270 



NATURE 



[July 18, 1907 



all-pervading a>ther shall be at rest under normal con- 

 ditions ; the effect of any local disturbance due to matter 

 must thus be a local effect, and the distant regions of 

 »ther will remain unmoved. There can be no question of 

 ascribing a uniform motion to the whole of the asther, 

 extending to the remotest infinity, because there is no con- 

 ceivable means of producing or altering such a motion. 

 In other words, an infinitely e.xtended aether postulates 

 absolute motion as a fact, in the only real sense of that 

 term, namely, motion relative to the remote quiescent 

 regions of the rtther ; and once that determination is made, 

 arguments from relativity of motion must lapse. 



The interesting point raised by Prof. Richardson, that 

 the steady field of a uniformly moving electron would 

 contain an infinite amount of moment of momentum, 

 requires detailed consideration ; but it is not without 

 parallel in more familiar departments of abstract physics. 

 Its scope may be illustrated by the steady motion of a 

 solid sphere in infinitely extended viscous fluid. The 

 sphere, even when in steady motion, experiences resistance, 

 and must be pushed along in order to maintain its motion. 

 This steady push must impart momentum to the fluid, 

 which increases in amount without limit as the time is 

 prolonged ; and it is, in fact, well known that the field 

 of flow around the sphere when it has reached its ultimate 

 theoretical steady state contains an infinite amount of 

 linear momentuin. But this circumstance does not vitiate 

 the dynamics of fluid resistance. For. in fact, the steadv 

 state of motion is very soon set up throughout the neigh- 

 bourhood of the moving sphere, while the continued supply 

 of momentum simply diffuses away into the distant regions 

 where the velocity is so slight that it does not react 

 sensibly upon the resistance to the sphere. Similar con- 

 siderations apply to the case of an electron set into steady 

 translatory motion through ipthcr. Here it is rotational 

 momentum that is steadily imparted to the surrounding 

 sether as time goes on, and is carried away into the distant 

 regions by wave-motion. This requires that the sether 

 exerts a torque on the moving electron, the reaction of 

 which on the aether is the source of the angular momentum 

 communicated to that medium. The possibility of per- 

 manent adjustment to a torque of this kind is not here 

 anomalous ; it is provided for in the fundamental hypo- 

 thesis of elastic resistance to absolute rotation of the 

 parts of the aether. There is, however, a fundamental 

 difference from the previous illustration of a solid sphere 

 moving through infinite viscous fluid. In that case the 

 force continually does work, leading to continued dissipa- 

 tion of energy into the viscous fluid. But in the electric 

 case the energy in the aether settles down to a steady 

 value, and no further energy is put into it, although a 

 constant stream of angular momentum is put into it so 

 long as tlie motion of the electron goes on. 



The validity of illustrating the nature of magnetic force 

 by velocity of the aether re.sts on an application of the 

 Principle of Least Action. The power of that principle 

 resides in its allowing dynamical inferences to be drawn 

 without requiring detailed scrutiny of the mechanism 

 through which the forces operate. But the exceptional 

 character of the hypothesis of rotational elasticity, or the 

 possibility of some flaw in the argument, might conceiv- 

 ably have put the application of the principle at fault. It 

 is thus essential, both for verification and for clearness of 

 view, to scrutinise in detail the circumstances of the motion 

 as determined by the Principle of Action, so far as possible. 

 It would appear that, as regards the interesting feature 

 discussed by Dr. Richardson, nothing has gone amiss. 



Even in the case of a sphere set in motion in frictionless 

 fluid, it may be said in the same wav that when the steady 

 motion has become absolutely established by propagation 

 outward, an infinite amount of momentum has been trans- 

 ferred from front and rear to the sides. 



Cambridge, July 8. J. Larmor. 



