Prof. Young on Newton's Rule for Imaginary Roots. 289 



day). If the magnet rotates in the opposite direction, its im- 

 pulses against the aether will be correspondingly increased, and 

 the result will be the same. 



Faraday, in certain papers originally published in the Philo- 

 sophical Magazine and the Philosophical Transactions, has in- 

 dulged in ingenious speculations upon the probable physical 

 character of the lines of magnetic force, and distinctly intimates 

 that he inclines to the opinion that they have in reality a physi- 

 cal existence, correspondent to their analogues the electric lines, 

 instead of being simply " representants of magnetic power," or 

 lines of resultant magnetic action. In speculating upon the 

 question in what this physical existence may consist, he remarks 

 that ' ' it may be a vibration of the hypothetical cether " (along 

 the lines), " or a state or tension of that aether equivalent to either 

 a dynamic or a static condition, or it may be some other state." 

 The results arrived at in the present paper are opposed to these 

 speculative ideas of the great English physicist, for our conclu- 

 sions are that the lines upon which the phenomena of induction 

 by a magnet depend are merely lines of equal magnetic action ; 

 but the action is that of a force whose existence has not here- 

 tofore been recognized, viz. the so-called impulsive force of the 

 magnet. 



[To be continued.] 



XXXVIII. On Newton's Rule for Imaginary Roots. By J. R. 

 Young, formerly Professor of Mathematics in Belfast College*. 



IT is not the object of the investigation at page 114 of this 

 Journal to determine the exact number of imaginary roots 

 in a given numerical equation : Newton's Rule does not under- 

 take so comprehensive an office. All that is aimed at in the in- 

 vestigation referred to, is the discovery of the number of inde- 

 pendent imaginary pairs; all of which have this peculiarity, 

 namely, they necessitate the entrance of imaginary roots, ful- 

 filling the first or second of the conditions at p. 114, into the 

 limiting cubics at p. 115. 



As a distinctive epithet, we may call those imaginaries in the 

 primitive equation which have this peculiar character primary 

 pairs', and the object is to ascertain how many of such pairs 

 enter the equation. 



The desired information, as appears from what has just been 

 said, is to be derived exclusively from the cubic equations alluded 

 to : these are each to be submitted to the first and second of the 

 tests for imaginary roots given at p. 114, the first test being 

 employed for the leading three terms of each cubic, and the 



* Communicated by the Author. 



Phil. Mag. S. 4. Vol. 30. No. 203. Oct. 1865. U 



