Dec. 25, 1879] 



NATURE 



185 



possibly come from the degradation of the gneiss rocks 

 occurring along the coast. Although corundum is com- 

 paratively abundant in the interior of Ceylon, it has 

 never been found in its matrix, but always either in 

 pocket holes in streams, or in drift, intermixed with 

 rounded pebbles of quartz. The character of the rivers 

 in the neighbourhood of the coast apparently precludes 

 the possibility of fragments of corundum being carried 

 down to the sea. 



A closer examination of the structure of the beach 

 reveals the fact that the heavier particles are frequently 

 deposited in extremely thin strata, transverse sections of 

 which exhibit the most beautiful curves. Examples of 

 this are seen in Figs. 1 and 2, which are half the natural 

 size, the light parts representing quartz, the dark ones 



Fig. 1. — About one-fourth natural size. 



magnetite. The explanation of this is apparently simple. 

 When the quartz fragments of which the larger portion of 

 the rock is formed have become consolidated, depressions 

 will be formed by the heavy particles of magnetite under 

 the influence of the waves, very much after the manner in 

 which pocket holes are formed in the rocky beds of nearly 

 all the mountain streams in the island. (It was in these 

 pocket-holes that the earlier sapphires were nearly always 

 found.) When once commenced this scouring process 

 would go on as long as the water was sufficiently agitated 

 to keep the fragments of magnetite in motion. Their 

 superior weight would have a tendency to keep them in 

 the hollows they had formed, and the carbonate of lime in 

 the water would fix them in position as soon as they were 

 left undisturbed by the waves. The succeeding waves 



-About one-fourth natural size. 



hat reached the hollow would fill it chiefly with quartz 

 fragments which would become cemented together, and 

 the process of scouring would go on as before. 



It may be noticed in explanation of the very beautiful 

 skein-like appearance of Fig. 2, that when once a stratum 

 of magnetite had become consolidated, it would be much 

 less liable to be removed by the scouring process than the 

 neighbouring quartz, on account of its superior hardness, 

 and therefore the original shape of the basin has been 

 retained, whilst other basins, represented by the dark 

 lines, have been formed above it, differing only slightly in 



shape from the original one. Some portions of this 

 beach are quarried for edging and coping stones which 

 are sent to Colombo. R. Aebay 



ON THE POTENTIAL DIMENSIONS OF 

 DIFFERENTIATED ENERGY* 

 T N his great work, which appears to be but little known 

 *■ in England, " Ueber die stille Bewegung hypote- 

 tischer Korper," Prof. Hans points out that the dimen- 

 sions of " ideal " matter may not only differ in degree, 

 but also in kind. He deduces, by means of implicit 

 reasoning from his three primitive "stations," that not 

 only must there be space of 4, 5, 6, &c, dimensions, but 

 also that there must be space of — 1, - 3, — 5, &c, 

 dimensions, and that there may be space of - 2, — 4, — 6, 

 &c, dimensions. Pursuing Hans's train of thought further, 

 Lobwirmski has quite recently interpreted space of ri, 1 '2, 

 i"3, &c, dimensions. Not only has fractional space been 

 thus proved to exist, but the same phi losop her has also 

 conclusively shown that if space of n. v' - 1 exists, it has 

 all the properties of angular magnitude ; e.g. like all 

 partly bounded infinities (theilweise bcgriinzte Unend- 

 lichkeiten), it is unmagnifiable. 



These speculations, which are really rather more hyper- 

 physical than metaphysical, immediately suggest the 

 analogous kinematic considerations, and have led me to 

 examine the potential dimensions of differentiated energy. 

 Before pointing out the main conclusion to which I have 

 been led, let me make quite clear the meaning of the 

 terms employed. "Differentiated energy" is that energy 

 which would survive if all matter were destroyed, and 

 simultaneously re-created in such a manner that all its 

 properties were inverted. By "potential dimension" I 

 mean the dimension which, by reason of the kinetic 

 energy of all other dimensions, is only able to vary 

 according to Lobwirmski' s groove {Kleise). 



Let us start from the idea of what is ordinarily con- 

 ceived to be a Thing, and imagine the Thing itself (not its 

 measure) to be saturated with the property a, after the 

 manner in which the circle is saturated with the straight 

 line in the spiral watch-spring (spiraijormi^er Haase- 

 sprutig einer Wacht). Further, let us suppose a to 

 change in such a way that all previous values of any one 

 attribute other than those dependent on its rate of varia- 

 tion can be arranged in a series, the functionally alternate 

 terms of which, up to a certain number whose value will 

 be given by taking each turn separately, and finding to 

 what amount its a property may, under the influence of 

 the given " groove " exceed the rt-property of its imme- 

 diately antecedent term, represent any convenient con- 

 verging series. The vigour of this change being, as 

 usual, measured by the degree of matter affected, and 

 also by the index of change in a given time, we have at 

 once the simple relationship 



-\% 



Accordingly, it is obvious as one of the simplest 

 corollaries from the above, that if we know the present 

 position, mass, direction of motion, and velocity of a given 

 piece of matter, we should be able within certain limits to 

 calculate its chemical composition. 



As an example of the application of this let us suppose 

 that the earth's satellite M has the mass C ; let its 

 direction of motion at any given time q be N. Let its 

 rectangular co-ordinates, at the same time, measured 

 from the absolute zero of position, be m, >i, and /. Let 

 O be its velocity, and H an arbitrary constant. We have, 

 substituting in the above equation— 



M = C,„ N„ 0/ H„ , 

 which has, at least, no closer resemblance to any other 

 body than it has to caseine. A. v. Nudeln 



■ The correspondent who has received the above letter has forwarded it to 

 us for publication. We are not aware that the general scientific opinion in 

 Germany is in consonance with the results reached in the letter. 



