KN()\\Li:i)r,i:. 



NOVKMUI.K. 191 : 



to tln' licliavioiir of tlic lt>\vtT forms of life lii'cotncs 

 still mort' c<)iiii)letL'. 



To assort, however, as Lfiimann lias (ioiic. lluil 

 living growth depends essentially ujion the agency 

 of crystallisation, is a conclusion to which all would 

 not care to accompany him. Notwithstanding the 

 array of evidence which he i)rings forward, much 

 more research and rational consideration are necessar\- 

 hcfore anything definite can be confidently sidniiitted. 

 .\s a tentative suggestion, nevertheless, the idea is a 

 striking one and affords an interesting contribution 

 to modern s(ieculation u])on the origin and mechanism 

 of life. 



Conclusion. 



The now acknowledged existence of liquo-crystal- 

 line types naturally strikes a blow at our definition 

 of the word "crystal." Hitherto, the term has 

 always been associated with the ideas of rigidit\' 

 and solidit}' ; but in the light of the evidence above- 

 mentioned, this old idea must be abandoned and one 

 must admit that under certain conditions, a liquid 

 may exhibit, if not always the accidental circum- 

 stance of form, at least the more important optical 

 properties which are the outcome of a molecular 

 arrangement. In this way. the barrier between the 

 solid and litjuid states is partially demolished. 



As to what constitutes the raison-d'efre of liquid- 

 cr\-stals, the h\-pothesis advanced by Lchmann 

 appears to be the most likely. Especially is this the 

 case after the failure of the ordinary theory, w hich 

 attempted an explanation on the basis of a simple 

 emulsion. Lehmann assumes the existence of some 

 directive force, called a "configuration-determining" 

 force, which produces a parallel arrangement of the 

 molecules in s[)ite of the liquid state, and each mole- 

 cule of the liquid, b}- virtue of this force, is supjiosed 



to be striving to arrange itself as |)art of a si>atial 

 configuration. \'orlander's independent observations 

 lend considerable colour to this notion. If, as he 

 declares, all "liquid-crystal" molecules possess long 

 chain formulae, their sha|)e may be taken to approxi- 

 mate to wires or plates and these will Ix; able to 

 arrange themselves in some definite order. On the 

 other hand, with molecules not so shaped, the space 

 they occupy n[)proximates more nearly to the 

 spherical, and so the liquid, being onlv a chance 

 aggregation of individuals, will appear isotropic. 

 This probably explains w hy it is that all liquids do 

 not display crystallinity, though their molecules 

 may be subject to this "configuration-determining" 

 force. 



To say more of Lihmann's brilliant achievements, 

 both experimental and theoretical, is not possible 

 within the narrow limits of this article. But from 

 what has been written, it will be gathered that his 

 work constitutes a noteworthy extension of our 

 knowledge of states of matter, particularlv of the 

 borderland between the solid and licjuid states: and 

 from the many developments which have accrued, 

 the whole subject should be one of surpassing 

 interest, not only to the physicist and the crvstallo- 

 grapher, but also to the student of rlumistrv or of 

 biolog\\ 



In conclusion, the author wishes to tender his 

 best thanks to Professor Lehmann himself for the 

 kindness he has shown in speciallv preparing the 

 photographs which illustrate this article. Readers 

 further interested in the subject are referred to 

 Professor Lehmann"s numerous published researches 

 and to his books upon the subject, the chief of 

 which, " Fliissige Ivristalle " and " Die neue \\'elt 

 der fliissigen Kristalle," are well worth consideration. 



CORRESPONDENCE 



THE FOLKTH DIMENSION. 

 To the Editors of " Knowledge." 



Sirs, — In a letter in your issue of September, Mr. H. Stanley 

 Redgrove states that " by the principle of the continuity of law, 

 or the uniformity of nature .... the existence of a third 

 dimension implies that of a fourth, and so on ad infinitum,'^ 

 and he argues that belief in a fourth and other dimensions 

 is of the same nature as our belief that the sun will rise 

 to-morrow. Our own unvarying experience of the sun rising 

 every day, as also the unvarying experience of man throughout 

 past ages, tells us that this is a law of nature. We believe 

 that what has occurred in tlie past will occur in the future. 

 Our experience of dimensions gives us the law that where 

 there is one there must be three, but it gives us absolutely 

 nothing else. There is nothing in it to lead us to believe, or 

 even to suggest to us, that there are other dimensions. There 

 is, consequently, no resemblance between belief in a fourth 

 dimension and belief that the sun will rise tomorrow. Mr. 

 Redgrove refers to detailed arguments for a fourth and other 

 dimensions in a book which he has published. These 

 arguments must be based not on experience but on some- 

 thing else. But experience — some kind of direct perception- 

 is the only possible basis of our knowledge of what exists. 



Henuon, N.W. JOHN JOHNSTON. 



THE TRISECTION OF AN .\N<;LE. 



To tlic Editors of " Knowledge." 



Sirs, — I noticed in a recent issue of your journal a state- 

 ment by one of your correspondents to the effect that a circle 

 could not be squared by geometric methods. 



Now, quite a number of years ago, I ascertained hy a 

 geometric diagram or theorem, not shown here, that the 

 circumference of a circle is eejual to the perimeter of a triangle 

 the base and altitude of which are each equal to the diameter 

 of the circle. 



Roughly 



A n and H C eiiual. 



This gives the ratio of the circumference of a circle to its 

 diameter as (using five places of decimals) 3-23606. 



Now, can you tell me? Has anyone stated this fact before 

 and demonstrated it. 



"GEOMA." 

 Brisbane. 



