July 14, 1923] 



NA TURE 



57 



then with a half-twist bring the ends together, and 

 fasten the corresponding ends each to each. Our 

 half-twist will .have brought one end of the lower 

 strip into contact with the other end of the upper 

 strip ; and what we then obtain, on opening out, 

 is the long loop (or " worble," to use Maxwell's word) 

 with its two curls, which Prof. Boys starts with. We 

 have simply split into two sheets our original one- 

 sided, one-edged surface, and obtained a new bifacial 

 surface thereby, precisely as Mr. B. M. Sen explains 

 in his recent paper on " Double Surfaces " in the 

 Proc. Lond. Math, Soc. 



We may vary the experiment by starting with 

 three sheets (or with five) instead of tw^o. The middle 

 sheet or strip, joining on to itself, will always remain 

 the half-twisted loop, the unifacial surface ; while 

 each adjacent pair of strips will constitute a bifacial 

 surface such as Prof. Boys describes. The median 

 loop will involve, or link together, all the others ; 

 but the manner in which these latter interlace with 

 one another is more complicated. The problem of 

 how to split an anchor-ring into two rings, interlinked 

 with one another, is a simple corollary. 



It is somewhat curious at first sight, but obvious 

 after all, that we arrive at precisely the same result 

 whether we split our sheet, or cut it longitudinally. 

 Begin with one broad strip, joining its ends together 

 into the half-twisted unifacial surface ; then make 

 one continuous longitudinal cut, not far from the 

 edge. This single cut gives us two complete loops, 

 one being the border and the other the median zone 

 of our broad strip. The median band has its 

 properties unaltered ; it is still the half-twist unifacial 

 surface, only narrower than before. The other, on 

 which our scissors have bestowed a second edge, 

 is the bifacial surface which Prof. Boys calls his 

 " puzzle band." D'Arcy W. Thompson. 



44 South St., St. Andrews, 

 June 19. 



Active Hydrogen by Electrolysis. 



Wendt and Landauer (Jour. Amer. Chem. Soc, 

 March, 1922, p. 513) failed to get any evidence for 

 the presence of active hydrogen, generated by the 

 action of an acid on a metal, or by the electrolysis of 

 a solution of KOH. Similar results were also obtained 

 by Y. Venkataramaiah (Proc. Sci. Assoc. Maharaja's 

 College, Vizianagram, July 1921, p. 2). We have 

 repeated the experiments, and find that hydrogen 

 is actually activated when a conducting solution 

 is electrolysed. We electrolysed a solution of dilute 

 sulphuric acid, employing a platinum tube with a large 

 number of pin-holes bored in it, and using a current 

 varying from 3 to 15 amperes. While the electrolysis 

 was going on, compressed nitrogen was bubbled 

 through the solution, through the platinum electrode, 

 to see if any ammonia were formed, as Wendt and 

 Landauer found that active hydrogen combines with 

 nitrogen to form ammonia. After a run of nearly 

 twelve hours, the presence of ammonia was tested in 

 the resulting solution. The result was positive. 



Another method was also tried, using an iron tube 

 as an electrode. It is known that nascent hydrogen 

 diffuses through metals like iron even at ordinary 

 temperatures. So it was found convenient to diffuse 

 nascent hydrogen through the iron tube and test for 

 the presence of active hydrogen by drawing it over 

 cold powdered sulphur, the presence of hydrogen 

 sulphide being tested for with a lead acetate paper. 

 Here also a positive result was found. 



The experiments with a metal and an acid are not 

 yet successful. The failure in the case of the experi- 

 ments of Wendt and Landauer, in our opinion, is due 



NO. 2802, VOL. 112] 



not only to the ditiiculties in removing the spray but 

 also to the action of active hydrogen on the spray 

 itself. Certain preliminary experiments conducted 

 by us show that active hydrogen is decomposed by 

 the spray with the formation of hydrogen peroxide. 



It is a pleasure to note from the latest number of 

 Nature to hand (May 5, p. 600), that Prof. A. C. 

 Grubb has succeeded by an ingenious experiment in 

 demonstrating the presence of active hydrogen in 

 the hydrogen generated by the action of hydrochloric 

 acid on magnesium. 



Y. Venkataramaiah. 

 Bh. S. V. Raghava Rao. 

 Research Laboratories, Maharaja's College, 

 Vizianagram, S. India, 

 May 28. 



The Transfinite Ordinals of the Second Glass. 



There is a theorem in the transfinite calculus 

 that any ascending sequence of ordinal numbers of 

 the second class has a limit which is also of the second 

 class. This theorem is important, being wanted to 

 prove that the aggregate of these ordinals is un- 

 enumerable. 



Now consider the set of numbers i, 2, 3, oj, w + i, 

 w-l-2, W.2, W.2 + I, w^, w^-j-i, etc. The mode of 

 formation is that each number exceeds the preceding 

 one by unity, except that if the plan we are following 

 leads us to a limit we write down only a finite number 

 of numbers according to that plan, and then write 

 down the limit and the limit increased by unity, 

 and so on. The set is normally ordered, and each 

 element has an immediate predecessor, whence we 

 easily see that it is a sequence. But it cannot have 

 any limit in the second class, for if ( the limit is a 

 the sequence must contain a and a -f- 1 . 



Does this contradiction with the first theorem 

 show that the ordinals of the second class form an 

 " inconsistent " aggregate ? It differs from that of 

 the Burali-Forti paradox in that we do not assume 

 that our aggregate has an ordinal number before we 

 get the contradiction. It agrees with it in that no 

 contradiction arises if we consider segments only of 

 the aggregate of ordinals. H. C. Pocklington. 



5 Well Close Place, Leeds. 



Shakespeare and the Indian Meteors of 1592. 



With reference to Mr. Denning's remark in Nature, 

 June 23, p. 848, I beg leave to point out that the 

 word in Persian for west, namely khawar, also means 

 east, and so it may be that the passage in the 

 Akbarnama means that the meteors were travelling 

 from east to west and not from west to east. 



Dean Inge lately observed in a lecture that there 

 was a mystery about what Shakespeare did in the 

 last five years of his life. May it not be that he 

 was travelling in Europe or on the high seas when he 

 saw so many stars shoot madly from their spheres 

 (" Midsummer-Night's Dream," Act II., Scene II.) ? 

 There is another allusion to meteors, " Yon fiery o's 

 and eyes of light," in Act III., Scene II., where 

 Lysander speaks of Helena's eyes. This seems to 

 show that Shakespeare's mind was running upon 

 stars and meteors. 



I may mention that in a letter to me Sir Sydney 

 Lee seemed to say that there was something in my 

 suggestion, and referred to another topical allusion 

 to natural phenomena in " Romeo and Juliet." 



H. Beveridge. 



53 Campden House Road, London, W.8. 



B 2 



