203 
showing a range of 0’9 magnitude. The mean magnitude at 
maximum is 9 '07 ; the highest yet observed is 8-4, and the 
lowest 101, the range of variation at maximum being there- 
fore VI magnitude, or nearly double that at minimum. 
The extreme range of variation in the star’s brightness is 
3 ’2 magnitudes. 
The following paper was read at the Annual General 
Meeting, April 20th, 1880 : — 
'' On an adaptation of the Lagrangian form of the equa- 
tions of fluid motion. Part I.,” by R. F. Gwyther, M.A. 
'fhe object of the Lagrangian form of equation is to follow 
the motion of a particular element; and, although the 
Eulerian forms suit the general purposes of fluid motion best, 
there are certain cases, as that of vortex motion in a 
perfect fluid (which may be termed steadily progressive) 
where the course of an element might be investigated with 
advantage. 
For this purpose 1 propose investigating the course of a 
fluid element, defined by means of surfaces moving with the 
fluid, and expressing the results as far as possible in terms 
of the parts of the element. 
This method leads to a more general integral form than 
that of Weber, and finally exhibits some of the known 
properties of fluid motion in a novel manner. 
If ^ be a scalar function of the position of a point in the 
fluid, its total differential after time is andifD;(^ = 0, 
the property of the point, of which (j) is the analytical 
expression, is unchanged during the motion. Nowlet^=/x 
be the equation to a surface all points on which enjoy the 
same property, such a surface will, if D^^=0, move with 
the fluid. 
The number of independent surfaces of this kind which 
can pass through any point, or the number of independent 
integrals of the equation Vtcjy — O is three, or the dimensions 
