PHYSICS. 329 



Joukowsky has made au elaborate mathematical investigation of the 

 laws of motion of a solid body having- hollows tilled up with .a homo- 

 geneous liquid. Various shapes of cavities were considered, as well as 

 the case where there was vortex motion of the liquid, with interior fric- 

 tion. Some of the phenomena resulting from the interior motion of the 

 liquid itself, in the case of the solid body, when caused to rotate, were 

 verified experimentally and thus proved to accord with theory. These 

 experiments showed that in a body whose rotation velocity decreases 

 from the surface to the center (as, for example, a glass sphere filled with 

 water while being put into motioii) the molecules How from the poles to 

 the equator; while, on the other hand, when the rotation is suddenly 

 stopi)ed the speed decreases from the center to the circumference and 

 the flow is from the equator to the poles. The general conclusion of the 

 inquiry is that if we have a hollow body filled with a liquid, and if this 

 system be put in motion, its motion will -tend toward a limit determined 

 by one of the princii)al axes of inertia of the body, taking the direction 

 of the principal moment of the communicated motion, and the whole 

 system will rotate about this axis as a single body, the speed of rotation 

 being constant and equal to the quotient obtained by dividing the force 

 applied by the moment of inertia of the system with regard to this axis. 

 The author thinks that this result may exjilain the fact that the planets, 

 notwithstanding the variety of their primary velocities, all rotate around 

 their axes of inertia. (Nature, February, 1886, xxxiii, 349.) 



Von Helmholtz has given to the Physical Society of Berlin a sketch 

 of the " doctrine of the maximum economy of action," in connection with 

 his oviii investigations in this direction. This doctrine was first pro- 

 pounded by Maupertius in 1744 in a treatise laid before the French 

 Academy. This treatise, however, contained no general statement of 

 the proposition, nor did it define the limits of its applicability, but only 

 adduced an example. But this example in the present state of our knowl- 

 edge is seen not to have been pertinent and not to have any relation to 

 the principle of the actio minima. Two years later. Maupertius pro. 

 pounded his principle before the Berlin Academy, proclaimed it to be 

 a universal law of nature and the first scientific proof of the 'existence 

 of God. But on this occasion, too, he did not prove the i)roposition nor 

 determine the limits of its applicability, but supported it by two ex- 

 amples, one only of which was correct. This principle, propounded with 

 such grand solemnity, but so weakly supported, was violently attacked 

 by K()nig, of Leipzig, and defended just as keenly by Euler. This mathe- 

 matician likewise failed to furnish the proof, which was not i)0ssible 

 until after the investigations of Lagrange. The form in which the 

 principle of the actio minima now exists was given to it by Hamilton, 

 and the Hamiltonian principle for ponderable bodies is in complete 

 harmony with the propositions of Lagrange. The elder Neumann, 

 Clausius, Maxwell, and Von Helmholtz himself had already extended 

 the Hamiltonian principle to electrodynamics. For this purpose, and 



