206 ON DETERMINATIONS OF THE ABSOLUTE VALUE, SECULAR CHANGE, 
magnet when suspended for vibration, has been carefully determined by repeated expe- 
riments made at Toronto with inertia rings of different weights and dimensions; and 
for greater security these experiments will be repeated with other rings at Woolwich 
when the series is closed. The intercomparison of the partial results with all the 
rings will give to the determination of the value of this constant a probable error, 
which, converted into terms of the intensity of the force, will enter as one of the con- 
stituents into the probable error of the value of the force at Toronto corresponding 
to the mean period of observation derived from the complete series. 
There is also another constant which enters into the absolute value, which has yet 
to be determined for the Toronto deflecting magnet, namely, that which enables us 
to eliminate the variation induced by the magnetism of the earth in the magnetic 
moment of a bar, in the different positions in which it is employed in the experiments 
of deflection and vibration. An apparatus for the determination of this constant has 
been constructed at Woolwich, where the necessary experiments will be made at the 
close of the series ; here also a comparison of different trials will give the probable 
error of the determination of this constant, which will thus enter into and be made a 
part of the probable error which shall ultimately be assigned to the final mean deter- 
mination of the absolute horizontal force at Toronto. 
For the purposes to be considered in this paper, however, it is not necessary that the 
values of the constants, representing the moment of inertia and the variation of the 
induction moment, should be precisely known : the mutual relation of the results ob- 
tained in different months would manifestly be the same, although the whole series 
might be affected by some slight inaccuracy in one or more of the constants employed 
in the calculation. It is not necessary therefore to wait until the constants above 
described have been determined with ultimate precision, in order to discuss the pro- 
bable error of a single monthly determination by the absolute method, and the value 
of a series of monthly determinations of this nature in investigating the secular 
change and the annual variation of the force. These will be the same, although the 
absolute value of the force when finally determined might prove to be one thousandth 
part greater for example, or one thousandth part less, than we may at present 
assume it to be. 
I subjoin therefore the following series of the results of the monthly observations 
at Toronto, from January 1845 to April 1849, as relatively correct; and as exhibiting 
the values of the horizontal force on the days of the respective months on which the 
observations were made, with an accuracy w'hich, as respects observation error strictly 
so called, must be greater than that which would be inferred from the probable error 
of a single monthly determination obtained in the usual manner ; because the pro- 
bable error so obtained will include, besides observation error properly so called, the 
effects of regular or irregular variations which may have affected the force itself on 
the particular days of observation. 
