254 The Rev. H. Lloyd on the mutual Action of permanent Magnets. 



eliminate the actual changes of declination which may occur in the interval of 

 the two parts of the observation, simultaneous observations should be made with 

 an auxiliary apparatus in another apartment ; or, should such an apparatus be 

 not at hand, the effect of the changes may be got rid of by making a series of 

 readings of the magnet a, with the deflecting magnets alternately in the two 

 positions. The amount of the deflection, thus determined, is to be applied 

 as a correction in measurements of the absolute declination : being a constant 

 quantity, or nearly so, its effect upon the declination changes may be disregarded. 

 Lastly, there being no disturbing force upon the magnet a, in the magnetic 

 meridian itself, the absolute horizontal intensity, determined by experiments of 

 vibration and deflection, according to the method of Gauss, will need no cor- 

 rection.* 



On the other hand, the disturbing force exerted upon the magnet b, by the 

 other two, is directed in the magnetic meridian itself, and therefore con- 

 spires with, or opposes, the force of the earth. The correction required for 

 its action is determined with the same facility as in the former case. We have 

 only to reverse the magnets a and c simultaneously, and to note the change of 

 position of the magnet b thereby produced. Half the change, converted into 

 parts of the whole force by multiplying it by a coefficient already known, is the 



ratio, -, of the disturbing force to the total force ; and, in order to correct for this 



f 

 force, we have only to multiply the observed results by the coefficient 1 ::p -, usmg 



F 



the upper sign when the disturbing action conspires with that of the earth, and 

 the lower when it is opposed to it. 



Finally, with respect to the magnet c, the disturbing action, being perpen- 

 dicular to the plane in which the magnet is constrained to move, is destroyed by 

 the reaction of its supports, and no correction is needed. 



* The remdtani of the force of the earth, and of the disturbing action, will of course differ, 

 theoretically, from the former ; but, in genera), by an inappreciable amount. If x denote the 

 earth's horizontal force, and J the deflection produced by the disturbing action, the resultant force 

 will be X secant i. Now, supposing J to be two minutes (which is greater than any amount it can 

 have with magnets of the size of those employed in the Dublin Observatory, and at the distances 

 recommended below) the resultant force will exceed x by the quantity .0000002x. 



