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.