!8o 



NA rURE 



[JuLV 1 8, 1901 



Survey, xxxvi. 1S86, subsidence of fine solid particles in 

 liquids, Ani. Joiirii. Sci. (3), xxxvii. p. 122 ; Carl Barus und 

 E. A. Schneider, Zeilschr. f. Pkysik. Chemie., viii. p. 285, 

 1891, iiber die Natur der colloidalen Losungen : G. Bodlander, 

 Jakrb. f. iMiii., ii. pp. 147-168, 1893; Gotting. Nachr., p. 267, 

 1893, versuche iiber Suspensionen : Stanley Jevons, Quart. 

 Joiirn. Sii., viii. p. 167, 1878 ; Picton and Linder, Chem. Soc. 

 fouryt. Ixi. pp. 1 14-172, 1892 : Ixvii. pp. 63-74, 1895 ; Ixxi. pp. 

 568-573, 1897, solution and pseudo-solution ; H. Schulz, 

 Joitrn. f. praict. Chemie.., xxv. p. 431, 1S82 ; Hardy and 

 Whetham, _/«;;-«. of Physiology, x\\\. p. 1899, P/iil. Mag. Nov. 

 1899: Hardy, Proc. Roy. Soc, Ixvii. p. 95, p. no, 1900; 

 W. J. A. Bliss, PAys. Revieu), No. 11, 1895 (2). 



H. S. Allen. 

 Blythswood Laboratory, Renfrew, N.B., June 27. 



The Teaching of Mathematics. 



Being myself a teacher of mathematics, I have followed with 

 much interest the vigorous crusade against the neglect of suit- 

 able scientific and mathematical training conducted by Prof. 

 Perry and others, and am in substantial agreement with Prof. 

 Minchin's remarks in his review in your columns of the series of 

 papers by Prof. Perry on " England's Neglect of Science." 



One thing has struck me in connection with .school " mathe- 

 matical " teaching as being a very illogical course of procedure 

 on the part of the dominant "classical cleric"' instructors of 

 youth alluded to — namely, the teaching of arithnietic. A boy, 

 whether classically or otherwise educated, is considered a dunce 

 if he is not merely not an expert with the multiplication table, 

 but even if he is unacquainted with such things as recurring 

 decimals, square and cube roots, &c., whereas no attempt is 

 generally made to give an insight into theory, the results, i.e. 

 the rules, are what he is expected to know. 



So dissociated to the ordinary mind is the science of arith- 

 metic from mathematics that I can remember a fellow collegian 

 actually remarking, "Mathematicians are bad at arithmetic" ! 

 It seems to me, on the other hand, that Euclid is much more 

 out of the line of what we mean by mathematics. In teaching 

 Euclid as a mathematical " subject," and, as some claim, as an 

 introduction to geometry, we are actually raising barriers to the 

 progress of a learner in grasping the meaning and uses of 

 geometry. We insist on the propositions being learned iii all 

 their cases, insisting on the absolute distinctness of propositions 

 which are merely particular cases of the same proposition, thus 

 tacitly suggesting the existence of some such commandment as 

 "Thou shalt not recognise the Principle of Continuity " — we 

 ignore the infinite and we teach to try and wriggle away from 

 the notion of a " limit." In fact, nearly all that really consti- 

 tutes mathematics is carefully avoided in teaching of Euclid, 

 whereas I have found, when I have dared once or twice to depart 

 from examination ideals, how true the following remarks of Mr. 

 C. Taylor in his prolegomena to " The Introduction to the 

 Ancient and Modern Geometry of Conies " are. When referring 

 to the work of Boscovich, he says : — " It is remarkable that 

 Boscovich enters upon these abstruse speculations in an elemen- 

 tary treatise for beginners. . . . The preface to the volume contains 

 an earnest plea for the introduction of the modern ideas into the 

 schools. He had taught the appendix viva voce to his own 

 tyros with the happiest results .... demonstrations are put before 

 him (the tyro) in an unsuggestive form which gives no play to 

 his inventive faculty ; and thus it comes to pass that of the 

 many students so few turn out genuine geometers . . ." 



