August 31, 1893] 



NA TV RE 



415 



Campanula rotundi- 



Jolia July 8,1893; July 2- IS, 1887-92 



Calluna Erica ,, 22, ,, ,, 19, 1887 



J asione montana I, ,, ,, 2, 1892 



C nil us arz'ensis ... ,, 1, ,, ,, 2, 1 889 



Scabiosa succisa ... ,, 22, ,, ,, 23, ,, 



GaUopsis Tetrahit ... ,, 15, ,, ,, 16, 1892 



The general result is, then, that the season was three wee'..s 

 early in March, but that by the first of April the advance had 

 increased to four weeks ; this was maintained through most of 

 ihe month, but May day was only some three weeks in advance ; 

 the fall continued slowly through May and June with an average 

 advance of a fortnight. In July, however, the effects of the 

 early spring had ceased to have any effect. These conclusions 

 are more likely to err on the side of moderation, for it mu-t be 

 remembered that the flowering time this year has been con- 

 trasted not with the average, but with the earliest record of 

 previous years. W. B. Crump. 



Mr. Love's Treatise on Elasticity. 



The second volume of Mr. Love's treatise will doubtless 

 be reviewed in Nature in due course ; but in the meantime 

 I desire to make some observations upon certain criticisms, 

 which this work contain^, on my own papers on thin ela^tic 

 shells, plates, and wires. 



The theory of thin plates, and shells in the form given by 

 Mr. Love, is ba^edupon those of Kirchhoff, .Saint-Venant and 

 Clebsch. All these theories are incomplete and defective, and 

 depend upon certain assumptions and approximations which 

 have been called in question, ar.d are by no means free from 

 difficulty. An attempt has been made — see pp. 92 and 207 — 

 to remove these objections by classifying the different cases 

 which arise, but whatever may be thought of the success of this 

 explanation, it requires the reader to wade through a long and 

 complicated analytical investigation before he is in a position 

 to apply the theory. 



On the other hand, the method of expansion originally 

 employed by Poisson, and afterwards by myself, coupled with 

 the hypothesis that the stresses R, S, T may be tiraledai zero, 

 is one of great power, and, as I showed a few years ago, enables 

 an approximate theory to be completely worked out as far as 

 terms involving the cube of the thickness of the plale or shell, 

 and Mr. Love is forced to admit on p. 236 that his own theory 

 is incapable of doing this. It is true that Clebsch and Saint- 

 Venant have raised objecli ns against the method of expansion 

 which I cannot regard otherwise than as frivolous ones ; but 

 aUhough an account of the first class of theories is no doubt 

 desirable, it is mujh to be regretted that Mr. Love has allowed 

 his bias against the second class of theories to lead him to 

 adopt a mode of treatment which greatly increases the 

 difficulties of the suhjecl, is less perfect, and which, I fear, will 

 retard its further progress by throwing unncctssary obstacles in 

 the way of students. 



On pp. 238 and 262, Mr. Love imagines that he has detected 

 an error in my own work as regards the values of T,. T^ (in his 

 notation P„ F,), but this conclusion is not warranted. His 

 investigation in § 353 expressly supposes the vibrations to be 

 non extensional, whereas in the investigation by which I have 

 calculated, T„ T, by means of the variational equation, exten- 

 sion is expressly suppostd to take place. If it were desired to 

 calculate the values of T], Tj by the variational method in the 

 case of inextensibility, it would be necessary to start with the 

 corresponding form of the potential energy, and to take account 

 of the fact that Su, Sv, itu are not independent, either by means 

 of indeterminate multipliers or by elimination. The two cases 

 are therefore not parallel, and the so called test is nugatory. If 

 a direct test were desired, it could be supplied by means of the 

 theory of the radial vibrations of a cylinder worked out to a 

 second approximation. 



The only other point to be noticed is that in the case of a 

 bent wire the values of the three couples given by Mr. Love on 

 p. 169 disagree with those obtained by myself. Mr. Love 

 assumes these couples to be respectively proportional to the 

 changes of curvature and twist, and he then proceeds lo calcu- 

 late the latter quantities in terms of the displacements by a 

 method which leaves nothing to be desired as regards elegance 

 and conciseness and comprehensiveness. But he can scarcely 

 be said to have given anything which can be called a proof that 

 these couples are actually proportional lo the above-mentioned 



NO. 1244, VOL. 48] 



quantities ; and a new and independent investigation is much 

 to be desired. A. B. Basset. 



Hotel de Russie, Bad-Ems, Nassau, Germany, August 23. 



