March 3, 192 1] 



NATURE 



impressed, but only the time taken to reach the steady 

 state is affected by its magnitude. The effects of 

 collisions and of molecular and demagnetising fields 

 are essentially the same as in Voigt's case. 



Like Dr. Chapman and others, 1 have considered 

 the possibility of dissociations increasing the intensity 

 of magnetisation of hot bodies, and I have plans for 

 experiments in this field. If the gyroscopic behaviour 

 of a magneton is to account for cosmical magnetism 

 (and it was the contemplation of this which led me 

 to the rotation experiments), we must, as has long 

 been evident, assume a constitution of the earth and 

 sun different from that of materials on which experi- 

 ments have previously been made. 



On my theory, a magneton in a diamagnetic or 

 paramagnetic body set into rotation is acted upon by 

 the same alignment forcive as if alone or in a ferro- 

 magnetic body. But the intensity of magnetisation 

 in the latter is small, for the same reason for which 

 it is small when the body is placed in an ordinary 

 magnetic field. In the former it is zero, because, on 

 the assumption I have made, with Weber and 

 Langevin, the magnetons are grouped rigidly together 

 so that no element with a magnetic moment can have 

 its orientation changed. This is the only point on 

 which Dr. Chapman's theory, as I understand it, 

 differs from mine. Rotation experiments on diamag- 

 netic and paramagnetic bodies by L^bedew and bv 

 Mrs. Barnett and myself have hitherto given no mag- 

 netisation. S. J. Barnett. 



Washington, D.C., January 31. 



I FULLY agree with Prof. Barnett's statement of the 

 theory of magnetisation by rotation, and regret that 

 through misunderstanding his treatment of magnetic 

 intensity I suggested that his theory required modifica- 

 tion. I am glad to know that he contemplates ex- 

 periments on the rotation of hot bodies ; this point, 

 h and the greater possibilities afforded if the magnetic 

 f ' elements remain intact at high temperatures, are the 

 matters to which chiefly I wished to direct attention. 

 Experiments made here with Dr. Oxley have nega- 

 tived my suggestion that diamagnetic and paramag- 

 netic bodies should also show magnetisation on rota- 

 tion, thus confirming the previous results mentioned 

 by Prof. Barnett; experiments on hot ferro-magnetic 

 bodies are not yet advanced sufficiently to state 

 whether they support the view that the earth's mag- 

 netism may depend on its high internal temperature. 

 Further trial seems to preclude the possibility of 

 trustworthy calculation at present, and the view must 

 be tested by experiment. Until this is done it seems 

 useless to enter into further details of the earth's 

 field and its secular variation. 



As regards the sun, later consideration of the 

 narrow radial limitation of its magnetic field leads 

 me to think that no simple magnetisation, bv gyro- 

 scopic action or otherwise, is the probable cause ; anv 

 such view requires two hypotheses, one to explain 

 the production and the other the neutralisation of the 

 field. A unitarv hvpothesis, such as the second of 

 those indicated by Sir J. Larmor in the British Asso- 

 ciation Report for 1919, seems preferable. 



S. Chapman. 

 The University, Manchester, Februarv 22. 



Transcendental Premises in Science. 



^ Perhaps you will permit one who belongs to a con- 

 siderable section of your readers who are neither 

 mathematicians nor neo-physicists to state how the 

 NO. 2679, VOL. 107] 



very remarkable discussion on Prof. Einstein's 

 theory in Nature of February 17 appears to some 

 of us. 



Mathematics to us is a very precise and complete 

 form of deductive logic applied to space and number. 

 It differs from ordinary logic only in having its 

 arguments set out in a symbolical shorthand instead 

 of in words, and thus enables a long deduction to be 

 condensed into a short statement. This unfamiliar 

 form of notation and condensation of the argument 

 are the chief stumbling-blocks to the outsider. 



Like other forms of logic, it is an art rather than 

 a science, namely, the art of drawing legitimate con- 

 clusions from premises. In essence, it has nothing to 

 do with the truth or falsity of the results. These 

 depend entirely on the nature of the premises. The 

 most faultless string of equations, like the most im- 

 maculate collection of syllogisms, mav conclude with 

 an absurdity or a stupendous error if the premises 

 are faulty. The logical mill by which the results are 

 obtained may turn out good flour or only chaff. This 

 depends entirely on what it is fed with. 



This is why the Philistine who is not a mathe- 

 matician sometimes shakes his head when he is pre- 

 sented with a series of equations on the blackboard 

 and his teacher says to him : " Look there. What 

 do vou say to that?" 



What the Philistine doubts is not the accuracy of 

 the deduction in this case, but the validity of the pre- 

 mises used in the new departure, which turns largely 

 on the nature of space and time as defined by the 

 neo-physicists. Granting that thev are legitimate, 

 the results are unquestionable. Are they legitimate? 

 Let us turn to space. The first remark I would 

 make is that, whatever its value, the definition in 

 question represents something entirely and confessedly 

 different from space as known to the great mass of 

 men and to all philosophers, mathematicians, and 

 physicists until the last few decades, and it has, there- 

 fore, no claim to be called space at all. 



Space was defined by Newton by two predicates, 

 namely, extension and immovability. I would pre- 

 sume to add a third one, quite necessarv as things 

 are now marching, namely, that any finite portion of 

 space may be measured by three co-ordinates at 

 right angles to each other and passing through one 

 point — or, in other words, space has three dimensions. 

 This is the only space known to human experience, 

 as it was to the early geometers. The addition of 

 a fourth or any number of other dimensions as 

 factors of space is inconceivable unless we entirely 

 alter the comprehension and connotation of the words 

 "space" and "dimension." You may call the result 

 what else you will ; you are misleading a great many 

 innocent people in calling it "space," like the 

 Pragmatist is doing when he defines the "truth" he 

 writes about as "the useful." 



When Riemann read his famous paper before the 

 Gottingen Academy at the instance of Gauss, who 

 presided on the occasion, he first introduced the notion 

 of space with more dimensions than three. He spoke 

 entirely as a pure mathematician. His premises were 

 not facts, but definitions of abstractions which could 

 not materialise into realities. With his abstract 

 postulates he was able to frame a series of equations 

 which were quite legitimate in form, but the con- 

 clusions of which were also abstractions, and could 

 not be presented in a mental picture or as repre- 

 senting anything in Nature. Since then, a large 

 literature has grown up in regard to these phantasms 

 of mathematical abstraction. Attempts — verv futile 

 attempts, as it seems to me — have been made to 

 translate the conclusions of Riemann 's equations into 



