February 17, 192 1] 



NATURE 



797 



virtual shape of an electron is by the distribution 

 of its field. 



/Ether being- incompressible, I expect that the 

 change is really a pure constant-volume distortion, 

 consisting of a pair of lateral extensions and a 

 longitudinal contraction, as suggested in my B.A. 

 address "Continuity," 191 3, in the Birmingham 

 volume, p. 25 (or in a separate publication by 

 Dent and Son, pp. 58 and iii). But all that is 

 significant for present purposes is the ratio of 

 the longitudinal to the lateral change — a ratio 

 I ommonly sf)oken of as the FitzGerald or Fitz- 

 (ierald-Lorentz contraction. 



It is customary to consider this as only a longi- 

 tudinal shrinkage, but it is just as easy to allow 

 for a possible lateral change too : — 



The velocity of light through the medium being 

 always c, and the speed of the light-conveying 

 medium relatively to the matter of the block being 

 -•, the effective or resultant speed for the to-and- 

 fro cross-current light-journey is ^(c* — f'), while 

 lor the up- and down-stream journeys the effective 

 -peeds are (c — v) and (cH-f) respectively. 



The intended perpendicular distances marked 

 out on the slab being both x, the distance along- 

 -tream becomes, say, /8.r (whichever side of the 

 slab gets periodically into that position as it 

 rotates), and the distance across-stream may be 

 calltd y.v ; so the respective single journeys are 



(along) ■ &x = (c-v)t^ = {c + v)U 

 (across) •^x=sj[c^ — v^')\^. 



The observation docs not consist in measuring 

 either <; or U or fj ; nor is even x measured with 

 precision. The whole object of the experimenter 

 is to measure the small excess, 



to express it as a fraction of wave length, and 

 to compare it with the distance 2.x. Repeated 

 ob.servations show that the excess is actually zero. 

 And with this additional datum, 



it is mere algebra to reckon that the necessary 

 effective contraction is 



while if we choose to add the constant volume 

 relation, jB-y*=i, we get also 



y-(i-»»/f«)-». 

 I he experiment therefore verifies the FitzGerald 

 ■ ontraction, and tends to confirm the electrical 

 theory of matter. 



I was interested, when visiting the University 

 of Chicago last winter, to find that Prof. Michel- 

 son himself was perfectly satisfied with this sort 

 i>f view of his experiment, and did not consider 

 that its interpretation necessitated any revolu- 

 iii»nary considerations. The FitzGerald contrac- 

 tion is a peculiarity which could scarcely have been 

 iletertcd in any other way, since it is really an 

 affair of the .-ether— the connecting medium in 

 uhich all molecules arc embedded — and affects 

 very kind of matter to the same extent. 

 NO. 2677, VOL. 106] 



.\n objection has been raised, with apparent 

 seriousness, that this contraction cannot be real, 

 since, if it were, the rim of a spinning-wheel would 

 contract more than the spokes, and so the ratio of 

 circumference to diameter would not be ir. This 

 is an instructive and rather humorous example of 

 the prevalent tendency to control physics by geo- 

 metry. We might argue similarly that the rim 

 of a wheel could not be a fraction of a degree 

 cooler than the spokes ; and it might be held — 

 indeed it has been held — that the state of strain 

 in an actual rotating wheel or disc would require 

 non- Euclidean geometry to express it. If the pro- 

 positions of geometry require physical measure- 

 ments to sustain them, they can scarcely be of 

 the kind we have been accustomed to associate 

 with the name of Euclid. .\nd if a special geo- 

 metry has to be invented in order to account for 

 a falling apple, even Newton might be appalled 

 at the complications which would ensue when 

 really diflScult problems are tackled. Neverthe- 

 less, that is the kind of geometry to which rela- 

 tivity introduces us — a geometry based on hypo- 

 thetical laboratory measurements with scales and 

 clocks, and one the propositions of which can be 

 interfered with by metrical observations. It is 

 therefore sometimes called a "natural" geometry, 

 free from metaphysics ; it might equally well be 

 called an abstract sort of theoretical physics, and 

 not geometry at all. 



Relativity Explanation of the Experiment. 



It is well known that the simple interpretation 

 above given of the M. M. experiment is not palat- 

 able to relativists ; they consider that it is a forced 

 and arbitrary explanation, and that they can 

 account for the M.M. result more naturally by 

 employing a geometrical device and by applying 

 certain general hypotheses. The Principle of 

 simple relativity is that a transformation to uni- 

 formly moving axes can make no difference to 

 anything essential ; and the accompanying obses- 

 sion is that no observer can detect any apparent 

 change in the velocity of light. 



In order to apply these principles, the method 

 adopted by a Relativist is to take two observers 

 instead of one, to supply them with personal clocks 

 and measuring rods, and then to make one of them 

 fly through the laboratory at speed v ; thus render- 

 ing accurate measurement rather difficult for him, 

 and introducing .some confusion into his ideas of 

 space and time — especially as he is not to be allowed 

 to know that he is moving. He may be at rest in 

 the a»ther, but evervthing not attached to him or 

 to his medium will be rushing along; accordingly 

 objects will appear to be contracted, and all clocks 

 but his own will .seem to go slow.' The only thing 



' It in not 9nny to ciptain wiihout nymlioU wtiy earthttound clfx It* «hoitld 

 *pp*»r 10 BO lilow 10 an aviator, and ati aviator'* rtock apiirar t • ro *Iow la 

 a man on lh« rroand. Th« plain man wotdd think that (hev would bolk 

 appear to go la«l Hurinc appmarh. and «low darins rt<r«««ion ; hut tlM 

 meaBtng i« not no timpic a« tlial. Nor in it l>«catiMt a pcndiditm lia« 

 l«nith«nffd. or anylhin? phya'cal or r«al of that ^>ri. The aratimcni 

 appears to h» that the other man'* clocli tnu<t he «*timat»tl a* relalivcijr 

 •low, 1»T each of two oh^nwri moviaK relativeir to each other, liecauaa 

 oiherwi<e they eotild meaaura differeM Tetocities of Itf ht ; which, thoofll 

 not repofnant to cotriBoa-tenM, b eeMtarr to the baaic Prii>dplc af 

 Relalieity, 