An Appeal to Mathematicians. 

 SI^"CE I have commenced the study of the "Ramayana" 

 (the great Sanskrit epic) in original Sanskrit, and its translations, 

 epitomes, anel commentaries by renowned European scholars, 

 I have been struck with the inadequacy the western scholars of 

 Indian chronology have shown in fixing the dale of Rama. 



I cannot but admire the method used by our modern Egypt- 

 ologists in computing the dates of Egyptian chronology, and 

 correcting the discoveries of some of the earlier researches in 

 that interesting branch of knowledge. Having discovered it 

 written in some old MSS. that in the reign of a certain kirg 

 sotne remarkable comet or eclipse was observed, or a 

 building was erected pointing to a certain star in the heavens, 

 which has since changed position, c&c, &c., our scholars have 

 obtained sufficient data to compute with tolerable correctness 

 a more or less trustworthy date for that king. 



There is no doubt that such refined discoveries could never 

 have been made if this branch of knowledge were left alone with 

 simile historians or simple chronologists — I mean, no light 

 would have been thrown over the pages of the dark history of 

 Egypt had not astronomical methods been employed to solve 

 the vital questions of Egyptian history. 



I am very much grieved to see that the chronology of India 

 has not at all been touched by any scientific investigator whose 

 conclusions could be relied on, though Indian chronology is row 

 proving to be far more interesting than the chronology of any 

 other country or nation of the world. India has now the honour 

 of being under the benign rule of the British nation, so forward 

 in scientific matters ; then does it not give grief to the lover of 

 India to see this important branch of past history so much being 

 neglected ? 



The second half of the eighteenth century and the first quaiter 

 of this nineteenth century had seen a few benefactors of imlia, 

 like Profs. Colebrojke, Muir, Wilson, &c., whose di,-coveiies 

 brought to light much interesting information al out 

 ancient India. It was a misfortune (or India of today that 

 au ong those benefactors they were few who could brirg in 

 mathematical astronomy to solve some vital points of Indian 

 chronology. Prof. Colebrooke wrote some valuable essays on 

 the Hindu system of astronomy, but it was our misfortune that 

 his attention was not drawn towards the Indian chronohgv; 

 otherwise he was a man who could have done much to settle 

 the dates of Hindu chronology. 



Rama has been a personsgeof Indian history whose existence 

 has not yet been denied by any scholar, yet see what conflicting 

 dates have been given to this mighty king of ancient India: 

 Sir William Jones places Rama in the year 2029 B.C., Tod in 

 1 100 B.C., and Bentley in 950 11. c. Govvesio would place him 

 about the thirteenth century before the Christian eia I 



Govvesio computes his date thus : — "From Rama to Siimitra, 

 the contemporary, as it appears, of Vikramadiiya (b c. 57), 

 fifty-six kings ruled in successson. By allowing on a reasonable 

 computation an average of a little more than twenty jeais 10 

 each reign, we auive at the thirteenth century before the 

 Christian era." (" Kamagana,'' vol. i. Introduction.) While 

 it is questionable whether any king by name of Suniitia ever 

 reigned in India, or was a conlcmpoiary with Vikramadiiya, 

 Govvesio confesses — "But lo this opinion I do not intend 10 

 attribute more weight than that of a piol able conjecture." And 

 so it is ; at.d a ridiculous one, too ; for Sumiira ' was not a king 

 contemporary with Vikiamadilya, \\\Xshe was one o( the queens 

 of the king Uasaiatha, the lather of Rama. 



1 now come 10 the point of my appeal. Here is the position 

 of the seven primary pl.Tnels at the lirih of Rama plainly written 

 in Canto xix. of the first book of the Ramagana : Moon in Can- 

 cer, Sun in Aries, Mercury in Taurus, Venus in Pisces, Mars in 

 Capricornus, Jupiter in Cancer, and Saturn in Libra. The 

 problem to be solved is this: Taking jaruary i, 1894, tas 

 starting-point, compute when the planets occupied the 

 positions resjicctively referred to ' above, and when a 'ain 

 they will occupy the same positions in the future? Th.uigh 

 the prolilem appears to be a simple one of peimutation 

 ai d combinatior, but I must confess with regret that none 



I "Sumiira "is a San^kr;t word of feminine gender. As Sar.skril was a 

 living lanKuage at the lime of Vikramadiiya, though perhap, oi.ly within 

 higher circle, ofsociety, jet it could not be believ.dlhat iliis word ii.ight 

 1 ave been so degecerated as to be used in opposite gender at ihal lime 



