290 DR. S. CHAPMAN ON THE LAW OF DISTRIBUTION OF MOLECULAR VELOCITIES, 
in the sense that either may be obtained from the other by interchanging the 
suffixes 1, 2. 
Notation for an Encounter. 
§ 4 (B) Before proceeding to the actual consideration of the dynamics of an encounter 
between two molecules m ]5 m 2 , it is convenient to explain the notation to be used. 
The symbols m 0 , /x l5 /jl 2 , /x 12 , and /u 21 are defined as follows:— 
m 0 = m 1 + m 2 , 
//j mjm 0 , yW -2 
m 12 = i>hjtn 2 — /hi — nijm^ = thl/h , 
Ul +fJ-2 — lj + U-2 = 1— 
V-12U-21 ” 1 • 
Velocities will be represented either by their x, y, z components or in vector 
notation. The components of the actual velocities of the molecules will be written 
(U, V, W), while those of other velocities, such as the velocity of the mass-centre G, 
or the relative velocity, will be written (X, Y, Z). The amplitude of a velocity will 
be denoted by C, and the vector itself by the same symbol in small type with a bar 
beneath, viz., c. 
The velocities of the molecules m l5 m 2 , and of G will be distinguished by the 
respective suffixes 1, 2, 0, while the suffix R, similarly, will indicate reference to the 
molecular velocities relative to G or to one another. As regards time, square brackets 
enclosing a symbol, such as [X„], [cj. will indicate reference to some particular 
(arbitrary) instant during the encounter; a symbol without brackets but with an 
accent (') will refer to any instant after the encounter, # while when there is neither 
bracket nor accent it will refer to any instant before the encounter. 
(32) 
(33) 
(34) 
so that 
(35) 
(36) 
Analysis of the Motions in an Encounter. 
§ 4 (C) In the above notation the initial and final molecular velocities are respec¬ 
tively Cj, Co and c\, c' 2 , or (if, V 3 W,), (U 2 , V 2 , W 2 ) and (U'u V\, W'i), (Ub, Vb, W' 2 ); also 
(37) C 2 =U 2 + V 2 +W 2 , 
* That is, any instant after the molecules have separated beyond the distance (which in actual gases 
is, at most, very small) at which their inter-action is appreciable; the words “ before the encounter ” are 
to be interpreted in a similar sense. In this sense the velocities of the molecules before and after the 
encounter are definite and constant. 
