January 19, 1905] 



NA TURE 



273 



important subject as the reality or unreality of hetero- 

 genesis, persons like Mr. Massee, who could speak authori- 

 tatively, should not think it necessary to make personal 

 observations, and should be content to offer in reply to 

 real and prolonged work only loose explanations which 

 will not bear any serious examination. 



.'\ further instance of the same lack of care is aJforded 

 in the last sentence of Mr. Massee's letter. Referring 

 evidently to my remark (Nature, November 24, 1904, 

 p. 77) as to the very different products that may be met 

 with in the scum forming on an infusion made from 

 unripe grasses as compared with that forming on an 

 ordinary hay infusion, he says : — " As these fungi only 

 develop on fading leaves it was not to be expected that 

 they would appear in infusions of young grass." This 

 sentence must have been penned without the writer having 

 taken the trouble to look at p. 87 of my " Studies in 

 Heterogenesis," to which reference was made when I 

 directed attention to the differences in question. Had he 

 done so he would have seen how little he had e.xplained 

 the differences noted on that and on the following page, 

 and he would also have seen that the most striking differ- 

 ence recorded is the complete absence of Zooglcea masses 

 (spoken of there as " areas ") in the scum forming on 

 infusions of unripe grasses. Of course if the Zooglcea 

 masses are not there it is easy for me to understand the 

 absence of the Fungus-germs which, as I maintain, are 

 produced therefrom. 



This point, as well as others in Mr. Massee's letter, 

 shows the great importance of bearing in mind two wholly 

 distinct aspects of my observations, corresponding with 

 different stages in the processes described. We have to do 

 (i) with the growth, the individualisation, and the pro- 

 cesses of segmentation talcing place in masses of Zooglcea. 

 We have also to do (2) with the question of the ultimate 

 destination, or the transformation, of the products of such 

 segmentation. These are two parts of the subject which 

 are to some extent distinct, and are well worthy of further 

 separate consideration.' 



In conclusion I would ask. Why do the bacteriologists 

 not tell us what they know about Zooglcea — whether they 

 are or are not aware of its developmental tendencies, and 

 why it should undergo processes of minute segmentation, 

 unless such processes are a result of an organising tendency 

 destined to have some definite outcome? Why, again, 

 should it or its segments so often tend to assume a brown 

 colour, while it is still nothing but Zooglcea, either 

 segmented or unsegmented? Again, why, if the brown 

 Zoogloea does not yield the brown Fungus-germs, should 

 there be this constant association of myriads of brown 

 Fungus-germs (in the absence of hyphae) in association 

 with brown masses of Zoogloea? How can they explain, 

 other than I have done, the actual organisation of a 

 Zooglcea mass, and the stages by which the brown Fungus- 

 germs seem to be formed therein? What process of 

 " infection " in a filtered hay infusion contained in a 

 closed pot could cause thousands of small Zooglcea masses 

 to go simultaneously through similar processes of this 

 kind — producing myriads of brown Fungus-germs — when 

 not a single hypha is anywhere to be found, and when at 

 first no Fungus-germs are to be met with outside the 

 Zoogloea masses themselves? I trust the bacteriologists 

 will vouchsafe to give us some information on these points, 

 or, if they cannot reasonably explain them, that they may 

 be induced to work at the subject, and satisfy themselves 

 that something important can be learned concerning 

 bacteria, even though it be outside their laboratories and 

 by methods other than their own. 



H. Charlton Bastian. 



Compulsory Greek at Cambridge. 



As a corrective to much vague discussion, perhaps the 

 following record of facts may be of interest. 



Entering the University of Cambridge in 1886, entirely 

 ignorant of the Greek language, I was, of course, obliged 

 to pass the " Little-go " in order to proceed to the natural 

 sciences tripos. The Greek subjects prescribed were the 

 Gospel of St. Mark, the Pluto of Aristophanes, and the 



1 My further observations on this subject will be found in the February 

 number of the Annnh and Magazine of Natural History. 



