304 KLBCTR08TATIC8 AND MAGNETISM. 



idea of inversion by reciprocal radii vectors, which is now well known to all 

 geometers, having been, we suppose, discovered and re-discovered repeatedly, 

 though, unless we are mistaken, most of these discoveries are later than 1845, 

 the date of Thomson's paper. 



But to return to physical science, we have in No. vn. a paper of even 

 earlier date (1843), in which Thomson shews how the force acting on an elec- 

 trified body can be exactly accounted for by the diminution of the atmospheric 

 pressure on its electrified surface, this diminution being everywhere proportional 

 to the square of the electrification per unit of area. Now this diminution of 

 pressure is only another name for that tension along the lines of electric force, 

 by means of which, in Faraday's opinion, the mutual action between electrified 

 bodies takes place. This short paper, therefore, may be regarded as the germ 

 of that course of speculation by which Maxwell has gradually developed the 

 mathematical significance of Faraday's idea of the physical action of the lines 

 of force. 



We have dwelt, perhaps at too great length, on these youthful contributions 

 to science, in order to shew how early in his career, Thomson laid a solid 

 foundation for his future labours, both in the development of mathematical 

 theories and in the prosecution of experimental research. Mathematicians how- 

 ever will do well to take note of the theorem in No. xm., the applications 

 of which to various branches of science will furnish them, if they be diligent, 

 both occupation and renown for some time to come. 



We must now turn to the next part of this volume, in which the 

 mathematical electrician, now established as a Professor at Glasgow, turns his 

 attention to the practical and experimental work of his science. In such work 

 the mathematician, if he succeeds at all, proves himself no mere mathematician, 

 but a thoroughly furnished man of science. And first we have an account of 

 that research into atmospheric electricity which created a demand for electro- 

 meters ; then a series of electrometers of gradually improving species ; and lastly, 

 an admirable report on electrometers and electrostatic measurements, in which 

 the results of many years' experience are given in a most instructive and 

 scientific form. In this report the different instruments are not merely described, 

 but classified, so that the student is furnished with the means of devising a 

 new instrument to suit his own wants. He may also study, in the recorded 

 history of electrometers, the principles of natural selection, the conditions of the 

 permanence of species, the retention of rudimentary organs in manufactured 



