AND METEOROLOGICAL INSTRUMENTS, BY PHOTOGRAPHY. 
87 
temperature of the magnet may be presumed identical with that of the water in 
which it is immersed. This is ascertained by a thermometer with a long cylindrical 
bulb reaching nearly from the top to the bottom of the vessel, by which means it is 
presumed that the average temperature of the water will be most nearly determined. 
These arrangements having been made, a simultaneous register of the two magnets 
is obtained, during the progress of which, the temperature of the magnets must be ob - 
served at recorded times, and at any convenient intervals of from a quarter of an hour 
to two or three hours, the intervals of observation being least at the highest and lowest 
temperatures of the trial magnet, when the change is most rapid. Having marked 
upon the register the epochs of observation, the differences between the changes of 
position of the lines at these points may be measured by a scale, and these differences 
will very accurately represent the scale-value of the changes of force due to the cor- 
responding changes of temperature of the trial magnet ; for ordinarily the tempera- 
ture of the standard magnet may be considered constant during each of the intervals 
of observation. 
A sufficient number of these differential scale-readings having been obtained, they 
may for reduction be conveniently arranged in five groups, between the temperatures 
32°, 45°, 60°, 75°, 90°, 100°. Denoting the differences of temperature by D, the mean 
temperatures of the periods of observation by M, and the scale-readings by R, the 
mean temperature of each group is found from the formula 
2(MxD) 
2(D) ^ 
and the corre- 
sponding mean value of R for an interval of 1° Fahr. from the formula 
2(DxR) 
2(D2) ’ 
which may be represented by AK, K being the temperature coefficient. As it has 
been found convenient to reduce magnetic observations to the temperature of 32° 
Fahr., let the excess of the above mean temperatures above that point be represented 
by t, and let x and be the coefficients of the first and second powers of t in the value 
of K ; then five equations will be obtained of the form 
AK.=^-1-3/^, 
which being solved by the method of least squares, will give probably correct values 
of X and y. From the form of the preceding equation, it follows that 
The above method has been applied to determine the temperature coefficients of two 
bar-magnets marked C.B, VIII. and C.B. IX=^. But as the premises on which the 
observations were made present the usual obstacles of a dwelling-house to the free 
action of magnetic instruments, namely, the large mass of iron contained in the grates, 
only one position could be found in which the effects of the most contiguous masses 
of iron would nearly neutralize each other : and in consequence of this difficulty, the 
register of the trial-magnet here obtained has been compared with that obtained 
* These magnets belong to a complete set of self-registering photographic apparatus intended to be pre- 
sented to the Observatory at Cambridge by the Master of Trinity College. 