NO. 1838, VOL. 71] 



usual grammar papers, and, in conjunction with a friend 

 similarly circumstanced to myself, I set to work to 

 " cram " these by as " scientific " methods as we could 

 devise, in order to pass with as little waste of time as 

 possible. 



Purchasing a copy of Wordsworth's " Primer of Greek 

 Grammar," we read the nouns, adjectives, and the active 

 voice of TuiTTtt — no more, and then started on the pre- 

 scribed books. These we translated by aid of a good 

 lexicon, word by word — thus learning the parts of the 

 irregular verbs, which form a favourite subject in the 

 grammar papers. Having been once through the books 

 by this method, we procured the translations, and read 

 these through five or six times, in order to become so 

 familiar with the subject-matter of the books that we 

 could translate most passages easily at sight after making 

 out the leading words in them. 



The actual time expended by us in the preparation of 

 Greek for the examination was carefully recorded, and 

 amounted to 1055 working hours, and we passed the 

 examination in the second class, with, I believe, a con- 

 siderable margin of safety even in Greek. I need hardly 

 add that my present knowledge of the language is nil. 



John C. Willis. 



Royal Botanic Gardens, Peradeniya, Ceylon, 

 December 28, 1904. 



Polyhedral Soap-films. 



The fact that polyhedral wire frames can be used for 

 the purpose of forming films across them is well known, 

 but there are some features of this subject, which I have 

 investigated, which may be of interest. 



If a frame of wire representing the edges of one of the 

 simpler polyhedra, such as a cube or octahedron, is dipped 

 into soap solution, then on taking it out it will have filnis 

 attached to its edges and meeting roughly at a point m 

 the centre of the figure, forming a number of pyramids 

 standing on the faces of the figure. If, however, a more 

 complex figure, such as the rhombic dodecahedron or the 

 eicosihedron, be taken, then the effect will be quite different ; 

 the film will then simply cover all the faces except the 

 one which was drawn out of the solution first. The former 

 thing will happen if the area of the ("-i) faces is greater 

 than that required to form the pyramids, while the latter 

 will occur if the reverse is the case. 



If, now, in the case of the cube, for instance, after the 

 pyramids have been formed, a film be applied to one of 

 the faces, then a certain amount of air becomes entirely 

 enclosed by film, and the bubble so formed settles in 

 the centre of the frame, forming roughly a cube suspended 

 in the frame by twelve sheets of soap-film. On closer in- 

 spection, however, it will be seen that the faces of this cube 

 are convex, thus showing that the air in it is compressed. 

 By inserting a tube this cubical bubble can be inflated or 

 reduced in size, all the time retaining its convexity, so 

 that if thus left in communication with the air it will 

 collapse of its own accord. A little consideration shows 

 the reason for this, namely, that three films meeting one 

 another cannot be in equilibrium unless their planes are 

 inclined to one another at 120°, since the tensions in all 

 three are equal. But since the dihedral angle of a tetra- 

 hedron, cube, or octahedron is less than 120°, therefore in 

 these figures the internal polyhedral film must always have 

 convex faces. . 



From this I expected to get an exact polyhedron with 

 plane faces in the case of the rhombic dodecahedron, since 

 its dihedral angles are all 120°. On trying this it was 

 found to agree remarkably with my assumption, only, as 

 may be gathered from what has gone before, it was not 

 quite so simple to obtain the central bubble as in the former 

 case. After the (n-i) faces had been covered with film 

 the figure was again immersed so as to displace about one- 

 half the air contained in it, and while thus immersed^ it 

 was turned round so as to cover the one open face with 

 liquid. On withdrawing it there was seen the plane-faced 

 rhombic dodecahedron. The same result can be obtained 

 by applying a film to the nth face and then exhausting 

 some of the enclosed air by means of a tube. By using a 

 tube, as in the former cases, the bubble can be enlarged 



