January 9, 1914] 



SCIENCE 



45 



of energy. To be sure, the notion of energy 

 could not become of universal application 

 until justified by multifarious experiment, 

 and yet this has now come to be a principle 

 in which we have more confidence than any 

 other, not only in physics, but in all the 

 natural sciences. But the principle of 

 energy is not the only generalization of 

 mechanics, nor in fact is it sufficient for 

 the establishment of the equations of me- 

 chanics. A more general one is found in 

 the so-called principle of least action, es- 

 tablished upon a secure basis by Hamilton. 

 From this principle all that we know of 

 dynamics can be deduced, and by dynamics 

 thus defined all the phenomena of celestial 

 mechanics can be explained, with an ac- 

 curacy almost beyond belief, the single law 

 of the inverse square sufficing for all heav- 

 enly phenomena with an accuracy probably 

 beyond that of our description of anything 

 else in nature. 



As one of the triumphs of the dynamical 

 method in the explanation of recondite phe- 

 nomena must be mentioned Maxwell's 

 theory of the electromagnetic field, leading 

 him to the discovery of the electromagnetic 

 nature of light, and the prediction of elec- 

 tromagnetic waves. But in spite of this 

 and other triumphs, the dynamical method 

 alone was not sufficient in many cases. 



Chemistry remained intractable by its 

 means, and all the phenomena involving 

 heat seemed outside its range. But it was 

 at this very point that a powerful addition 

 to the dynamical method came to its aid. 

 As remarked above, the principle of con- 

 servation of energy would not have become 

 so intrenched had it not been for its ex- 

 perimental confirmation, especially in the 

 domain of the relations between heat and 

 work, as carried out by Joule. The prin- 

 ciple of equivalence, which has since been 

 considered as the first law of thermodynam- 

 ics, then, extended the dynamical generali- 



zation to a far larger field, and explained 

 the disappearance of dynamical energy by 

 its reappearance in the form of heat. But 

 even then certain phenomena remained in- 

 tractable by dynamical means, such as the 

 well-known phenomena of heat conduction. 

 To turn aside for a moment, the treatment 

 of heat conduction by Fourier furnishes an 

 admirable example of a merely descriptive 

 theory, in which everything is exactly de- 

 scribed, but it is of no moment for the 

 theory whether heat is a fluid substance, a 

 form of energy or an agitation of mole- 

 cules. The laws of flow of heat, although 

 merely descriptive, by analogy led to other 

 great generalizations, notably in connection 

 with the flow of electricity and with mag- 

 netism and electrostatics. 



The method of analogy, always an at- 

 tractive but dangerous one, led in connec- 

 tion with heat to a generalization which led 

 to possibilities that dynamics could not 

 furnish. The analogy of the working of 

 water in a mill by falling from a higher to 

 a lower level led Carnot to a conclusion, 

 which though based on an imperfect anal- 

 ogy, led to most important results regard- 

 ing the possibility of thermal changes. 

 From his statement regarding the efficiency 

 of heat engines, as based upon the fall in 

 temperature of the heat employed, has re- 

 sulted the second law of thermodynamics, 

 or the principle of entropy, which together 

 with the principle of energy has given us 

 a method of enormous power, which may be 

 indeed extended to those sciences toward 

 which the dynamical method has shown 

 itself as yet powerless. It was to the meth- 

 ods of thermodynamics that chemistry was 

 destined to yield, largely through the efforts 

 of our countryman, Willard Gibbs, and of 

 Helmholtz. The reason for the failure of 

 dynamics alone in chemistry may be stated 

 as follows. The method of dynamics re- 

 quires the complete specification of a system 



