the intensity of magnetic forces , &c, 1 1 
paratus. N, S, (Fig. 2,) denote the ends of the instrument 
to be placed towards the magnetic north and south ; c, the 
centre of the needle ; n and 5, its north and south poles ; 
, (Tn , the north and south of the north magnet ; 3 , o*g , 
the north and south poles of the south magnet : the magnets 
being fixed on boards which, sliding in grooves, may be 
made to approach or recede from the needle at pleasure. 
In the observations which I first made on the effects of 
changes of temperature, the centres of the magnets were at 
the same distances from the centre of the needle as they were 
during the observations on the diurnal changes in the direc- 
tions of the needle, which it was my object to reduce, and 
which will be given in the conclusion of this paper : this dis- 
tance was 21.21 inches. We have therefore in this case 
R = 21.21 inches, and, from what I have before said, r= 2.14 
inches, and ^==5.14^ if we substitute these values in the 
equation (C), it will become 
M. — F. (.004690814 + .000829329 cos. <p) = o. (a) 
Observing then the value of <p at any particular tempera- 
ture of the magnets, by means of this equation I could 
readily obtain the corresponding value of F in terms of M ; 
and by varying the temperature of the magnets, I obtained 
the variation of the intensity of their forces, corresponding 
to such change of temperature. The observations contained 
in the following table were made thus ; I first noted the time, 
which is set down in the first column, and then the tem- 
perature of the north magnet ; after which I placed the ther- 
mometer on the pole of the south magnet : I next observed 
the westerly point, at which the needle was held in equilibrio 
