January 27, 192*1] 



NATURE 



693 



lattice if the metal is pure. Obviously, the composi- 

 tion of this layer will depend upon that of the bulk 

 of the liquid and upon the aftinities of the iron ions 

 for the nitric acid and the water. We may regard 

 the nitric acid as ionised, but not so the water, because 

 its ionisation is known not to be increased by the 

 presence of dissolved electrolytes. Owing to the sym- 

 metry of the water molecule, it is impossible to say 

 which H atom will break away and which will remain 

 in the OH group in the event of ionisation. 



Now it is highly probable that the chemical force, 

 between ions even, is not wholly electrical, and we 

 may assume that the nitrate ion and the water mole- 

 cule will be attracted to their respective iron ions 

 with forces which result in the setting up of an 

 e.m.f. in the metal. If this e.m.f. is large enough, 

 one of the metal ions will be discharged into the liquid 

 momentarily as ferric nitrate, and in the model the 

 atoms marked (a) will form water,, the remaining 

 H will be momentarily liberated, and positive current 

 will flow as indicated by the arrows. 



Two factors will make for passivity : a low elec- 

 trode potential and homogeneity of the double layer 

 above .\B. Impurities in the metal will modify its 

 electrode potential as well as the composition of the 

 double layer. We find passivity a common property 

 of the noble metals almost irrespective of the com- 

 position of the double layer, whereas with highly posi- 

 tive (active) metals passivity is never observed. In 

 the case of intermediate metals passivitv occurs only 

 with certain kinds of double layers, and if these are 

 unstable periodic action may result. Since the forces 

 are not wholly electrical there is less chance for an 

 electrostatic equilibrium — and consequent passivity — 

 to be set up, and for this reason it seldom occurs with 

 these metals. 



A sufficient disturbance of the surface layer, by 

 scratching, touching with a more electro-positive 

 metal such as zinc, placing in a magnetic field, or 

 heating, will, in conformity with experience, activate 

 passive iron. It is significant that Smits and Lobry 

 de Bruyn (Proc. K. .\kad. Wetcnsch. Amsterdam, 

 vol. xxi., p. 382. loio) find that chlorine ions activate 

 anodicallv polarised iron. Thus it seems that irpn 

 ions in the surface of the metal haw a preferential 

 .iflTinitv for CI' over NO,'. W. HuGHRS. 



Bedford Modern School, January lo. 



The Space-Time Hypothesis before Minkowski. 



It is, perhaps, not generally realisc<l that the theory 

 of space and time, to which Minkowski was ted on 

 experimental grounds, had been formulated on general 



fruiciples sixty-five years previously by Hamilton, the 

 rish mathematician. The point is, however, of 

 interest, not merely as a question of priority, but for 

 the insight it affords into the philosophic basis of the 

 theory, as well as for the useful mathematical 

 methods it suggests. 



It is curious, therefore, that there should be a lack 

 of recognition that the worW of Minkowski is in ail 

 points identical with the system of quaternions of 

 Hamilton, and that the latter mathematician sj>eci. 

 fically regarded this system as a four-dimensional 

 expression of space and time, in which space bears 

 to time the relation which <J - I bears to unity, time 

 bring the scalar part of the quaternion. 



Quotations may be given from Hamilton's letters 

 and' manuscripts, cited in his " Life " by Graves, which 

 leave no doubt on this matter. 



Thus, vol. ii.. p. 478 : 



" I^t me suggest one leading thought, which will 

 perhaps sound paradoxical, that time and space are 

 imaginary, each with respect to the other. . . . Any 



NO. 2674, VOL. 106] 



expression for the peculiar relations of space in the 

 forms of time, or for those of time in the forms of 

 space, must therefore involve a seeming contradiction 

 . . . it will be a 'mathematical imaginary.' This 

 seems to me to be the clue, the secret of the matter." 



Vol. iii., p. 635 : 



"The mathematical quaternion ... in technical 

 language may be said to be ' time pX'us space,' or 

 'space phis time,' and in this sense it has, or at least 

 it involves a reference to, four dimensions." 



In another place : 



" My real is a kind of fourth dimension equally 

 inclined to all directions of space." 



Many other allusions will be found which prove 

 that this idea was fundamental in the views of 

 Hamilton, and that he held to it with the greatest 

 tenacity, although there were at that period no experi- 

 mental considerations to justify it, and although De 

 Morgan and other mathematicians seem to have dis- 

 couraged it, or ridiculed it. At the same time it does 

 not appear that Hamilton has given an analysis 

 of space and time which exhibits with sufficient clear- 

 ness the concept of direction in space as being 

 peculiarly attached to the symbol V — i, and the con- 

 cept of positive and negative unity as being similarly 

 connected with the two directions of time, towards the 

 future and the past. 



It is, however, easy to supply such an analysis, the 

 clue being given by noting that to define a number 

 by the equation *'+i=o virtually defines it as "a unit 

 which cannot be differentiated from its own negative 

 by any qualitative distinction." 



It indeed appears to have been in the thought of 

 Hamilton, as it must occur to anyone who considers 

 the matter, that the connection between a root of the 

 equation x'+i=o and a direction of space is to be 

 looked upon as more than a mere symbolism ; but 

 the general philosophic bearing of such considerations 

 on the whole nature of space and time is scarcely 

 appropriate for discussion here. It may, however, be 

 remarked that they indicate a point of view in which 

 time and three-dimensional Euclidean space lose their 

 apparently contingent character, and approach the 

 necessity of the laws of arithmetic, of which they 

 appear as a kind of derivative. 



It should be added that practical advantage might 

 be derived by mathematicians from the application 

 of the methods of quaternions to the theory of rela- 

 tiyitv, for, besides offering a convenient mode of 

 development of the geometry of four dimensions, 

 either Euclidean or hyperbolic, according as Tq or 

 </Sq' is taken as the element of length, they suggest 

 important possibilities in connection with the inversion 

 of a linear quaternion function analogous to the 

 physical applications by Tait of the linear vector 

 function. E. H. Stnob. 



Dublin, January 6. 



Heredity and Acquired Characters. 



Will you permit a statement from a humble 

 student? Between twenty-two and twenty-seven years 

 ago, while in Malabar, opportunity was taken bv me 

 to ascertain whether the arms of rowers on the back- 

 waters and the arms of the toddy.<lrawers were longer 

 in proportion to the height than in the case of the 

 rest of^the population, for here seemed to offer a test 

 whether " inheritance of the effects of use " was 

 evident. In both cases the men belonged to a caste 

 which had not changed its occupation for many 

 hundreds, perhaps some thousands, of years : the former 

 indigenous, while legend attributed the ancient home 

 of the latter to Ceylon, where thoy were occupied in 

 the same way — climbing and tapping the palm-trees 



