NA TURE 



[Februarv 1 6, 1899 



(5) Similar triangles are equal in all respects — sides equal to 

 sides, angles equal to angles, areas equal to areas. Similar 

 triangles are to each other as their bases. 



(6) Similar triangles are to one another in the duplicate or 

 subduplicate ratio of their homologous sides. Their areas are 

 as the scjuare or square root of their bases according as it is in 

 the duplicate or subduplicate ratio. 



(7) Similar triangles are to one another as their bases. They 

 arc also to each other in the duplicate ratio of their homologous 

 sides. 



(8) Triangles are said to be similar when they have their 

 corresponding sides equal and are equal in area. Similar 

 triangles are to one another in the duplicate ratio of their 

 homologous sides. 



Each of these exhibits a pleasing variety and a liberal-minded, 

 large-hearted toleration of conflicting views. 



Such examples might be multiplied almost indefinitely, and 

 they show clearly the impotence of the dictum ' ' similar triangles 

 are to one another in the duplicate ratio of their homologous 

 sides" to convey any real knowledge to the mind of the ordinary 

 learner. "Duplicate ratio" and "homologous" are mere 

 sounds, to the latter of which violence is often done, inasmuch 

 as I have frequently met with " homolicus '' and " harmologous " 

 sides. 



Now, as regards the amount of time which is spent in the 

 schools by young boys in acquiring the elementary facts and 

 conceptions of geometry from Euclid's book, I know that very 

 many months are occupied in attaining to the twelfth proposition 

 of the first Book. I have before me, in fact, a fair-sized 

 treatise written for the purpose of guiding boys along Euclid's 

 e.xact path to this proposition. 



There is absolutely nothing in the first twelve propositions 

 that could not be taught far more effectively to a boy of ordinary 

 intelligence in a few days, if only a rational style of teaching 

 geometry were adopted ; but if the exact language and pedantic 

 professionalism of the school Euclids must be followed, to the 

 weariness of the boy's mind and the ((uenching of his interest, 

 it becomes a very long process indeed — ending, in the case of a 

 large number, in utter failure. 



.Moreover, the current practice which insists on compelling 

 boys to study geometry in an order and language characteristic 

 of mediaeval times, when no physical sciences existed, is a 

 hindrance to the study of such sciences now, inasmuch as 

 geometry is one of the foundations of, all exact science; and 

 it is obvious that if an intelligent knowledge of geometry is 

 postponed, the physical sciences must be kept back also. 



The plea that Euclid's book is unrivalleil as an exposition 

 of clear logical method and arrangement, and, as such, must 

 be the foundation on which to build geometry, is vain — for the 

 simple reason that it is not in England (where Euclid is 

 worshipped), but in France and Germany (where Euclid is 

 unknown as a text-book), that the great discoverers in geometry 

 have been produced. 



The late M. Paul Bert, Minister of Public Instruction in 

 France, published a little book on the proper method of teaching 

 geometry to beginners, in which he severely satirised the faults 

 of the existing procedure; and, again, the late Rev. W. .\. 

 Willock (father of Dr. Sophie Bryant), in his " Elementary 

 ■Geometry of the Right Line and Circle," has similar excellent 

 remarks on this subject. " It is almost certain," says Dr. 

 Willock, "that Euclid wrote his 'Elements' not for boys, 

 but for grown-up, hard-headed thinking men." 



Certain concessions have been made to the advocates of 

 reform, led chiefly by Mr. Mayward — notably by the University 

 of (Jxford and the Civil Service Commissioners; and, in the 

 existing stale of affairs, it is not reasonable to expect more. 



It will be clear from the foregoing that, in my opinion, a 

 more rapid progress in the .study of science generally would 

 ensue from any system which would facilitate and accelerate 

 the understanding of geometry by buys in the very elementary 

 stage ; and to this end I would suggest that the initiative 

 should be taken by the Universities of Oxford and Cambridge. 

 Durvast system of competitive examinations renders it necessary 

 that a fixed source of authority on the order of deduction in 

 geometry should exist. Such a source is Euclid at present ; 

 but a better one might, without serious difficulty, be drawn 

 up by a University Committee, and its adoption by the schools 

 and colleges throughout the country would follow as a matter 

 of course. The chief difficulty is to avoid " fads " ; but I 

 learn, from conversation with a distinguished master in the 



NO. 1529. VOL. 59] 



largest of our public schools, that sympathy would not be 

 wanting in an attempt to improve existing methods. 



