268 Prof. Sylvester on Newton's Rule for the [May 18, 



ant point is, that in no tissue have I been ahle to demonstrate an ' end' to 

 a nerve. In all cases the nerve-cell or nucleus exhibits fibres proceeding 

 from it in at least two opposite directions. The apparent cessation or 

 thinning off of the nerve-fibre in many tissues results from its becoming 

 so thin as to be invisible, unless special methods of investigation are 

 resorted to. It has also been shown that near nervous centres, and near 

 their peripheral distribution, the bundles of nerve-fibres and the individual 

 nerve-fibres divide into very numerous branches. The bundles of coarse 

 or fine fibres given off from a large or small trunk consist of fibres which 

 pursue opposite directions in that trunk, one set passing as it were from, 

 the other towards, the nervous centre. The nerves distributed to striped 

 muscle of all kinds and to the various forms of unstriped muscle in verte- 

 brata and in invertebrata, are arranged so as to form networks and plexuses, 

 but no indication of terminations or ends is to be seen. 



These facts seem to render it probable that the fundamental arrangement 

 of a nervous apparatus is a complete and uninterrupted circuit. This view 

 is supported by the existence- of at least two nerve-fibres in all peripheral 

 organs and by facts observed in the branching and division of individual 

 nerve-fibres and of compound nerve-trunks. I have also shown that in 

 nerve-centres it is doubtful if apolar or unipolar cells ever exist. All 

 nerve-cells have at least two fibres proceeding from them in opposite direc- 

 tions, and the multipolar cells in the brain and cord exhibit lines across 

 them which are probable indications of the paths taken by continuous 

 currents which traverse them in many different directions. 



The general inference from this anatomical inquiry is, that a current 

 probably of electricity is constantly passing through all nerve-fibres, and 

 that the adjacent tissues are influenced by the varying intensity of this 

 nerve-current rather than by its complete interruption and reestablishment; 

 so far as I know, no fact has ever been discovered which would justify the 

 conclusion that there exists any arrangement for making and breaking 

 contact in any part of the nervous system. In all cases it is probable that 

 every nervous circuit is complete, and that there is no interruption of the 

 structural continuity of a nerve-fibre at any part of its course. 



May 18, 1865. 

 Major-General SABINE, President, in the Chair. 



His Royal Highness Louis Philippe of Orleans, Count of Paris, was 

 admitted into the Society. 



The following communications were read : 



I. " On Newton's Rule for the Discovery of Imaginary Roots of Equa- 

 tions." By J. J. SYLVESTER, F.R.S. Received May 4, 1865. 



In the first part of my " Trilogy of Algebraical Researches," printed in 



