The present problems of dynamics differ materially from those of the last century. The explanation of the orbital and axial motions of the heavenly bodies by the law of universal gravitation was the great problem solved by Clairaut, Euler, D'Alembert, Lagrange, and Laplace. It did not involve the consideration of frictional resistances. In the present time the aid of dynamics has been invoked by the physical sciences. The problems there arising are often complicated by the presence of friction. Unlike astronomical problems of a century ago, they refer to phenomena of matter and motion that are usually concealed from direct observation. The great pioneer in such problems is Lord Kelvin. While yet an
undergraduate at Cambridge, during holidays spent at the seaside, he entered upon researches of this kind by working out the theory of spinning tops, which previously had been only partially explained by Jellet in his Treatise on the Theory
of Friction (1872), and by Archibald Smith.
Among standard works on mechanics are Jacobi's Vorlesungen
über Dynamik, edited by Clebsch, 1866; Kirchhoff's Vorlesungen
über mathematische Physik, 1876; Benjamin Peirce's
Analytic Mechanics, 1855; Somoff's Theoretische Mechanik,
1879; Tait and Steele's Dynamics of a Particle, 1856; Minchin's
Treatise on Statics; Routh's Dynamics of a System of Rigid
Bodies; Sturm's Cours de Mécanique de l'École Polytechnique.
The equations which constitute the foundation of the theory of fluid motion were fully laid down at the time of Lagrange, but the solutions actually worked out were few and mainly of the irrotational type. A powerful method of attacking problems in fluid motion is that of images, introduced in 1843
by George Gabriel Stokes of Pembroke College, Cambridge.
It received little attention until Sir William Thomson's discovery
of electrical images, whereupon the theory was extended by Stokes, Hicks, and Lewis. In 1849, Thomson gave the
maximum and minimum theorem peculiar to hydrodynamics, which was afterwards extended to dynamical problems in general.
A new epoch in the progress of hydrodynamics was created, in 1856, by Helmholtz, who worked out remarkable properties
of rotational motion in a homogeneous, incompressible fluid, devoid of viscosity. He showed that the vortex filaments in such a medium may possess any number of knottings and twistings, but are either endless or the ends are in the free surface of the medium; they are indivisible. These results suggested to Sir William Thomson the possibility of founding on them a new form of the atomic theory, according to which every atom