238 



♦ KNO^A^LEDGE 



[June 1, 1886. 



axis in its owu plane (also square to the paper) in the direc- 

 tion of the arrows. L is a long focus lens placed at its own 

 focal distance from R M, and F M a very slightly concave 

 mirror at a considerable distance (say a third of a mile or 

 more) from tlic revolving one. Let us suppose the revolving 

 mirror to be in the position shown at E M, then a study of 

 the figure will show how the rays from the slit will foil on 

 E M, be by it reflected on to the lens L, and being converged 

 by tliat lens will form an image of the slit, say at .«'. Then 

 the mirror F M is fixed at s', so that its plane shall be at 

 right angles to the axis j-s' of the pencil of reflected r.ays. 

 Now suppose that r s' falls on the lens L, then the light, 

 after passing through the lens, will emerge parallel to '/• L, 

 fall perpendicularly on F M, and be reflected back by pre- 

 cisely the same route that it came ; and if we suppose E- M 

 to remain stationary during the interval, the image of the 

 slit S will be reflected on to S itself, and would be in the 

 middle of the field of a telescope placed immediately over S. 

 We have said if E M remains stationary, but we niay go 

 farther than this and say that though the mirror E M be 

 rotating i-apiilly, yet, if during the interval which is occu- 

 pied by the light in getting from E M to F M and back, 

 E ]M has not had time to alter its position sensibly, the 

 image of >S will equally coincide with the slit S itself. But 

 now let us imagine that the mirror E M is spinning round 

 at such a tremendous rate, in the direction of the arrows, 

 that while it occupies the position E ]\I when the ray starts 

 for F M, by the time that ray gets back it has turned into 

 the position E' M', then it will be seen that the image of S 

 will no longer coincide with !S itself, but will be reflected to 

 S', a point somewhere to the left of it (the angle S r S' being 

 obviously double that through which E M has turned), and 

 if we want to see this image in our telescope we shall have 

 to shift it from its position immediately over S to a new 

 one S' T. A glance at the figure will show that the distance 

 we have to move our telescope will depend upon the rate at 

 which the mirror is i-otating, and on the time occupied by light 

 in travelling from E jM to FM and back again. A little very 

 rudimentary mathematics will now enable us to calculate the 

 velocity of light. We measure first SS' the displacement of 

 the image of S, or the distance through which we have to 

 move our telescope ; then the distances S,?' and r,s' , and 

 finally the number of turns per second that our mirror EM 

 is making. Call SSV, S;- = a, r,s' = c. V = the velocity 

 of light; < = time occupied by light in travelling from »• to 

 s' and back again. 6 = the angle turned through by EM in 

 time f and N = the number of times EM I'otates in one 

 second. 



In one second EM turns through an angle of 2ffN : so 

 that in t seconds it will turn through 'iKNt, hence 0=27rN<. 



Now in turning through this angle 0, the mirror has 

 changed the jjosition of the reflected ray from rS to rS'. 

 Therefore the angle 8rS'=2d. Further SS'=S)- tan SrS'=:« 

 tan 2t). So that S,S' (our d) =a tan i-'St. t, though, is 

 the time occupied by the light in going from r to s' and 



coming back again : whence t^^ and d=a tan —-_"'- . 



V V 



As this angle 20 is necessarily very small, we may for 



a X 8-Nc 



our purpose use 20 for tan 2fl, and say d= ^ or 



\ 



V= 



SttNoc 



In Michelson's original experiments the centre 



r of the rotating mirror EM was 28-14 feet from the slit S ; 

 i.e. a=28'14 feet. The distance r,s between the centres of 

 the min-ors EM and FM was 661-49 yards; i.e. c=661-49 

 yards. The distance SS' was 4-45 "inches: i.e. fZ=4-4-5 

 inches, and the mirror EM rotated 2.57 times per second, or 

 N=2.57 nearly. If we substitute these cpiantitics in the 



formula above, we shall find as the resulting velocity of light 

 184,2.38 miles per second. 



Should the reader fail to grasp the principle of this 

 method, he is earnestly urged to re-peruse, step by step, the 

 explanation given above. When the idea is once gi'asped, 

 the succeeding description of Professor Newcomb's refined 

 apparatus and methods of observation should present no 

 difficulty whatever. 



Let us see what are the essential conditions of construction 

 of the apparatus. First, then, we cannot deal with a ray of 

 ordinary light as a mathematical line, so that a lens, or 

 system of lenses, becomes imperative ; and confining our- 

 selves for the time being to a single lens, if we are going to 

 observe a luminous slit, then this slit and the (fi.xed) concave 

 mirror must be in the conjugate foci of our lens, and the 

 rotating mirror must be in the path of the ray. This lens 

 must, ex necessitate, be either between the slit and the re- 

 volving mirror, or between the revolving mirror and the 

 distant one. In the former case, however, we are met by 

 the objection that only very small deviations can be 

 accurately measured, as a wide one would send the return 

 ray through a different part of the lens from the out-going 

 ray, and so I'ender measurement very uncertain. Now it 

 must be quite evident that our object is to make the angle 

 to be measured (SrS' in fig. 1) as large as possible. This 

 means, in practice, that either the .slit S, or the fixed concave 

 mirror FJNl, shall be as far as possible from the rotating 

 mirror. There are numerous objections to removing the slit 

 to any considerable distance, hence in practice it is the fixed 

 mirror which is jilaced as far as possible from the rotating 

 one. But here again we are met with a difficulty. When 

 the image of the slit is returned and reflected from the 

 rapidly turning mirror, its brilliancy is diminished in the 

 ratio of the diameter of the fixed mirror to the circumference 

 of the circle whose radius is the distance of that mirror from 

 the revolving one. Moreover, in traversing a great distance, 

 reflection, absorption, and dispersion, will all cause further 

 loss of light; so that we require some arrangement that shall 

 render the feeblest return ray visible ; in other words we 

 want our field of view as dark as possible. 



Now the first device employed by Professor Newcomb 

 for this purpose was to emjiloy two telescopes — one for send- 

 ing the ray out, and the other for receiving the return flash. 

 In order that the two reflections, however, should take place 

 from the same part of the rotating mirror, tliese two tele- 

 scopes would require to be in the' same horizontal plane. 

 But it is abundantly obvious that no small deviations could 

 possibly have been measui'ed with this arrangement, as the 

 two telescopes would have been in one another's way. It 

 was, moreover, found that, in addition to this drawback, the 

 quantity of light irregularly reflected from the mirror when 

 the sun shone upon it inconveniently illuminated the field 

 of view. Hence the telescopes were placed one above 

 another, and the mirror elongated sufficiently to receive the 

 rays from each telescope. As we shall presently see, the 

 rotating mirror was capable of being turned in either 

 direction, so that measurements of deviation could be made, 

 so to speak, both to the right and left of the slit. Hence 

 all uncertaint}- as to measurement from a zero point was 

 eliminated. Eeverting now to the subject of the darkening 

 of the field of view so as to render the faint reflected image 

 of the slit cons])icuous, we may briefly say that the whole 

 apparatus was contained in a dark room in which there were 

 only two openings, one for admitting the light from the 

 heliostat to the slit, and the second for sending and receiving 

 the reflected light. This light came through a small opening 

 in a blackened box some fifty yards distant in the path of 

 the ray. The result of the whole arrangement was that just 

 enough difl'used light entered the I'eceiving telescope to 



