225 



the humidity of the atmosphere is probably about one-half of 

 the total range ; so that the limit of error of declination due 

 to this cause may be considered to be 0''5. 



It will, of course, be understood that the effect here stated 

 is that produced on the individual thread ; and it is given 

 merely as an example of the amount of error to be expected 

 under ordinary circumstances. If the separate fibres which 

 compose the thread were perfectly parallel, and equally 

 strained, we have no reason to suppose that the changes of 

 moisture would produce any change of torsion. 



The next subject which claims our attention is the dis- 

 turbance produced in the position of the magnet by the action 

 of the other magnets of the Observatory, or by any other extra- 

 neous magnetic forces. The course which has been pursued 

 at the Dublin Magnetical Observatory in determining the 

 effect exerted by other magnets is very simple, and admits of 

 the utmost precision. It consists in reversing the acting 

 magnet (or turning its magnetic axis through 180°), and ob- 

 serving the new position of the magnet acted on ; the diffe- 

 rence of the two positions is double the error sought. In fact, 

 the moment of the force exerted by the former magnet upon 

 the latter is 



2^ {sin(^ + 0)-3sin(0-0)}; 



in which m and rri denote the magnetic moments of the two 

 magnets, Z) the distance of their centres, and ^ and ^ the 

 angles which their magnetic axes form with the joining line.* 

 The value of this quantity is unaltered, although its sign is 

 changed, when 180° + ^ is substituted for 0; and, conse- 

 quently, the disturbing effect is equal^wA opposite to that pro- 

 duced in the original position of the acting magnet. 



It is scarcely necessary to advert to the advantages of 

 this course over that which is sometimes adopted, and which 



* Trans. Royal Irish Academy, vol. xix. p. 163. 



