March 23, 18 76 J 



NATURE 



40: 



existence of animals of this group were described by Leidy, in 

 1872, under the name of L'tHtatherium." 



Intricate questions of priority, such as those in which the 

 nomenclature of many of the recent American palxontological 

 discoveries is unfortunately involved, cannot be discussed and 

 settled in brief abstracts ; but I see that the above statement 

 conveys a wrong impression, which I shall be glad to correct. 

 Bones of some of these animals were discovered by Prof. Marsh 

 and Lieut. Wann, of the Yale College exploring party, near 

 Sage Creek, Western Wyoming, in September 1870, and de- 

 scribed by the former in the following year (American yottrnal 

 of Science and Arts, July 1871, p. 351), though referred pro- 

 visionally to the genus Titano'.herium. There seems, however, 

 to be no doubt that Leidy's name, Uintatherittm {Proceedings of 

 the Academy of Natural Sciences, Philadelphia, 1872, p. 169 ; 

 read July 30, published August i), was the earliest of the new 

 generic designations applied to any of the group, and therefore 

 ought to be adopted for the whole, until it is clearly shown that 

 any sufficiently important distinctions exist between them to 

 warrant their separation into different genera. 



March 18 W. H. Flower 



Morell's "Euclid Simplified " 



It is only quite recently that my attention has been directed 

 to the review of " Euclid Simplified" in Nature, vol. xiii. pp. 

 201-204. I shall endeavour to condense my reply to the criticisms 

 contained in that review as much as possible, taking them ia the 

 order in which they occur, which will simplify the controversy. 



And firstly, it is objected that " the title ' Euclid Simplified ' 

 is a misnomer, for the method of Euclid (the geometer) is de- 

 parted from altogether." I reply by explaining that by far the 

 greater part of the theorems and problems, and also the method 

 followed throughout in " Euclid Simplified" are taken directly 

 from Amiot's "Elements de Geometric" (15th edition, 1873)- 

 In his preface to another work, " Lecons Nouvelles de Geo- 

 metrie Elementaire" (1865), Amiot says: " Les elements de 

 geometric que nous venons de reimpriraer et cette seconde edi- 

 tion des Lecons nouvelles de geometric, sont deux ouvrages dif- 

 ferents. Le premier n'est que I'expose de la geometric des 

 anciens ; le second est un essai de geometric generale, c'est-a-dire 

 qu'il comprend nan seidem^it les Elements d'Euclide, mais encore 

 les principes de la geometric modenie, qui est resume'e et, pour 

 ainsi dire, personnifie dans les travaux de M. Chasles, notre 

 geometre par excellence." I infer that in adopting and follow- 

 ing Amiot's "Elements," I have followed the ancients and 

 Euclid, though shortened and simplified. 



At a subsequent part of the review the writer is exposed to 

 severe animadversions for his intention to produce what is repre- 

 sented to be an epitome of the brilliant discoveries of M. Chasles. 

 This matter can also be set at rest by referring to the extract 

 from the preface of M. Amiot, previously given. Mr. Morell 

 has only projected a compilation and translation from Amiot's 

 "Lemons Nouvelles," and from Rouche and De Comberousse 

 (i"^ Partie. Geometric Plane. Appendice), also treating of 

 modem geometry. 



Passing from the title to the contents, I admit that the typo- 

 graphical errors are unfortunately numerous, nor is it possible to 

 avoid this except by employing the best and most expensive prin- 

 ters. The misprints maner and cord, the omission of the word 

 "side" before "of the equilateral triangle," and the passage re- 

 lating to the quadrilateral A B C D must be referred to this 

 category. The latter passage is translated from Legendre (edition 

 1868 [net 1872], p. 78), and requires the fourth side ^ Z> to be 

 added, which has been omitted by the printer. For " without 

 changing" read also "thereby changing" — in this case I confess 

 an oversight of the writer. 



I proceed next to meet the strictures of the reviewer relating to 

 Gallicisms and the use of terms new to boys. In defence I might 

 point to the Hellenisms and Latinisms in our School Euclid, and 

 affirm that Gallicisms are more nearly akin to modern English. 



I content myself with pointing to the employment of terms, 

 condemned in " Euclid Simplified," by writers of approved 

 excellence, including Gerard's " Elements of Geometry." It is 

 objected that I write, p. 168, " The centre of similitude is the 

 meeting-place." I find at p. 36 of Mr. Gerard's " Elements of 

 Geometry," " The meeting point of two lines." . . . Again the 

 terms "perpendicular to the centre, perpendicular to the 

 middle," censured in " Euclid Simplified," ought to be taken in 

 connection with the ensuing words: "to the centre of the 

 straight line A A' " and " to the middle of A B." Thus ampli- 



fied, the terms agree with those used by Mr. Wormell — "per- 

 pendicular to Z> .£ at its middle point C." " The perpendiculars 

 to the sides of a triangle at their middle points." (" Modem 

 Geometry," pp. 78-81.) 



