June io, 1892,] 



SCIENCE. 



331 



has occurred during a comparative calm on some occasions, 

 whilst on others, though a strong gale has been setting in- 

 shore, I have not noticed any difperence in the lake's level, 

 so it would seem that this occurrence is not altogetlier at- 

 tributable to the wind backing up the water. Another 

 curious feature is the periodical rise and fall which, accord- 

 ing to the natives, takes place every twenty-five years, and 

 W'hicli is shown by the water marks on the shores. At the 

 time of my visit the lake was between eight and nine feet 

 below high-watermark, and the people told me that certain 

 lands then under cultivation would again be flooded in due 

 season, and that the peninsula on which my camp was 

 pitched would again become an island." Similar changes 

 of level have been noticed, both in Lake Tanganyika and 

 Lake Nyassa, and it is very desirable in the interests of 

 geograpliy as well as the development of the continent that 

 continuous observations should be made, in order to discover 

 what is the real character of these changes. 



LETTERS TO THE EDITOR. 



,ii*# Correspondents are reqiiested to be as brief as possible. The writer's name 

 is in all cases required as proof of good faith. 



On request in advance^ one hundred copies of the number containing his 

 communication ivill be furnished free to any correspondent. 



The editor will be glad to publish any queries consonant with the character 

 of the journal. 



The Relative Hardness of Cut Diamonds. 



Will tou allow me to add the result of my experience to the 

 testimony of Mr. Kimz that the hardness of diamonds is not per- 

 ceptibly reduced hy cutting and polishing ? In the earlier years 

 of my experience in ruling upon glass I was accustomed to select 

 a gem with a saioothly glazed surface, and, splitting the stone in 

 a cleavage plane inclined at a rather sharp angle to the natural 

 face selected, this s^pjit face was then ground and polished. 



In this way I was ai'le to obtain at several points short knife- 

 edges, which gave superb results in ruling. It was soon found, 

 however that after ruling several thousand rather heavy lines the 

 diamond was liable to lose its sharp cutting-edge, and this ex- 

 perience became so Irequent that I was compelled to resort to the 

 method now employed, that of grinding and polishing both faces 

 to a knife-edge I have one ruling diamou'i prepared in this way, 

 -which has been in constant use for four years, and its capacity 

 for good work has not yet been reduced in the slightest degree. 



A diamond prepared by Mr. Max Levy of Philadelphia has given 

 even better results, and so far it shows no evidence of wear. 



Wm. a. Rogers. 



Colby University, Watervllle, Me., June 6. 



The Notion of Four-Fold Space. 



In a paper by Professor T. Proctor Hall, entitled "The Possi- 

 bility of a Realization of Four-fold Space," a digest of which 

 appeared in Science for May 13, the author, after making certain 

 allusions, remarks " there is therefore nothing inherently absurd 

 or improbable in the supposition that any of us may attain to a 

 concept of four-fold space ' as clear as the designer and the 

 draughtsman have of three-fold space.'" The word "there- 

 fore" refers to what immediately precedes, and here we read: 

 " Perhaps most of us can remember times in the course of our 

 education when new conceptions of quantity entered into our 

 conscious life, conceptions which correspond in a general way 

 with those of length, area, and volume, in that they enable us to 

 find at once such relationships as are most frequently required for 

 practical purposes by a general, synthetic, instinctive method .... 

 The sense of propriety, the sense of honor, and numberless other 

 ■■inbred' or 'instinctive' concepts are examples of this mental 

 tendency." There is no such connection, however, between this 

 and the succeeding paragraph, quoted above, as to justify the 

 assertion made with reference to the conception of four-fold space, 

 and the utmost that can be properly inferred is, that, in the words 

 of the following sentence, " such a conception would be of great 



value to all classf s of scientists " — assixming always that it is a 

 possible conception, tliat is, possible to us with our present mental 

 constitution. I do not propose to enter into this question, but it 

 seems to me that Professor Hall's argumfnt is open to criticism in 

 other resjiects 



For instance, he does not sufficiently meet the objection based on 

 the fact that "our conception of threefold space is derived, 

 directly from sensations in three-fold space, and that the concep- 

 tion of four-fold space cannot be derived in a similar way, nor 

 yet from sensations in three-fold space.'" It may be admitted that 

 from the sense of sight we get only a two-dimensional sensation, 

 and that the existence of a third dimension is solely a matter of 

 inference. Yet. this inference has a physiological basis, and is 

 justified by universal experience in past and present generations, 

 so that we know that it expresses the truth. The conditions 

 relative to the conception of four-fold space are quite different. 

 There are apparently no grounds on which a fourth dimension 

 can lie inferred, and so far from such an inference being in 

 accordance with experience, this entirely opposes it. To render 

 the truth of such an inference probable, it would have to be 

 shown that the existence of a third dimension is inferred solely 

 from that of two-dimensional space, and yet even then, as the 

 conception of a three-fold dimension would be supported only by 

 that of a two-fold dimension, it would hardly form a sufficient 

 basis for the existence of a fourth. In fact this would ultimately, 

 like the second, be based on the conception of two-fold space. 



The conditions of the question are such that the hypothesis of a 

 fourth dimension cannot be made as real to us as that of the 

 existence of a third dimension ; any more than Professor Hall's 

 plane being, that is, a being who has no conception of volume, 

 could understand a geometric solid. It is one thing for a person 

 who knows all about three-dimensional space to explain how an 

 imaginary plane being might be able to form such a conception, 

 but a totally dilferent thing for the plane being to perform the 

 operation. The conduct of animals shows that they act according 

 to the same view of space that we do, and yet none of them 

 could form any idea of the relations of the faces of a cube, al- 

 though propably some very clever dogs can be taught the number 

 of its faces. How much less coidd any plane being form an idea 

 of those relations. In supposititious cases of this kind, it is 

 always assumed that the imaginary being would be limited only 

 in his ideas of space, but surely this notion is erroneous. A being 

 thus deficient would, by virtue of the lavr of organic correlation, 

 be equally deficient in other respects, and would rank in an infe- 

 rior grade of organic development. Such being the case, it is 

 impossible to imagine a plane being acting as a three-dimensional 

 philosopher, and constructing a theory of the evolution of circles, 

 true or false. 



It seems to me that those who endeavor to imagine the possi- 

 bility of four-dimensional space look in the wrong direction. It 

 is very questionable whether, as we are at present constituted, we 

 can possibly form any such idea of space, but there is another 

 view which is worthy of consideration. We know space only in 

 relation to formed matter, and if such matter were to disappear, 

 space would, as so related at least, disappear also. According to 

 present conditions such a state of things would seem to be highly 

 improbable, but we can nevertheless, from what we know of the 

 past, conceive its possibility. If we trace the evolu ional stages 

 of organic nature back through the higher animals from man we 

 reach the worm, from which, according to Heeckel. they have all 

 sprung. Going still further back we come to the primitive 

 moneral ancestor of all organic existence on the earth. But we 

 can retrace the path of evolution beyond the primordial sHme, 

 until we arrive at its beginning when, says Professor Crookes, 

 " primitive matter was formed by the act of a generative force, 

 throwing off at intervals of time atoms endowed with varying 

 quantities of primitive forms of energy." Before this there 

 existed, we are told, the formless fluid, from knots and voids in 

 which the chemical elements were formed. 



But what has had a beginning can come to an end, and we can 

 imagine therefore all organic and inorganic forms being reduced 

 to the primitive elements, and these elements themselves resolved 

 iuto the formless fluid from which they were derived. Professor 



