lO 



NATURE 



[March 3, 192 1 



pictures in which Unes with the most wonderful con- 

 tortions have been supposed to represent the effects of 

 adding new dimensions to space. They are useful 

 only as illustrations of the enormous gap separating 

 this so-called hyperspace from the space of human 

 experience. There have latterly been attempts to go 

 much further and to import the creations of Rie- 

 mann's imagination into the analysis of physical 

 problems, into speculations on the construction of 

 space beyond the range of human vision, and to 

 postulate on the existence of space of different kinds, 

 including curvilinear space, all of which I deem to 

 be entirely outside the province of legitimate induc- 

 tion. The word "curvilinear" describes a predicate 

 or function of matter, but not of space; as well 

 might it be applied to a vacuum. Nor do I exactly 

 know what Prof. Einstein means by relative space 

 as used by him. The word "relative " has a perfectly 

 recognised meaning in philosophy as the antithesis 

 of "absolute." If it is used by him in this sense, 

 assuredly there is no novelty in it. It was the 

 fashion of the philosophers of the ancient world and 

 of the schoolmen of medieval times to separate space 

 and time from the other phenomena of Nature. They 

 held that both have an objective existence, and 

 are not, as they deemed, entirely subjective and 

 transient, like the more obvious presentations of 

 sense. There are many rebels against this 

 notion now who claim that space is as much 

 entitled to be called a subjective phenomenon as is 

 colour or taste, and that a man void 6f the senses 

 of sight and touch could have no cognisance of what 

 we mean by space. As to the size of any portion of 

 space being relative only, I happen to have myself 

 a personal proof of it in the fact that, my two eyes 

 having lenses of different curvature, any object seen 

 with one appears to my consciousness as one-third 

 larger than when seen by the other. In the sense here 

 mentioned I understand the word "relative," but I 

 fail to understand what Prof. Einstein means by it. 



Meanwhile, let us try to be content with our 

 limitations. One of the earliest antinomies recorded 

 was the question of whether space is limited or un- 

 limited. It remains an antinomy still, and must 

 remain so. The one alternative is as incredible and 

 unimaginable as the other, and the Sphinx refuses to 

 reply when she is aske<.l about it. There is no cal- 

 culus available by which men with limited faculties 

 and all prone to error can map out infinity, 

 discover the secrets of the realms beyond the stars, 

 and transcend the world accessible to our senses, and 

 which alone can be equated with, and adequately 

 tested by, inductive methods. Let us leave to the 

 pure mathematicians the delightful occupation of 

 rambling through wonderland with their imagina- 

 tion. It would be unreasonable to deprive them of 

 their mental relaxations and amusements in the land 

 of dreams in which they have such ample scope for 

 mental dexterity. All I maintain is that these dreams 

 are entirelv out of place in that branch of inductive 

 thought called science. My most shifted friend Mr. 

 Hobson, of Queens' College, Cambridge, a very 

 original mathematician, in a lucid account of the 

 aims and purposes of pure mathematics, emphatically 

 protests against mixing up that empyrean study with 

 the mundane realities of plebeian physics. 



Lastly, let us remember a graphic phrase of 

 Mansel when dealing- with transcendentalism in philo- 

 sophy. He warned his pupils that " a man who tries 

 to look down his own throat with a candle in his 

 hand must take care that he does not burn his back 

 hair." 



I have touched only the fringe of the subject raised 

 NO. 2679, VOL. 107] 



in this most interesting discussion, for which we are 

 all grateful, but I feel that whether the space dis- 

 cussed in it is limited or not, yours is very definitely 

 limited, and I must trespass on it no further. 



Henry H. Howorth. 

 45 Lexham Gardens, February 21. 



Natural History of Porto Santo. 



The Island of Porto Santo, one of the Madeira 

 group, is probably best known to biologists on account 

 of the famous rabbit still found commonly there. 

 Darwin showed that the animal differed conspicuously 

 from the English rabbit, and inferred that it had 

 evolved into a new race since its introduction into the 

 island some hundreds of years ago. Haeckel gave it 

 a distinctive name, Htixleyi. It is, indeed, a distinct 

 race or subspecies from the English rabbit, but 

 zoologists had failed to observe that it was identical 

 with the Lusitanian animal, which had not then been 

 segregated by them. Thus the Porto Santo rabbit 

 loses its importance as evidence of evolution, being, 

 in fact, the South European subspecies of OryctoLagus 

 cuniculiis. 



To the modern biologist, however, Porto Santo has 

 far more attractive features. It is a small island, 

 some 6^ miles by 3 miles, but of irregular shape, with 

 a number of adjacent islets. Yet on this small area 

 are found as many as forty-one native species of 

 Helicoid snails, the very much larger island of 

 Madeira having only thirty-seven. A few of the 

 forty-one are now extinct, being- represented only 

 by fossils or empty shells. On the other hand, 

 the number may be considerably increased if we 

 add the varieties and local races, some of them quite 

 distinctive. In addition to the native species, there 

 are some which have been introduced, and Helix 

 pisana, in particular, exists in countless myriads, with 

 many variations. It seems to have been no obstacle 

 to the spread of this snail that the island was already 

 occupied by a prodigious number of land mollusca. 

 Whether the advent of H. pisana reduced the numbers 

 of the native species it is hard to say, but the latter 

 still abound everywhere. 



The largest and finest snail of Porto Santo is 

 Pseudocampylaea Lowei, Ferussac, or gigantea, 

 Lowe. It is a quite common fossil in beds which 

 must apparently be referred to the Pleistocene, but 

 it has been found living, and a perfectly fresh shell 

 is to be seen in the British Museum (Natural 

 History). I found no living specimens, but ob- 

 tained several shells in ploughed fields, showing 

 the pink apex and traces of the bands ; cer- 

 tainly not fossils. It may be that agriculture has 

 been the principal cause of the extinction (it is prob- 

 ably now extinct) of this fine mollusc. Leptaxis 

 fluctiwsa, Lowe, is another species which seems to 

 be extinct, but I found a recent shell showing the 

 coloured banding. The islets about Porto Santo are 

 extremely interesting. The Ilheo de Cima, on which 

 the lighthouse stands, is about 1200 metres long and 

 less than 500 metres across at its widest part. It is 

 scarcely 300 metres from the main island, and thet^ 

 are half-submerged rocks in the channel. Yet on this 

 islet we find swarming under stones the very distinct 

 and remarkable snail Geomitra turricula, Lowe, found 

 nowhere else in the world ! The large Pseudo- 

 campylaea portosanctana, Sowerby, which is a 

 sort of smaller edition of P. Lowei, abounds on the 

 main island. But on the Ilheo de Cima it has not 

 merely one distinct race, but two. On the top of the 

 islet, near the end facing the main island, we find a 

 very large, dark, depressed race, the greatest diameter 



