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NATURE 



[SEPrEMBER^ ^5^ • 1 92 I 



...;^ oh . 



Letters to the Editor. 



f'l'he E'ditor does not hold himself responsible for opinions ex- 

 ■ .pressed by hts correspondents. Neither can he undertake to 

 ' return, or to correspond with the writers of, rejected manu- 

 scripts intended for this or any other part of Nature. 

 No notice is taken of atioiiytnous comniiinications.^ 



Uniform Motion in the >Ether. 



I SHOULD like to say a few words relative to Dr. 

 Jeffreys's comments on my letter on the above sub- 

 ject in Nature of August 11, p. 746. 



Poincare asserted that optical phenomena were, in 

 his opinion, rigorously independent of any motion 

 other than the relative motion of the bodies concerned, 

 and this is, I believe, a cardinal tenet of relativity. 

 In my judgment, the case of the moving mirror shows 

 such rigorous independence to be logically impossible, 

 but I do not quite gather whether Dr. Jeffreys accepts 

 or rejects that point of view. 



Allowing for the FitzGerald contraction, and. also 

 for the aberration, there will be, for an observer on 

 the earth, a general apparent equality of the angles 

 in question only when the motion of the earth is 

 in the plane of the mirror. (I was guilty of a. slip 

 here, but so, I think, was Dr. Jeffreys, since, even 

 disregarding the aberration, a motion of the earth 

 normal to the mirror could scarcely allow of the 

 same standard of angular equality for both earth and 

 mirror, the motion of the latter in this case not being 

 normal to its own plane.) Clearly, the existence of 

 such equality determined by and determining one 

 specific direction, is an optical phenomenon which 

 de{3ends on the absolute motion of the earth, not 

 merely on the relative motions of earth and mirror ; 

 and if this be admitted it appears to me that the 

 whole structure of relativity falls to the ground, in 

 so far at least as it may not be able to dispense with 

 logic. 



As to other points, I believe that if Dr. Jeffreys 

 will consider more closely the manner in which a dis- 

 tortion of the apparatus by the FitzGerald contrac- 

 tion would introduce discrepancies' into stellar 

 measurements, he will see that these discrepancies, if 

 discriminable, would reveal, not the relative motion 

 of stars and earth, but the absolute motion of the 

 latter ; and a comparison of this with the ordinarv 

 estimation of the earth !s motion relative to the stars 

 would show whether the whole material universe had 

 a drift in space. Again, I do not find it possible to 

 agree with Dr. Jeffreys that the Michelson-Morley 

 experiment conducted through water would be of little 

 interest. Indeed, it seems to me that this might con- 

 stitute a crucial test of the whole theory. Supposing 

 Fizeau's law for the light velocity in moving water to 

 be of general application, I believe I am correct in 

 saying that the change of length that must be suffered 

 by the apparatus in the direction of the earth's 

 motion, if the result of the experiment in water 

 moving with the earth is to be negative, should be 

 in the proportion 



instead of 



i' 



as in the FitzGerald contraction, v being the velocity 

 of light in water at rest in the aether and u being 

 small. This would represent only about one-half of 

 the latter contraction, and the test should therefore 

 be decisiv'C under the suppositions made. It is true 

 that I have not allowed for the effect of the FitzGerald 

 contraction upon Fizeau's law, but I do not know 

 that there is general agreement as to the method of 

 NO. 2707, VOL. 108] 



estimating this effect, and it seems very improbable 

 that the result would be a complete elirnination of v 

 from the expression giving the contraction. 



E. H. Synge. 

 Dublin, August 15. 



If we refer several events to the same system of 

 position and time co-ordinates, and then consider the 

 same events referred to another system, the position 

 co-ordinates and times in the two systems are con- 

 nected by a set of algebraic relations, called the 

 I^rentz-Einstein transformation. The FitzGerald 

 contraction refers only to a part of these relations 

 between the co-ordinates ; an argument that assumes 

 it and omits to consider the other relations is not 

 dealing with the principle of relativity. If the posi- 

 tions and times in two systems of reference B and C 

 are connected with those in another system A bv 

 such transformations, those in system C can be found 

 in terms of those referred to B by algebra, and it is 

 found that the relation between B and C is another 

 Lorentz-Einstein transformation, and involves no 

 mention of A whatever. 



In Mr. Synge 's problem of the mirror, we may call 

 the "aether " system A, the earth system B, and the 

 mirror system C. Even if there was a fundamental 

 aether, his suggested experiment deals only with the 

 relations between B and C, and, in consequence of 

 the above theorem, can therefore be treated in terms 

 of their relative motion alone. The "absolute" 

 motion never enters into the question. It would 

 enter, of course, if we tried to tackle the problem bv 

 referring everything to system A, but it would be 

 found that the absolute motion eliminated itself when 

 the angles of incidence and refraction were compared. 

 Aberration does not affect the problem, for it increases 

 or reduces both angles equally. 



I see no reason to alter anything in my previous 

 note. It is perfectly true that the theory of relativitv 

 makes certain positive predictions, and would have to 

 be modified, seriously if any of these were proved false 

 by experiment. But it is not true that it predicts 

 anything that involves the absolute motion of the 

 earth in space. Nothing but experiment could refute 

 it ; its self-consistency is perfect. 



Harold Jeffreys. 



I 



Relation of the Hydrogen-ion Concentration of the Soil 

 to Plant Distribution. 



In a series of papers from 1916 onwards Wherry 

 has studied the relation between soil reaction and 

 plant distribution in the United States. He made 

 use of colour tests with indicators for determining 

 the hydrogen-ion concentration of the solution obtained 

 by agitating soil taken near the plant with water. 

 In this manner he showed that the distribution of a 

 species may be limited in a very definite way by the 

 soil reaction, in expressing which it is convenient to 

 record the results in terms of the logarithm of the 

 reciprocal of the hydrogen-ion concentration in grams 

 per litre. This is denoted by the symbol pH, neu- 

 trality is at pHy, centi-normal hydrochloric acid is at 

 pH2, and sea-water at about pHS. 



Wherry has given the limits for a number of 

 American plants, and shown the soil reaction to be 

 expected in various types of soil. A paper dealing 

 with the subject has also appeared recently in 

 Sweden, giving results obtained by O. Arrhenius, but 

 this is not accessible here as yet. 



During the last year determinations of the pH ' 

 values of soils have been carried out by the writer in 

 India and the British Isles with the view of extending 

 our knowledge of plant distribution. It has been 



