242 



NATURE 



[January 12, 1899 



discharge in gases ; studies of the mysterious photo- 

 electric effects at the surface of bodies and throughout 

 the body of a gas, and that cloud-producing action which 

 seems to provide us with the opportunity of isolating 

 electrons, obtaining a drop of liquid with only one of 

 these upon it ; studies of kathode rays and of the velocity 

 of the electric carriers in them. The argument by which, 

 in this concluding study, there is an attempt to prove 

 that these cannot be either larger than molecules, nor of 

 a comparable size, is not particularly conclusive. Among 

 the reasons given for concluding that these carriers are 

 not larger, it is assumed that-the resistance to their motion 

 would obey the laws of motion of a body moving slowly 

 through a viscous medium. This is not at all true of a 

 minute projectile moving with a velocity of at least one 

 hundred times the velocity of the molecules of the gas. 

 To such a projectile the gaseous molecules would be 

 practically at rest, and the resistance would be, as Lenard 

 observed, proportional to the density of the gas. The 

 argument against their being of a size about the same as 

 that of the other gaseous molecules depends on the 

 assumption that the effective size of a molecule is inde- 

 pendent of its rate of motion, a conclusion which is at 

 variance with the known laws of diffusion of gases at 

 various temperatures, and is contrary to such a probable 

 hypothesis as that the actions between molecules is more 

 like that between centres of force with rapidly changing 

 forces near them than like that between hard spheres. 

 For a comet to be deflected by a given amount when 

 going near the sun, it should pass much closer to the 

 sun if its velocity is large than if its velocity is small. 

 The effective size of the sun as a deflecting cause for 

 comets very largely depends on the velocity of the comet. 

 On these principles rapidly moving molecules might go 

 much further through a gas than the free path of an 

 ordinary molecule. When the disagreement between 

 the theory of hard spheres and the observed laws of 

 diffusion at different temperatures is measurable, and it 

 only corresponds to alterations of velocity to about twice 

 the normal, we may naturally expect great variations 

 when dealing with velocities of about one hundred times 

 the normal, which would correspond to a temperature of 

 some 2,000,000 C. 



At the same time, there is a good deal of other evi- 

 dence in favour of the suggestion that in kathode rays 

 we are dealing with carriers of smaller mass than atoms. 

 One would naturally conclude that we were here dealing 

 with what might be described as disembodied electrons, 

 i.e. with electrons separated from the atoms with which 

 they seem in general so intimately connected. Most 

 theories of electrolysis assume that an electron can be 

 transferred from the atom in the liquid to the plate, and 

 almost any theory of metallic conduction must involve 

 the transference of electricity from molecule to molecule 

 in the conducting solid. The only difference between 

 these cases and that of the supposition that kathode rays 

 are torrents of electrons is as to the distance the electron 

 can travel from molecule to molecule. If it can ever 

 leave one molecule to join on to another, why may it not 

 jump some centimetres of space between them.' This 

 reconciles to some extent the radiant matter and pure 

 ether theories of the kathode rays. It makes them 

 essentially an ether phenomenon, while at the same time 

 NO. 1524, VOL. 59.] 



they are streams of particles : it m.ikes them light on the 

 emission theory. 



It ought to be possible to test whether these emissions 

 are material or not, by collecting them in a small vacuum 

 tube. It is not generally appreciated how very small a 

 mass of gas there is in a small highly exhausted vacuum 

 tube, though it contains enormous numbers of molecules.. 

 At the pressure of a millionth of an atmosphere, which is 

 quite a large pressure of about a dyne per sq. cm., there 

 could be collected in a few minutes in a tube of several 

 cubic millimetres capacity a quantity of hydrogen which 

 it would require 100,000 years collecting at the same rate 

 in order to collect a gramme of it. 



In every way the book is suggestive, interesting, and 

 inspiriting, and as such should fulfil its purpose of 

 provoking research and advancing science. 



GEOMETRY OF POSITION. 

 Lectures on the Geometry of Position. By Theodor 

 Reye, Professor of Mathematics in the University of 

 Strasburg. Translated and edited by Thomas F. 

 Holgate, M.A., Ph.D., Professor of Applied Mathe- 

 matics in North-western University. Part I. Pp. 

 xix 4- 248. (London : Macmillan and Co., Ltd. New 

 York : The Macmillan Company, 1898.) 



AT last there is an English edition, translated in 

 America, of the first part of Prof. Reye's " Geo- 

 metrie der Lage," of which the first edition appeared as 

 long ago as 1S66. The methods followed offer so many 

 advantages, and the style adopted is so lucid, that we 

 heartily welcome this translation, and we with confidence 

 express the hope that it will awaken new interest in 

 the study of this charming subject in this country as 

 well as in America. 



The book owes its origin to lectures delivered to 

 engineering students at the Polytechnic School at 

 Ziirich. They were undertaken with the view of giving 

 the students that geometrical knowledge which they 

 required in order to listen with advantage to Culmann's 

 lectures on graphical statics. 



Culmann based his new science upon the very abstract 

 "Geometrie der Lage" by Von -Standi, and this pre- 

 scribed the course which Reye had to follow. He did 

 so willingly, and says in the preface to the first edition : — 



" One principal object of geometrical study appears to 

 me to be the exercise and the development of the power 

 of imagination in the student, and I believe that this 

 object is best attained in the way in which \'on Standi 

 proceeds." 



The object of Reye's lectures, therefore, is not only to 

 impart knowledge of conies and quadric surfaces, &c., 

 but also and especially to educate the student's mind in 

 the faculty of easily and readily realising geometrical 

 figures in space, a faculty very important to engineers. 



" Geometry of position," as opposed to " metric 

 geometry," with which alone Euclid deals, excludes all 

 measurement. But whilst the older authors and founders 

 of this modern science based it on Euclidian propositions, 

 Von Standt has shown that these can be altogether 

 avoided, and Reye follows this course rigidly. 



Here everything is based upon harmonic points in a 

 range, and harmonic rays in a pencil, or, as the trans- 

 lator calls it, a sheaf. 



