5 inch. 
For the balance magnet ; let a brass rod be fixed to the magnet near its south 
end, but free to expand towards the north, and liaving as much to the north of 
the axle as to the south ; it is obvious that when the temperature increases the 