I must not encroach further on your valuable space, altho'ugh 

 many points come to one's mind, such as the exclusion from so- 

 called "higher algebra" papers of the theory of determi- 

 rtants, arithmetic without logarithms, applied mathematics with- 

 out the calculus, &c., but, in hopes that the attack may be 

 vigorously pushed home, subscribe myself yours sincerely, 

 Henry Smith School, Hartlepool. F. L. Ward. 



Curious Rain drops. 



On Thursday last, July 11, about 6 p.m., the day having been 

 sultry, the sky became dark and overcast, threatening rain. Only 

 a few scattered drops fell, however (the t'nreatened rain passing 

 aS), but these sparse rain-drops drew my attention by their 

 curious appearance on the sill of the window near which I sat. 



Each rain-drop had broken up into a number of smaller drops, 



NO. 1655, VOL. 64] 



which arranged themselves in a circular form around a central 

 one, in the manner here shown . . 



Perhaps some one of your readers would kindly explain the 

 cause of this, and if it was due to some electrical condition of 

 the atmosphere. M. .S. 



Bowdon, Cheshire, July 14. 



THE MVCEN.-EAN QUESTION.^ 

 'X'HE occasion for the following remarks on that diffi- 

 -'■ cult and much disputed subject, the Mycenaean 

 Question, is furnished by the appearance of the timely 

 volume on the " Oldest Civilization of Greece." by Mr. 

 H. R. Hall, of the British Museum, and as public interest 

 in the whole question has been considerably quickened 

 by the iinportant discoveries of Mr. A. J. Evans in Crete, 

 this book, in which certain of the principal results of the ■ 

 Cretan excavations are discussed, will be heartily wel- 

 comed by the broad-minded school of classical archaeolo- 

 gists in general, and by the student of ancient Oriental 

 civilisations in particular. 



It is now some twenty-five years since the spade of 

 Schliemann brought to light the remains of the oldest 

 civilisation of Greece : and as it was soon recognised 

 that these remains belonged to the period of the Bronze 

 .'\ge, it was clear that they must be older than the classical 

 period of Greek culture. The excavations which were 

 made subseguently in several parts of the Greek world 

 by the various investigators who were emulating 



.Schliemann's example proved that this Bronze Age 

 culture was not confined to any particular part of Greece, 

 but extended over the whole Hellenic area. Such dis- 

 coveries compelled classical scholars to abandon many 

 preconceived notions, and they found it necessary to revise 

 entirely their ideas about the origins of Greek civilisa- 

 tion ; it is not to be wondered at that many excellent 

 scholars of the " old school " still find it difficult to make 

 their views fall into line with the new order of things in 

 classical archaeology. This is most evident when the 

 dating of Mycenrean antiquities has to be considered, for 

 if the Mycenaean culture, being of the Bronze Age, is 

 necessarily pre-classical, its floreat must be assigned to 

 the second millennium before Christ. An important con- 

 firmation of this view seems to be supplied by the 

 evidence derived from the excavations which have 

 been made in Egypt in recent years, where a 

 large number of objects, pottery, &c., of Mycenaean 

 origin have been found ; and m many cases 

 such objects have been discovered side by side with 

 native Egyptian objects which must belong to the 

 period which lies between i;.c. 1500 and B.C. 1000. The 

 discoveries of Mr. A. J. Evans, however, all seem to 

 point to a still earlier date for the first development of 



1 "The Oldest Civilization of Greece: Studies of the Mycen^n Age. ' 

 By H. R. Hall, M.A., Assistant in the Department of Egyptian and 

 Assyrian Antiquities, British Museum. Pp. .v.K.viv -^ 346 ; with 76 illustra- 

 tions. (London : D. Nutt, 1901.) Price 15^. net. 



