56 



SCIENCE 



[N. S. Vol. XLVII. No. 1203 



the first magnitude and an immense stride 

 in the direction of the unification of nat- 

 ural causes. But it did not satisfy the 

 thoroughgoing dynamical prejudices of 

 Lord Kelvin, who insisted to the end of his 

 life that he did not "understand" the 

 electromagnetic theory and that it "has 

 not helped us hitherto." Maxwell himself 

 was scarcely less desirous of finding a 

 dynamical foundation for his theory. In 

 fact, its first form was a detailed mechani- 

 cal model of vortices and idle wheels; in 

 the final form details were avoided by the 

 use of the generalized dynamics of La- 

 grange and Hamilton, and Maxwell suc- 

 ceeded in showing that certain parts at 

 least of his theory could 'be based upon 

 dynamical principles. 



This use of Lagrangian and Hamiltonian 

 methods in the investigation of physical 

 phenomena was a new weapon in the hands 

 of those who sought to reduce them all to 

 a djTiamieal basis. It has been used with 

 effect by J. J. Thomson, Larmor, and (in 

 application to statistical mechanics) by 

 Gibbs. It makes feasible the ultimate re- 

 finement and completeness of dynamical 

 explanation; in place of the potential 

 energy in the Lagrangian function we may 

 substitute the kinetic energy of concealed 

 motions and thus the last vestige of unex- 

 plained distance-forces may be swept away. 



The most thoroughgoing and successful 

 example of this method is the very com- 

 prehensive theory of the physical universe 

 contained in Larmor 's "JSther and Mat- 

 ter" published in the last year of the nine- 

 teenth century. His ether is identical with 

 MacCuUagh's rotationally elastic medium; 

 it has imbedded in it centers of rotational 

 strain (the electrons), out of which the 

 atoms of matter may be built up. The 

 only assumptions are that the positive and 

 negative electrons are somehow prevented 

 from destroying each other and that they, 



with their fields of strain, are capable of 

 motion through the fixed medium. From 

 Hamilton's principle, the Maxwellian equa- 

 tions for the free ether are deduced and, in 

 the presence of matter (electrons), whether 

 at rest or in motion, the same relations 

 hold as those found experimentally. The 

 rotational elasticity of the medium may be 

 produced gyrostatically, so that the poten- 

 tial energy may, if one chooses, be replaced 

 by kinetic. It is interesting to observe that 

 the position, velocity and momentum of a 

 material particle, in this theory, are reaUy 

 Lagrangian, generalized values. The mo- 

 tion of the centers of strain (e. g. in a 

 straight line) cause a slight twisting and 

 untwisting motion of the ether where the 

 true mass and momentum reside. Thus 

 the apparent mass of Larmor 's electron 

 varies with its speed as that of cathode 

 rays was afterward found to do; but its 

 dynamical orthodoxy is as sound as that 

 of a steam-engine governor, whose moment 

 of inertia varies with its angular velocity. 

 Notwithstanding the triumphs of the 

 dynamical school of thought, its assump- 

 tions and methods were subjected to search- 

 ing criticism on philosophical grounds par- 

 ticularly by Kirchhoff and Maeh. In 

 Kirchhoff's "Lectures on Mechanics," 

 published in 1876, he explicitly renounces 

 the attempt to find the causes of natural 

 phenomena or to " explain ' ' them in the 

 traditional sense ; the purpose of mechanics 

 itself (to say nothing of the parts of 

 physics more remote from common obser- 

 vation) is simply the description of phe- 

 nomena. Forces as causes of motion are 

 rejected; they are merely convenient ab- 

 breviations for certain functions of ob- 

 served motions. In the first lecture he 

 points out that Newton by no means dis- 

 covered that the force of gravitation was 

 the cause of the motion of the planets 

 which Kepler had described; he only 



