Two methods are employed in hydrodynamics, called the **Eulerian** and Lagrangian, although both are due originally to Leonhard Euler.

In the **Eulerian** method the attention is fixed on a particular point of space, and the change is observed there of pressure, density and velocity, which takes place during the motion; but in the Lagrangian method we follow up a particle of fluid and observe how it changes.

The Lagrangian method being employed rarely, we shall confine ourselves to the **Eulerian** treatment.

The **Eulerian** Form of the Equations of Motion.

The remainder of the first volume relates to the **Eulerian** integrals and to quadratures.

The second volume (1817) relates to the **Eulerian** integrals, and to various integrals and series, developments, mechanical problems, &c., connected with the integral calculus; this volume contains also a numerical table of the values of the gamma function.

The latter portion of the second volume of the Traite des fonctions elliptiques (1826) is also devoted to the **Eulerian** integrals, the table being reproduced.

The phenomenon is known as the **Eulerian** nutalion, since it is supposed to come under the free rotations first discussed by Euler.

The absence of g from the latter expressior indicates that the circumstances of the rapid precession are verb nearly those of a free **Eulerian** rotation (~ 19), gravity playing only a subordinate part.

This is, in fact, the invariable line of the free **Eulerian** rotation with which (as already remarked) we are here virtually concerned.

This revolution is called the **Eulerian** motion, after the mathematician who discovered it.

Were these currents invariable their only effect would be that the **Eulerian** motion would not take place exactly round the mean pole of figure, but round a point slightly separated from it.

Newcomb's explanation of the lengthening of the **Eulerian** period is found in the Monthly Notices of the Royal Astronomical Society for March 1892.