Geori;e M. Minthin. 



The Cataloguing of Periodical Scientific Literature. 



SoMK three years ago, I alluded, in a work on "The Theory 

 of Bibliography" (pp. 81-82), to the importance of learned 

 societies undertaking to catalogue the literature they produce. 



I pointed out that it was already necessary to supply tables 

 of contents to each journal, bulletin, &c., issued, and that a 

 very slight amount of extra care would transform such tables 

 of contents into technical Catalogues of articles, useful alike to 

 the librarian and student — of which extra copies might be struck 

 oft" at no expense. I referred to the noteworthy efforts of the 

 R. Istituto Lombardo di Scienze e Lettere in registering the 

 articles of foreign scientific journals in its Bulletin, and showed 

 the advantages which would accrue if each society did its own 

 work first. 



I am happy to state that the society referred to has taken my 

 remarks in the spirit in which they were written : and, in pub- 

 lishing vol. XXX. of its Reiidiionti in 1S97, has issued accom- 

 panying sheets ("Titoli da ritagliare per le schede dei Cataloghi 

 per Autori e per Oggetti ") containing full titles (printed on 

 one side only) of the articles appearing in the volume, under 

 .Author, Subject (and Place). 



Melzi, Gilkerto. — Sopra alcune recce dell' isola di Ceylan. 

 Rend. 1st. Lomb., serie 2, vol. xxx. p. 89. (Milano, 

 1897.) 



Ceyi.an.— S. Melzi.— Sopra alcune rocce dell' isola di 

 Ceylan. 



Rend. 1st. Lomb., serie 2, vol. xxx. p. 89. (Milano, 

 1897.) 



Geologia : Ceylan. — G. Melzi. — Sopra alcune rocce dell' 

 isola di Ceylan. 



Rend. 1st. Lomb., serie 2, vol. xxx. p. 89. (Milano, 

 1897.) 



(// would be advantageous to give the full pagination, e.g. 

 // 89-102.— A. C.) 



The advantages of such a course are obvious. 



If each English learned society followed suit, and catalogued 

 its own publications at the moment of issue, it would be only 

 necessary to send the results to a central bureau (say the Royal 

 Society), and the work of cataloguing our scientific periodical 

 literature would be half-finished. There would still remain 

 the task of editing — of sorting, classifying, and of occasional 

 amplification or excision : but such work would be immensely 

 lightened and facilitated if the preliminary actual cataloguing 

 were already accomplished and in print. 



This is the first and fundamental principle of co-operation 

 in regard to the literature of the learned societies. Perhaps the 

 Royal Society has already urged its application.' If not, may 

 I take this opportunity of drawing attention to the matter? 

 Frank Camikkll 



January 16. (of the Library, IJriiish Museum). 



Plague in China. 



In the " Encyclopa;dia Britannica" (ninth edition, vol. .xix. 

 p. 168), Dr. J. F. Payne writes: "It is remarkable that of 

 late years reports have come of the occurrence of Oriental 

 plague in China. It has been observed in the province of 

 \'unnan since 187 1 ... it .appears to be endemic, though 

 there are rumours of its having been brought from Burmah, 

 and become more noticeable after (he suppression of rebellion in 

 that province [1S72]." However, the following passage I have 

 lately found in Hung Liang-Kih's " Peh-Kiang-Shi-Hwa " 

 (British Museum copy, 15,316, a, tom. iv., fol. 4, b), bears 

 witness to the much earlier occurrence of the pest in Yunnan, 

 inasmuch .is the author, who was born in 1736, and died in 

 1809, speaks of his contemporary dead thereby :— " Shi Tau- 

 Nan, the son of Shi Fan, now the Governor of Wang-Kiang, 

 was notorious for his [poetic] gift, and w.as only thirty-six years 

 old when he died. . . . Then, in Ch.iu-Chau [in Yunnan] it 

 happened that in daytime strange rats api^eared in the houses, 

 and lying down on the ground, perished with bUiod-spitting. 

 There was not a man who e-scaped the insi.intaneous death 

 after being infected with the miasma. Tau-Nan composed 

 thereon a poem, entitled " Death of Rats," the masterpiece of 

 his : and a few days after, he himself died from this '■queer rat 

 epidemic.'" KlMAi.isi Minakata. 



7 Etlie Road, Walham Green, S.\V., February 11. 



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