‘2*2 MK. BROOKE ON THE AUTOMATIC REGISTUATION OF MAGNETOMETERS, 
photographic register of the variations of the instrument is now to be obtained by 
the means described in the two first papers of this series*, the temperature of a ther- 
mometer enclosed in the zinc box, and placed as near as possible to the magnet being 
simultaneously recorded at convenient intervals of time, corresponding to tempera- 
ture changes of not more than two degrees. If the change of temperature is slow, 
that is, if a variation of 40° Fahr. is spread over a space of at least six or eight hours, 
the temperature of the mercury may fairly be assumed to be the same as that of the 
bar. If, in order to avoid the consumption of time, or for any other reason, it should 
be found desirable to observe during more rapid changes of temperature, some such 
means as those before mentioned must be employed to ensure a uniformity of 
radiating eapacity in the magnet, the compensator, and the thermometer. 
A photographic register of the bifilar variations during known changes of tem- 
perature having been thus obtained, should now be compared with that of another 
bifilar instrument of which the temperature has undergone comparatively little varia- 
tion, as will be the case under ordinary circumstances: a comparison of these will 
readily show whether the instrument under trial is over- or under-compensated, and 
the requisite correction may be made by shifting the sliding clamps. A few repeti- 
tions of the same process will suffice to give the requisite accuracy of correction. 
It may be remarked that the most satisfactory method would be to register 
simultaneously a carefully compensated instrument on the same sheet of paper ; the 
means of doing this are not however at present in existence. 
Compensation of the Balanced Magnetometer. 
The horizontal displacement of the centre of gravity by metallic expansion is the 
most palpable means of effecting a compensation for the changes of temperature in 
this instrument; the only question is the precise method by which the numerical 
value of the temperature coefficients can be most nearly represented. The plan 
adopted has been that of attaching a small thermometer parallel to the axis of the 
magnet, and as nearly as possible in the same horizontal plane with the centre of 
gravity of the magnet and its appendages. The statical moment of the mercury 
displaced from the bulb of the thermometer by any given elevation of temperature, 
as above 32° Fahr., may be represented by the same formula which expresses the 
temperature coefficients, namely, 
cx-\-ex^. 
For let w be the weight of mercury contained in one degree of the tube, and let 
the tube be taken such that the distance from the centre of the bulb (which is pre- 
sumed to be a symmetrical figure of revolution) to the point 32° Fahr. may be he, 
and length of one degree 2he ; then at any temperature 32°-j--*° the statical moment 
of the mercury displaced by a small change of temperature, dx, will be te {kc-\-2hex) dx, 
* Published in the Philosophical Transactions, Part I., for 1847. 
