through Space occupied by Ether. 191 



simultaneous positions of eight particles, whose undisturbed 

 distances are 0, *1, . . . "7. Remark that the orbit for the 

 first of these ten particles is a straight line. 



§ 11. We have thus in § 10 solved one of the two chief 

 kinematic questions presented by our problem: — to find the 

 orbit of a particle of ether as disturbed by the moving atom, 

 relatively to the surrounding ether supposed fixed. The other 

 question, to find the path traced through the atom supposed 

 fixed while, through all space outside the atom, the ether is 

 supposed to move uniformly in parallel lines, is easily solved, 

 as follows: — Going back to fig. 3, suppose now that instead 

 of, as in § 10, the atom moving from right to left with 

 velocity *1 and the ether outside it at rest, the atom is at rest 

 and the ether outside it is moving from left to right with 

 velocity -1. Let '2, '3, '4, '5, '6, '7, '8, '9, 0, '1, % % '4, '5, 

 '6, '7, '8 be the path of a particle of ether through the atom 

 marked by seventeen points corresponding to the same num- 

 bers unaccented showing the orbit of the same particle of 

 ether on the former supposition. On both suppositions, the 

 position of the particle of ether-at time 10 from our original 

 era, (§ 10), is marked 0. For times 11, 12, 13, etc., the 

 positions of the particle on the former supposition are marked 

 1, 2, 3, 4, 5, 6, 7, 8 on the left half of the orbit. The positions 

 of the same particle on the present supposition are found by 

 drawing from the points 1, 2, 3, ... 7, 8 parallel lines to the 

 right, 1 '1, 2 '2, 3 '3, ... 7 '7, 8 '8, equal respectively to 

 •1, '2, *3, . . . "7, "8 of the radius of the atom, being our unit 

 of length. Thus we have the latter half of the passage of the 

 particle through the atom; the first half is equal and similar 

 on the left-hand side of the atom. Applying the same process 

 to every one of the ten orbits shown in fig. 4 (p. 192), and to the 

 nine orbits of particles whose undisturbed distances from the 

 central line on the other side are "1, - 2, . . . '9, we find the set 

 of stream-lines shown in fig. 5 (p. 1 93) . The dots on these lines 

 show the positions of the particles at times 0, 1, 2, . . . 19, 20 

 of our original reckoning (§ 10). The numbers on the 

 stream-line of the particle whose undisturbed distance from 

 the central line is *6 are marked for comparison with fig. 3. 

 The lines drawn across the stream-lines on the left-hand side of 

 fig. 5 show simultaneous positions of rows of particles of ether 

 which, when undisturbed, are in straight lines perpendicular 

 to the direction of motion. The quadrilaterals thus formed 

 within the left-hand semicircle show the figures to which the 

 squares of ether, seen entering from the left-hand end of the 

 diagram, become altered in passing through the atom. Thus 

 we have completed the solution of our second chief kinematic 

 question. 



