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SCIENCE 



[N. S. Vol. XL. No. 1038 



cones unknown to Csesar. Axes may be so 

 chosen as to make any two events contempo- 

 raneous. They need merely be parallel to the 

 time axis selected. Similarly there are four 

 equations of motion, the fourth being the 

 energy equation, as energy itself is possessed 

 of inertia. Finally, the equations of electro- 

 magnetic field in their magnetic and electric 

 aspects, like the rotations, are given by the 

 geometry of a vector with six components. 



The treatment of motion is thus profoundly 

 generalized, and Minkowski remarks that if 

 these new transformations had been discovered 

 by a mathematician " aus freier Phantasie," by 

 an untrammeled imagination, they would have 

 constituted a triumph in mathematics of the 

 very first order. But, even under present cir- 

 •cumstanees, as soon as such developments were 

 •demanded by the laboratory, finding that 

 within the atom the ^Newtonian world is cer- 

 tainly discredited, mathematics was at once 

 ready to embody the new conception in a way 

 that makes the bonds of mathematics and 

 physics closer than before. 



Vast and beautiful as these generalizations 

 are, we must nevertheless confess that they 

 are still but a coarse reproduction of nature; 

 for in none of them is there any unequivocal 

 or imperious demand for gravitation. Gravity 

 still acts at a distance, as did the electrical 

 vector in the days of Weber. Nor is the most 

 generalized electromagnetic field able to ac- 

 count for the spectrum distribution of radia- 

 tion, in the development of which energy 

 threatens to pursue, if it has not already 

 entered, the route of atomistic physics occupied 

 by chemistry. 



While mathematics is easily able to cope 

 with the problems of relativity, even in their 

 most generalized aspects, since they never 

 break with continuity, the questions are more 

 menacing in the second class of the recent 

 demands of experimental physics, which came 

 to a crisis in certain straightforward experi- 

 ments on radiation made at the Eeichsanstalt 

 (Lummer and Pringshen, 1899; Christianson, 

 1884). The question dates back to Kirchofi's 

 black body (1859), in which emission and ab- 

 sorption are equal. Some time after came 



Stefan's universal law of black body radiation 

 (1879) and the theoretical verification on the 

 part of Boltzmann in 1884. There was a 

 period of intermission, in which the question 

 of the equi-partition of the energy of a gas 

 among the degrees of freedom of its molecules 

 was vigorously discussed but without leading 

 to available conclusions. However with the 

 introduction of the black body by Kirchoff and 

 the treatment of its radiation as a case of 

 thermodynamic equilibrium, it was possible 

 to assign both temperature and entropy to 

 such radiation. But there was one further 

 fundamental step to be taken and that was the 

 definition of entropy apart from the Carnot 

 engine and the intelligent manipulator, who 

 is always an implied part of that wily machine. 

 The second law was to be freed from reference 

 to anything of a biological nature. Helmholtz 

 had often insisted that the second law is the 

 result of the order of physical size of the 

 agent, in comparison with the atomic size, 

 of his lack of equipment to control the indi- 

 vidual molecule. To a being of molecular 

 dimensions, there would be no irreversibility; 

 whereas irreversibility has a very real meah- 

 ing to the grosser attributes of the corrupter 

 of nature. It was to the genius of Boltzmann 

 (18YY) that the fulfilment of this task waa 

 allotted. He was the first to give to entropy 

 a purely mathematical signification, defining 

 it as the logarithm of the probable occurrence 

 of any thermo-dynamic state, be it a distribu- 

 tion of velocities, be it a definite distribution 

 of discontinuous radiation energy-elements. 

 Along this line, therefore, the new thermo- 

 dynamics proceeded effectively. The first step 

 came from W. Wien, whose displacement law 

 of 1893 is embodied in the shift of the maxi- 

 mum of spectrum energy density, from red to 

 violet, with increasing temperatures. Wien 

 showed that a universal function of the ratio 

 of temperature to frequency must here be in 

 question. The determination of this universal 

 function was the culmination of the insight 

 and consistent labors of Planck (1900), who 

 by postulating the energy quantum, became 

 the creator of modem thermodynamics; for 

 this energy element is a saucy reality, whose 



