Appendix.] 



TERRESTRIAL MAGNETISM 





•'■i 



rU 



r 



Vjjl 



4« 



j! 





He 



i 



by 



0'- 



r f , 



of vibration is as small as above directed, the correction for it may be 

 disregarded, except wlien great accuracy is sought 



It is desirable to commence the observations for the determination of 

 the absolute horizontal force with the experimenis of vibration ; then to 

 Hiake the series of deftection experiments ; and then to repeat the expe- 

 riments of -vibration. The experiments of deflection and vibration thus 



described will cr-- plcte a single determination. There should be three 

 such determinations with each of the 3* 67-inch magnets at a base 

 station; and all should not be made on the same day, lest it should 

 happen to be a uay on which the magnetism of the Earth is disturbed. 



The constant tt'-* K (page 34) is obtained from tt, denoting the ratio of 

 the circumference of a circle to its diameter, and K the moment of inertia 

 of the magnet, including the stirrup (and its appendages) in which the 

 magnet rests during the experiment of vibration- To determine the 

 moment of inertia, the magnet, stirrup. &c. is vibrated a second time 

 with the addition of a metal ring, of which the exterior and interior 

 diameters, as well as the weight, are accurately known. If r and r' 

 denote the exterior and interior radii, (in decimals of a foot,) and w the 

 weight, (in grains,) the moment of the inertia of th<: ring Is 



K' 



^(r2 + /2) W; 



and if T denote the time of vibration without the ring, and T^ the time 



of vibration with the addition of the ring, the moment of the inertia of 



the magnet and stirrup in the vibrations without the ring is given by 

 the formula, 



K 



^'{t^^ 



T^ 



T 



a 



As this determination requires several repetitions, it is usually made 

 before the instrument is put into the hands of the observer ; but as its 

 value must be found afresh if any alteration be made at any time in the 

 stirrup or its appendages, a ring is always supplied for the use of the 



observer. 



If the temperature of the magnet be not the same in the experiments 

 of deflection and vibration, the value of »i X as obseiyed at the time of 

 the experiments of vibration, must be reduced to that which it had 

 at the time of the experiments of deflection. For this purpose it is 

 necessary to know the amount of change in the magnetic moment of the 

 magnet occasioned by one degree of temperature. This is called the 

 temperature coefBcient, and is usually denoted by q. As its determina- 

 tion requires apparatus with which ships are not supplied, it has been 

 customary to furnish it with the instrument. Then if t and to be the 

 temperature of the magnet at the times of deflection and vibration 



'j^ 



