through Space occupied l>y Etlier. 189 



diagram the successive positions thus determined for any 

 particle o£ the ether, according to the positions 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 semicircle C 20 AC , with dia- 

 meter C 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 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 , 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 18 =1, and C 3 C 10 =C 1( A 8 = -8, and therefore C 10 Q' 

 = *6. The position of the particle of ether, which when 

 undisturbed is at Q', is found for any instant t of the dis- 

 turbance as follows : — 



Take C C = £/10; draw Q'C, and calling this / find / — r 

 by formula (9), or Table I. or II. : in Q'C take Q'Q = /-»•. 

 Q is the position at time t of the particle whose undisturbed 

 position is Q'. The drawing shows the construction for t = 2, 

 and t=5, and £=18. The positions at times 2, 3, 4, 5, ... . 

 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 

 Qf 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, "1, '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 hitherto, or to times 1, 2, 3 . . . after mid-orbit 

 passages. Lines drawn across the orbits through 1, 2, 3 . . . 

 on the left, show simultaneous positions of the ten particles at 

 times 1, 2, 3 after mid-orbit. The line drawn from 4 across 

 seven of the curved orbits, shows for time 4 after mid-orbit, 