Before I dismiss this question of terminology, I wish to sug- 

 gest that recent works on geometry in high repute, especially 

 those I have just named, introduce very fully terms with which 

 boys are not at all acquainted, and which are new in English. 

 I briefly enumerate a list of these new importations : Escribed, 

 exscribed, explements, intercepts (used as a noun), circiun- 

 scriptible, intangence, bisectrix, extangent, median, a plane lune, 

 octant, and many moie which cannot be introduced here for want 

 of space. 



Considering the further criticisms, I beg to explain that no 

 notice of the Association for the Improvement of Geometrical 

 Teaching was inserted in the preface because absence from 

 England and ill-health had severed me from all knowledge of 

 its proceedings and of its Syllabus. 



If the enunciations are loosely and inelegantly worded, Amiot 

 must bear the blame which attaches in a greater degree to our 

 translations of Euclid. 



Further, the objection made to my use of the terms " capable 

 angle " must extend to the use of t.he same term in Gerard's 

 "Elements," p. 310. 



In the definition of the parallelogram the printer has omitted 

 "and parallel," words which I find in my MS. The term 

 lozenge is used as synonymous with rhombiis by Wormell (" Ele- 

 mentary Course of Geometry," p. 65), and Gerard, p. 235. The 

 definition of the circumference is that of Amiot ("Elements," 

 p. 40) and Gerard (p. 76). That described by the reviewer as the 

 common school-boy definition is Wormell's, p. 28. The expres- 

 sion " a circumference is generally described in language by one 

 of its radii" is thus given in Amiot: "On designe ordinaire- 

 ment une circonfcrence par I'un de ses rayons." I shall pass 

 over the criticisms about "the" and "a" as too minute, also 

 the remark about major and minor arcs met by Def. 36. Problem 

 VII. shows any boy of ordinary intelligence how to bisect a line. 



Derivation in notes is not treated syntactically, and can 

 also be dismissed. But the remarks of the critic about the 

 use of R as meaning right angle are met by referring 

 to Wormell's (p. 173) use of GCM as greatest common 

 measure. The term pentedecagon is used by Gerard (p. 202). 



The proof of the'ratio of two rectangles —, is Legendre's ; and 



at p. 67, after showing that — = 4, he adds : " Ainsi le rect- 

 angle R contient quatre fois le rectangle pris pour unite " [i.e., r). 

 This conclusion in my book is criticised. 



The reasoning to Theorem VI. (p. 14S), which is called 

 defective in the review, only errs by excess of proof. 1 

 have little more to add. The " Essentials of Geometry" are 

 almost entirely a translation of a useful Spanish work by noted 

 mathematicians. ^ The 205 exercises are throughout from Amiot, 

 and as these 205 exercises are literally all from Amiot, it is a 

 serious charge to say, like the reviewer, that many of them are 

 objectionable in geometry. In Exercise 30 " a " quadrilateral is 

 a misprint : read "this."^ J. R. Morell 



"Weight" and "Mass" 



The correspondence which has recently appeared in Natxjre 

 on this subject has great interest for those engaged in teaching 

 Physics. I confess I regretted to learn that " gravity " had 

 been diverted from its long recognised meaning in science — that 

 pointed out by Mr. Stoney — at Glasgow, to be employed for 

 one of the meanings of the word "weight." The symbol "g " 

 is "gravity " represented by its initial letter, so that if the mean- 

 ing of the word be changed, consistency would require that the 

 symbol should be altered. I find, practically, no difficulty in 

 restricting the word " weight " to the sense of force, insisting on 

 the use of the phrases "mass of so many pounds, ounces, or 

 grammes," and " force equal to the weight of a mass of so many 

 pounds, grammes," &c. ; for which, after sometime, I allow the 

 use of the phrase, "the weight of so many pounds." 



On another point of nomenclature I would suggest that those 

 who, like myself, think it necessary to use the British units co- 

 ordinately ^vith the metric, should adopt some analogue to the 



' ITieir names w-ill be given when I recover the book or get another copy. 



2 The work of Mr. Wonnell to which reference is made in this letter is 

 (with one exception) his excellent "Modern Geometry," published by 

 Murby. 



