PROPERTIES OE HATTER IN THE GASEOUS STATE. 
779 
In dealing with the second case, that in which the isothermal surfaces are curved, 
the three conditions—steady momentum, density, and pressure—are all of them 
important. These conditions reduced to an equation between the motion of the gas, 
the variation in the absolute temperature, and the variation in pressure, in which, as in 
the equation of transpiration, the coefficients*are functions of the absolute temperature, 
the diameters of the apertures, and the ratios of the diameters of the apertures to the 
mean range. 
The reduction of the conditions of equilibrium to this equation, however, involves 
the assumption that the gas should not be extremely rarefied. In order to take this 
case into account a particular example is examined, and the equation so obtained, 
together with the equation obtained from the conditions of steady.motion, is shown to 
lead to the results of impulsion and the phenomena of the radiometer. 
Section VI.— Notation and Preliminary Expressions. 
65. In arranging the notation I have endeavoured as far as possible to make it 
similar to the notation already adapted to the kinetic theory of gases by previous 
writers. With this object I have adopted almost entirely, both as regards symbols 
and expressions, the notation used by Professor Maxwell in his paper “ On the 
Dynamical Theory of Gases.”'" But his notation, copious as it is, has fallen far short 
of my requirements. I have had to take under consideration certain quantities which 
have not hitherto been recognised; and what has particularly taxed my resources in 
symbolising, is that I have had, according to my method, to devise symbols to express 
each of twenty-four partial or component quantities which spring from any one of 
certain quantities, which have hitherto been dealt with as simple quantities. 
Explanation of the symbols. 
66. u, v, w, are used to represent the component velocities of a molecule with 
reference to the fixed axes x, y, z. 
7), £ are used to represent the component velocities of a molecule with reference 
to axes parallel to x, y , 2 , but which move with the halves of the mean component 
velocities of the molecules which pass through an element in a definite time. 
U, Y, W are used to represent the component velocities of the moving axes. 
Throughout this investigation bars over the symbols indicate the mean taken over 
some group of molecules ; when no further indication as to the particular group is 
given, it is to be understood that the mean is taken from the entire group in a unit of 
* Plait Trans. 1807. 
