August 25, 192 1] 



NATURE 



817 



To reduce the field of the earth locally to zero 

 by means of a falling elev'ator or " lift " is feasible 

 for observers inside the lift, so long as it is small. 

 But if, in an extensive falling chamber, gravity is 

 to be imitated or neutralised exactly, its parts 

 must fall in different directions, or with different 

 accelerations, or both. 



The elimination or avoidance of the idea of abso- 

 lute rotation, through imitating or replacing 

 centrifugal reaction by the influence of the stars, or 

 by an imaginary distribution of attracting matter 

 in distant space, round the earth or other rotating 

 body, is preposterous, and cannot be seriously 

 contemplated. 



I know that the mathematical physicists who 

 allow themselves to assist their exposition by 

 employing illustrations of this kind must be well 

 aware of the limitations attending their use ; but 

 I do not think that philosophers always are, and 

 they may not always attend to the cautionary 

 language employed by careful expounders. In 

 fact, the so-called " principle of equivalence," like 

 other popular wordings of extreme relativity, is 

 liable to lead an incautious exponent to go 

 beyond what is legitimate or necessary, and to 

 land him in paradox. Yet if not pushed to absurd 

 extremes, and if the wording is carefully guarded, 

 the principle of equivalence is useful enough ; for 

 it is true that any effect on bodies produced by 

 their weight can be imitated by whirling them on 

 a revolving table. Mechanically the princfple is 

 used in industrial separators of various kinds, and 

 in any operation requiring an enhanced value of 

 gravity ; and the principle extends to optic and 

 electric effects also. 



Reference to Mercury's Orbit again. 

 The theory of relativity, though originally sug- 

 gested by electrical theory, was developed without 

 further reference to that theory, and reduces an 

 orbit to a mere spatial relation determined by the 

 central body. But it should be clear that, unless 

 an aether is admitted, the gravitational potential 

 or potentials essential to the theory must represent 

 an action-at-a-distance of the central body on 

 space. In the third article (Nature, August i8, 

 p. 784), when discussing the orbit of Mercury, I 

 did not seek to explain how it was that an extra 

 small perturbation was necessitated by the prin- 

 ciple of relativity ; because no question about it 

 has arisen, and because it has been done, so far 

 as reasonably possible, at least for the bending 

 of light, by Prof. Eddington, in chap. vi. of his 

 book "Space, Time, etc."; while the equations 

 are in chap. v. of his "Report" to the Physical 

 Society of London ; or, in another form, in 

 Cunningham's "Relativity," second edition. The 

 theory for a planetary orbit is similar to the light- 

 path theory ; but it is difficult to put the gist of it 

 into ordinary language. Suffice it to say (i) that 

 Newton showed, in the "Principia" (Book i., 

 sect, ix.), that the inverse square law is the only 

 one to give an exact elliptic orbit, and that the 

 slightest interference with that law would bring 

 about a specified revolution of the orbit in its own 

 NO. 2704, VOL. 107] 



plane, i.e. an apsidal progression; or, in vaguer 

 words, would prevent the same orbit from being 

 retraced or repeated by the planet. And (2) that 

 the Relativity theory, virtually though not expli- 

 citly, does interfere with the exact law of inverse 

 square, especially for a near planet. For in the 

 ordinary equation for orbital revolution in general, 



^/i\ i_Pr=' 



de\r) r h^ 

 (with P as the acceleration at distance r from the 

 central body M, and |/i as the constant rate of 

 sweeping areas), the right-hand side is constant 

 only for an inverse square law, P = GM/r-. But 

 relativity adds to the right-hand side, which ordi- 

 narily would be GM//i^, another term, namely 

 3GAl/ c^r^; and this small term is the one respon- 

 sible for the departure from an exact conic-section 

 orbit. The discrepancy thus Introduced turns out 

 to be right for Mercury, and Insignificant fot other 

 planets ; while it does not interfere with their 

 eccentricities. Moreover, the same term is re- 

 sponsible for the bending of a ray of light. So the 

 double success Is very striking, and the jubilation 

 entirely justified. 



To sum up this portion. 



Force is essentially a human conception derived 

 from our muscular sense; and, from the psycho- 

 logical point of view, is as basic as motion, and 

 more directly apprehended than matter. Unforced 

 motion Is straight and uniform,^ not varying or 

 curvilinear, and acceleration is not a fundamental 

 property of matter, nor a diversion of empty space, 

 but is always the result of pressure exerted upon a 

 mass by other bodies, or in the last resort by the 

 circumambient medium. 



To geometrise physics, even If legitimate foi 

 convenience of calculation, is ultimately to com- 

 plicate it. Directly the operation becomes com- 

 plicated It becomes needless, or even obstructive 

 The new facts can be accepted, and the relativity 

 equations can be used, but a physical explanation 

 can still be looked for, and our knowledge, of the 

 universe wall not be complete until it is found. 

 We cannot be for ever satisfied with a blindfold 

 mathematical method of arriving at results. We 

 can utilise the clues so given, and admire the 

 Ingenuity which has provided them, but that is 

 not the end ; It is only the beginning. The ex- 

 planation is still to seek, and when we really know 

 the properties of the aether we shall perceive why 

 it is that things happen as they do. 



CONCLUSIOX. 



The relativity method, by aid of its differential 

 geometrical analysis, seeks to interpret all that is 

 directly experienced through our senses as a mani- 

 festation of the peculiarities of space. Matter 

 and all its functions are thus reduced to a kind of 

 subjective space-time geometry, and everything 

 absolute has disappeared from the physical world. 



An alternative view of what may be the outcome 



* Straightness means that no reason for deflection in any direction can be 

 assigned ; and the absence of any accelerating or retarding cause yields 

 uniformity. 



