226 Proceedings of Boy al Society of Edinburgh. [sess. 
of the atom at successive times with short enough intervals 
between them, to show clearly the path and the varying velocity 
of the particle. 
§ 10. Look, for example, at fig. 3, in which a semi-circum- 
ference of the atom at the middle instant of the time we are going 
to consider, is indicated by a semi-circle C 20 AC 0 , with diameter 
C 0 C 2 o equal to two units of length. Suppose the centre of the 
atom to move from right to left in the straight line C 0 C 20 
with velocity *1, taking for unit of time the time of travelling 
1/10 of the radius. Thus, reckoning from the time when the 
centre is at C 0 , the times when it is at C 2 , C 5 , C 10 , C 18 , C 20 are 
2, 5, 10, 18, 20. Let Q' be the undisturbed position of a particle 
of ether before time 2 when the atom reaches it, and after time 
18 when the atom leaves it. This implies that Q'C 2 = Q'C ]8 = 1, 
and C 2 C 10 = C ]0 C 18 = ‘8, and therefore C-^Q'^G. The position of 
the particle of ether, which when undisturbed is at Q, is found for 
any instant t of the disturbance as follows : — 
Take C 0 C = £/10; draw Q'C, and calling this r find r — r by 
formula (9), or Table I. or II.: in Q'C take Q'Q = r' -r. Q is the 
position at time t of the particle whose undisturbed position is Q'. 
The drawing shows the construction for t = 5. The positions at 
times 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 are 
indicated by the dots marked 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 
6, 7, 8 on the closed curve with a corner at Q', which has been 
found by tracing a smooth curve through them. This curve, 
which, for brevity, we shall call the orbit of the particle, is 
clearly tangential to the lines Q'C 2 and Q'C 18 . By looking to the 
formula (9), we see that the velocity of the particle is zero at the 
instants of leaving Q' and returning to it. Fig. 4 shows the 
particular orbit of fig. 3, and nine others drawn by the same 
method; in all ten orbits of ten particles whose undisturbed 
positions are in one line at right angles to the line of motion of 
the centre of the atom, and at distances 0, T, *2, . . . ‘9 from it. 
All these particles are again in one straight line at time 10, being 
what we may call the time of mid-orbit of each particle. The 
numbers marked on the right-hand halves of the orbits are times 
from the zero of our reckoning ; the numbers 1, 2, 3 . . . etc. on 
the left correspond to times 11, 12, 13 . . . of our reckoning as 
