386 



SCIENCE 



[N. S. Vol. XXXVIII. No. 977 



many places of decimals as correspond to 

 the order of accuracy aimed at. 



Whenever, then, a commensurable nmn- 

 ier is really associated with any natural 

 phenomenon, there is necessarily a note- 

 worthy circumstance involved in the fact, 

 and it means something quite definite and 

 ultimately ascertainable. Every discon- 

 tinuity that can be detected and counted is 

 an addition to knowledge. It not only 

 means the discovery of natural units in- 

 stead of being dependent on artificial ones, 

 but it throws light also on the nature of 

 phenomena themselves. 



For instance: 



The ratio between the velocity of light 

 and the inverted square root of the product 

 of the electric and magnetic constants was 

 discovered by Clerk Maxwell to be 1 ; and a 

 new volume of physics was by that discov- 

 ery opened. 



Dalton found that chemical combination 

 occurred between quantities of different 

 fractional numbers; and the atomic theory 

 of matter sprang into substantial though 

 at first infantile existence. 



The hypothesis of Prout, which in some 

 modified form seems likely to be substanti- 

 ated, is that all atomic weights are com- 

 mensurable numbers; in which case there 

 must be a natural fundamental unit under- 

 lying, and in definite groups composing, 

 the atoms of every form of matter. 



The small number of degrees of freedom 

 of a molecule, and the subdivision of its 

 total energy into equal parts correspond- 

 ing thereto, is a theme not indeed without 

 difiiCTilty but full of importance. It is re- 

 sponsible for the suggestion that energy too 

 may be atomic! 



Mendelejeff's series again, or the detec- 

 tion of a natural grouping of atomic 

 weights in families of seven, is another ex- 

 ample of the significance of number. 



Electricity was found by Faraday to be 



numerically connected with quantity of 

 matter; and the atom of electricity began 

 its hesitating but now brilliant career. 



Electricity itself — i. e., electric charge — 

 strangely enough has proved itself to be 

 atomic. There is a natural unit of electric 

 charge, as suspected by Faraday and Max- 

 well and named by Johnstone Stoney. 

 Some of the electron's visible effects were 

 studied by Crookes in a vacuum; and its 

 weighing and measuring by J. J. Thomson 

 were announced to the British Association 

 meeting at Dover in 1899, a fitting prelude 

 to the twentieth century. 



An electron is the natural unit of nega- 

 tive electricity, and it may not be long be- 

 fore the natural unit of positive electricity 

 is found too. But concerning the nature of 

 the positive unit there is at present some 

 division into opposite camps. One school 

 prefers to regard the unit of positive elec- 

 tricity as a homogeneous sphere, the size 

 of an atom, in which electrons revolve in 

 simple harmonic orbits and constitute 

 nearly the whole effective mass. Another 

 school, while appreciative of the simplicity 

 and ingenuity and beauty of the details of 

 this conception, and the skill with which it 

 has been worked out, yet thinks the evi- 

 dence more in favor of a minute central 

 positive nucleus, or nucleus-group, of 

 practically atomic mass; with electrons, 

 larger — i. e., less concentrated — and there- 

 fore less massive than itself, revolving 

 round it in astronomical orbits. While 

 from yet another point of view it is insisted 

 that positive and negative electrons can 

 only differ skew-synunetrically, one being 

 like the image of the other in a mirror, and 

 that the mode in which they are grouped 

 to form an atom remains for future discov- 

 ery. But no one doubts that electricity is 

 ultimately atomic. 



Even magnetism has been suspected of 

 being atomic, and its hypothetical unit has 