Tn Nature of July 4, Mr. E. Cunningham discusses my 

 statement of an objection to identifying the magnetic vector 

 with translational velocity of the Eether. Mr. Cunningham 

 says : — " If it were definitely stated that the magnetic force 

 in the free aether was proportional to the velocity of the 



NO. 1968, VOL. 76] 



a'ther relative to the observer the objection would be 

 valid"; and certainly any theory which embodied such a 

 doctrine would stand self-condemned. My argument, how- 

 ever, was not directed against this obviously untenable 

 view. 



If, for the free aether, we assume that magnetic force is, 

 within a constant factor, identical with a;thereal velocity, 

 then we can determine the velocity of the aether at any 

 point by measuring the magnetic force at that point. For 

 the value of the magnetic force there is a perfectly definite 

 physical criterion, which is independent of any arbitrarily 

 chosen frame of reference, and hence we should have the 

 means of determining absolutely the velocity of the aether. 

 Thus, on our assumption, absolute motion attains to a 

 definite physical significance which has no counterpart in 

 the postulates of ordinary dynamics; and, this being so, 

 dynamics must fail to give a true account of electromag- 

 netism. 



.\ccordingly, when we identify the magnetic vector with 

 translational .ethereal velocity, and at the same time assume 

 that we are dealing with a dynamical system, we should 

 expect to be led to results inconsistent with known 

 electromagnetic relations. Consider, in fact, the unac- 

 cclerated motion of a charged body (or of an electron) 

 through a space where there is no magnetic intensity. Then 

 pass to the case where the space in question is uniformly 

 pervaded by magnetic force in a direction transverse to the 

 motion of the charged body, while at the same time a new 

 component is added to the motion of the body, identical in 

 direction and magnitude with the a>ther-drift which we 

 assume to constitute our magnetic field. We have thus 

 impressed a uniform velocity on the whole system con- 

 sidered, and if the system is fundamentally a dynamical 

 one. no new acceleration will thus have been introduced : 

 that is, the charged body will move w'ithout acceleration 

 across the lines of magnetic force. C. V. Burton. 



Cambridge, July 12. 



Root Action and Bacteria. 



In Nature of June 6 (p. 126), Mr. S. Pickering has a note 

 on " Root Action and Bacteria " in which he concludes 

 that the proper functioning of roots depends on the 

 presence of bacteria. 



Experiments I have made here both in the field and in 

 water culture with a large number of varieties of plants 

 do not lead dircctlv to the same conclusion. Water cultures 

 have been made on a fairly large scale, three harvests of 

 ninetv plants being taken in a large number of dishes, each 

 containing two litres of water. After the third harvest, the 

 water was allowed to stand and evaporate to half its 

 volume. On attempting to'use this water for further water 

 cultures, all the plants sown in it died within two days 

 and some within half an hour, the time varying with the 

 variety of plant that was transplanted into the water, and 

 with the variety that had previously been grown in the 

 water. 



Further, boiling this water neither increases nor 

 diminishes its toxicity to plants. It is, moreover, imma- 

 terial whether the nutrient solution is such as to become 

 acid or alkaline after use ; neutralisation in either case 

 does not make it possible to grow plants in it. 



My experiments lead to the conclusion that the roots of 

 all the plants so far tried excrete a substance that is toxic 

 to .all plants (including that by which it is excreted), but 

 in different degrees. 



Similarlv, in the field Sesanum indiciim will not grow 

 (on stiff black soil) within 2 feet of Sorghum vulgare ; all 

 the plants tried appear to decrease the yield of neighbouring 

 plants of the same variety by about 50 per cent. 



The effect of the toxic substance both in the field and in 

 water culture is completely neutralised by tannic and 

 pyrogallic acids, carbon black, and other substances. 



It is, of course, possible that bacteria in the soil have a 

 beneficial action by elaborating antitoxins similar to those 

 mentioned. 



I have not yet been able to isolate the toxic substance 

 contained in the polluted water of my cultures. 



F. Fletcher. 



Poona, June 21. 



