598 



SCIENCE 



[N. S. Vol. XXXIX. No. 1008 



distant body is not compensated by a reaction 

 appearing at the source or on any other por- 

 tion of matter. We thus have cases of actions 

 without reactions, if matter alone is con- 

 sidered. 



It must be clearly understood that the dis- 

 crepancies involved in the results of the ra- 

 tional mechanics, which have been cited, do 

 not become appreciable except under unusual 

 conditions. We can still consider mass as an 

 absolute constant and the equations of dynam- 

 ics as exact, unless matter has a velocity ex- 

 ceeding 18,000 miles a second, or for changes 

 of state which involve enormous quantities of 

 energy, such as those associated with radio- 

 active bodies or those which accompany the 

 formation of the chemical atom. At the pres- 

 ent day we have made no progress in attain- 

 ing any of these conditions, for even in the 

 case of radio-active bodies we should need to 

 find a method of liberating their energy in 

 hours rather than in hundreds of years. Thus 

 the problem would have remained academic, if 

 theorists had not advanced the hypothesis that 

 electricity is atomic in nature and that the 

 electron, as the least portion of electricity is 

 called, ordinarily attains a velocity which does 

 exceed a velocity of 18,000 miles a second; 

 that radiation must be explained as a transfer 

 of an entity, energy, through space; and that 

 the chemical atom of the radio-active elements 

 decomposes spontaneously and of all other 

 elements is theoretically decomposable with 

 the evolution of an enormous amount of 

 energy. All of these theoretical cases would 

 make the discrepancies between the laws of 

 mechanics significant. 



It would exceed the limits and the purpose 

 of this article to attempt to follow M. Lange- 

 vin in his exposition of the properties of elec- 

 tricity and of matter, of inertia, of radiant 

 energy, and of the principle of relativity. 

 After all, these abstruse questions are proper 

 for the discussions of specialists as they deal 

 with the nature of matter in a state quite 

 outside the limits of observation. But how- 

 ever the hypotheses of electrons and the ether 

 may impress the world as being matter of defi- 

 nition and words rather than of substance, yet 



from them follow conclusions which can be 

 tested experimentally. And the conclusions to 

 be drawn from the new mechanics are inter- 

 esting. 



For example, from the assumption that the 

 mass of a body varies when it gives out heat 

 or light, we must conclude that if a pound of 

 water at 32° Fahrenheit were heated to 212°, 

 its inertia or mass would be greater. Unfor- 

 tunately, when we calculate the increase of the 

 mass for this or for any practicable heating 

 of a body, we find that it is entirely too small 

 to measure. 



Again, let us put a known mass of hydrogen 

 and oxygen in a closed vessel and cause them 

 to unite to form water. Since the union of 

 these gases liberates an immense amount of 

 energy in the form of heat which will be 

 radiated from the walls of the vessel, the mass 

 of the water must be less than the combined 

 masses of the two gases. But unfortunately 

 again, the calculated decrease in mass is only 

 a five-billionth part and thus entirely too 

 small to measure. 



Lastly, the radio-active bodies give ofl^ an 

 amount of energy much greater in proportion 

 to the mass acting than can be obtained by 

 any chemical or other process. We might 

 hope to measure the decrease of mass in these 

 cases, but we can not, because these bodies 

 give off their energy far too slowly. 



Such, in the main, is M. Langevin's exposi- 

 tion of the new ideas in mechanics. There is 

 not the least doubt that this rigorous search- 

 ing of the classical mechanics has been a most 

 important advance in science, and we are cer- 

 tain to find its laws must be revised in order 

 to make them conform to the more rigorous 

 exactness which is now required of mathema- 

 ticians. But it is equally certain the laws of 

 mechanics have withstood this criticism 

 extraordinarily well, in so far as they have 

 been unshaken when we are dealing with mo- 

 tions which can be attained by bodies of sen- 

 sible mass.^ 



- That is, Newton 's laws of dynamics are rigor- 

 ous when bodies of tangible size, acting in meas- 

 urable spaces and times, are investigated. They 

 are approximations for exceptional cases; in much 



