1877.] 



and Induction-coefficients of Magnets. 



219 



the experiment is repeated with water at 35° F. After this another series 

 of observations is commenced with water at 85° F., 60° F., and 35° F., 

 and this is again repeated once or twice. 



The observations are first corrected for changes of the earth's magnetic 

 force during the experiment by means of simultaneous readings of the 

 curves given by the self-recording magnetometers of the Observatory ; 

 and the reduction is performed according to the method given by the 

 following formula, due to Prof. B. Stewart, the coefficients determined 

 being q and q, which represent the decrease of the magnetic moment of 

 the magnet produced by an increase of temperature of 1° F. 



Demonstration of the Formula for finding Temperature-correction. 



Let ^-=Jr 3 s ^ nu be the normal equation of equilibrium at temp. t , 

 then m{ 1 — q(t — t ) — q'(t — t ) 2 } = JX^ 3 sin (u — du) is the altered equation. 

 Hence |r 3 X sin u{ 1 — &c. } = -|Xr 3 sin (u — du) ; 



.*. sin u — sin uq(t — 1 ) — sin uq(t — t ) 2 = sin(u — du). 

 Let sin u (q) = x, sin u {qf ) = y ; then 



* (* — + y (' ~~ ^ ) 2 =sin u — sin (u— du). 



Demonstration of the method of using the Self-recording Magnetographs 

 in eliminating the effects of disturhance in ascertaining Temperature- 

 correction. 



(1) Let the Horizontal Force alter; 



let ^=|r 3 sin w be the normal equation, 



and -g- = \r z sin (u— du) the altered one. 



Hence ^ = |r 3 cos u du ; 

 hence du = ^5 tan u . 



(2) Let the Declination alter ; the equation is still ^ = ^r 3 sin u ; hence 



the angle of deflection remains the same, or the deflected magnet makes 

 the same angular change as the declination magnetograph. 



Of the temperature-coefficients of 109 magnets which have been ex- 

 amined, the value of q' has only been determined for 79. Taking the 

 whole series we find the following : — 



