in 



needles to the coil ; 3. the removal of obstructions to the rota- 

 tion of the needles ; 4. the means of inducing in the needles the 

 least difference of polarity that is consistent with their func- 

 tion ; 5. a method of detecting and preventing derangement 

 of the needles, arising from forces which cause in them a ten- 

 dency to stand transversely to their true position ; 6. a con- 

 struction of the needles which renders available the operation 

 of a strong or a weak directive force, as may be required ; 

 7. the introduction of a controlling graduated magnetic power 

 for regulating the deflecting influence of voltaic forces on the 

 needles. 



" I venture to hope that those improvements, along with 

 the several adjustments and facilities added, will render the 

 instrument more convenient, will increase its sensibility, and 

 contribute to the accuracy of its indications." 



The President observed, that all the facts respecting the 

 position of equilibrium of the astatic needle, to which Mr. 

 Donovan had directed the attention of the Academy, and 

 which (as far as he was aware)' he has been the first to notice, 

 were simple and immediate consequences of theoretical laws. 



When two magnetic needles are united by a fixed vertical 

 axis passing through their centres, and perpendicular to both, 

 the moment of the force exerted by the earth upon them is 

 the sum of the moments which it exerts upon each needle 

 separately, and is, therefore, 



X(Msin u + M' sin u) ; 



in which M and M' denote the viagjietic moments of ihe two 

 needles, u and u' the angles which their magnetic axes make 

 with the magnetic meridian, and A' the horizontal component 

 of the earth's magnetic force. In the state of equilibrium this 

 moment is nothing ; so that if u« and Mq' denote the correspond- 

 ing values of u and u, there is 



M sinuo + M. sin Mo' = 0- (0 



