On the Number of Imaginary Roots in an Equation, 113 



radiated off as heat-pulses. The explanation is the same as that 

 of the molecular absorption and subsequent radiation of the 

 sethereal pulses of radiant heat, already given (p. 426). When 

 the condition of things is such that the particles in the circuit 

 become polarized, a greater amount of heat should be developed, 

 because a part of the electric movement within the molecular 

 atmospheres, which was before confined to their upper portions, 

 now occurs at greater depths, where the universal aether is more 

 dense. Thus, when the resistance to the passage of the current 

 becomes greater, more heat is developed. Heat may also be 

 evolved, under special circumstances, as a consequence of a com- 

 pression of the molecular atmospheres produced by the current. 

 We shall see, in the remaining portion of this memoir, that it 

 is to these same impulses of the moving electric upon the universal 

 (ether that are to be ascribed all the external actions of the cur- 

 rent — as attracting or repelling wires conveying currents in the 

 same direction with the given current or in the opposite direc- 

 tion, giving motion to the magnetic needle, developing mag- 

 netic or diamagnetic currents in the compound molecules of 

 adjacent masses, and inducing currents in wires or metallic 

 bodies in the vicinity. 



[To be continued.] 



XfV. Demonstration of Newton's Rule for determining the num- 

 ber of Imaginary Roots in an Equation. By J. R. Young, 

 formerly Professor of Mathematics in Belfast College*. 



I REQUEST permission to submit the following investigation 

 to the examination of the readers of this Journal for the 

 following reasons. 



In l The Times ' of June 28 there appeared an article, in large 

 type, headed "A Mathematical Discovery," which announced 

 that Professor Sylvester had succeeded in demonstrating what 

 everybody else had failed in their attempts to prove, namely, 

 Newton's Rule for Imaginary Roots, and that he would expound 

 his views in a Lecture to be delivered that evening at King's 

 College. 



I was present at the Lecture, and felt it to be due to myself 

 to draw Professor Sylvester's attention to the fact that a demon- 

 stration of the Rule in question was published, so long ago as 

 the year 1843, in a tract of mine entitled " Researches respect- 

 ing the Imaginary Roots of Numerical Equations." He stated, 

 in reply, that my investigation was, like all that had preceded 

 it, a failure : it was no proof at all. 



Seeing that so much interest has been excited on the subject 

 * Communicated by the Author. 



Phil. Mag. S. 4. No. 201. Vol. 30. Aug. 1865. I 



