28 



NATURE 



[May 10, 1888 



" Geography and natural history abound in words 

 which express the separateness of an object, its isolation, 

 its one-liness. Similar to the number I, and to the 

 pronoun I, there are found in different languages and 

 dialects referring to local separation, the words i, hi, ey, eye, 

 egg (and here think of the Latin ego and the Greek eyw), 

 eyot, ait, inch, innis, He, isle, inver, insula, isola, isla ; 

 and connote some of these with the animal eye and egg, 

 having a similar separation as an island in geography. All 

 the latter have the same meaning, and express a portion 

 of land segregated, cut off from other land and surrounded 

 by water — oneness." 



With the above we may compare Shakespeare's use of 

 the word eye in the passage — " The ground, indeed, is 

 tawny. With an eye of green in V (" Tempest," Act II., 

 sc. 1). 



Respecting the celebrated twos in profane myth and 

 history, we read in the next chapter : — 



" Prominent among these are Romulus and Remus ; 

 Brutus and Cassius ; and in Irish legend Eber and Airem ; 

 concerning whom we are informed that Eber was slain by 

 his brother Airem. He was the hero of the Ivernians, the 

 ancient non-Celtic inhabitants of Ireland. Airem was the 

 ancestor of the Celts who conquered the country." 



The Hibbert Lecture, May 1886, is referred to in a foot- 

 note as the source from which this Irish version of the 

 story of Romulus and Remus was taken. It is new to us, 

 and will probably be so to most of our readers. 



In the chapter on Number Three we are told the origin 

 of the heraldicy?<?#r de lys : — 



"It was the device of three fishes tied together with a 

 ribbon, which formed the fleur de luce — luce being the 

 name of the fish ; but which was afterwards transfigured 

 into the more elegant emblem of the fleur de lys, the 

 flower of the iris, taking the place of ths fish, its three 

 petals still presenting a trine." 



It will be remembered that Justice Shallow, in the 

 opening scene of the " Merry Wives of Windsor," speaking 

 of " the dozen white luces " in his coat, remarks that " the 

 luce is the fresh fish." 



To the noble army of circle-squarers we leave the task 

 of refuting the following argument ; merely remarking 

 that it may with equal facility be used to disprove the 

 quadrature of the parabola, which has been believed 

 in by all orthodox mathematicians since the time of 

 Archimedes : — 



" In a quadrangle, the space may be divided into the 

 minutest squares, leaving no space undivided ; but in a 

 circle, every square applied to its periphery will always 

 leave an angular space ; and however far the process 

 of smaller angles may be carried, an ultimate undivided 

 space will remain." 



Apparently our author is not quite satisfied with this ; 

 for in the next paragraph (on p. 47) he proves, in another 

 manner, that the circle cannot be squared. In both proofs, 

 for the words " a circle " we may substitute " any curve, 

 including the parabola," without thereby affecting the 

 argument. 



We have never heard of Montrecla, to whom we are 

 referred for an account of attempts to square the circle ; 

 but possibly Montucla is meant, who in 1754 published 

 a " History of Researches relating to the Quadrature of the 

 Circle," a second edition of which (by Lacroix) appeared 

 in 1831. This conjecture is strengthened by the fact that 

 our author's list of the principal calculators of n ends 

 with Vega (born in 1754 and murdered in 1802), who 



obtained its value to 140 decimal places, making no 

 mention of Rutherford and Shanks, who in more recent 

 times pushed on the calculation to 500 and 707 places 

 respectively. 



From Chapter VII., which treats of a variety of subjects, 

 including among them " the number of the beast " and 

 the fine distinction between six and half-a-dozen, we select 

 for comment the following sentence : — 



" Six, also, is the least number of the points of fixature ; 

 so that a body cannot under all circumstances be im- 

 movable unless secured (or resisted) at six points." 



Having only common-sense to guide us, and being unable 

 to divine what train of reasoning could have led the 

 author to the above conclusion, we should imagine that 

 whenever any two points, A, B, of a body are fixed every 

 other point in the straight line AB is also fixed, so that the 

 body can only rotate round the line AB. Consequently 

 if any third point (not in the straight line AB) is also 

 fixed the body is immovable. Do the words " under all 

 circumstances" imply that the body is immovable even 

 when all six of our author's " points of fixature " are in the 

 same straight line ? If not, we are at a loss to know what 

 they mean. 



The appendix contains among other things a method 

 of filling up magic squares which is said to have been 

 communicated by a Russian mathematician to Prof. 

 Sylvester and by him to a friend of the author. As some 

 portions of the Russian Empire are not very far distant 

 geographically from the land of the Chaldaeans, this tradi- 

 tion may have had its origin among the magicians, 

 astrologers, Chaldaeans, and soothsayers of the Court of 

 Nebuchadnezzar, to whom magic squares were doubtless 

 well known. We hope Mr. Hopkins will be able to trace 

 it to its source; even though it would take some time to 

 do so, and the appearance of a second edition of " The 

 Cardinal Numbers " might thereby be delayed. The public 

 need not be impatient, for they can in the meantime allay 

 their curiosity concerning the properties of magic squares 

 by a perusal of the " Mathematical Recreations"of Ozanam 

 and a host of more modern writers. 



OUR BOOK SHELF. 



The Romance of Mathematics. Being the Original 

 Researches of a Lady Professor of Girtham College 

 in Polemical Science, with some Account of the Social 

 Properties of a Conic ; Equations to Brain-Waves ; 

 Social Forces ; and the Laws of Political Motion. By 

 P. Hampson, M. A., Oriel College, Oxford. (London: 

 Elliot Stock, 1886.) 



OUR first acquaintance with the title, which we have 

 copied in full, was limited to its four opening words. 

 These suggested various ways in which the subject might 

 be treated ; we had no idea that the task before us was 

 to examine and report upon a somewhat mildy># d 1 esprit. 

 The editor, who poses as a Cambridge student and 

 quondam pupil of the Girtham Professor, and subse- 

 quently as her husband, discovers, in a well-worn desk, 

 certain lectures, essays, and other matter. In his intro- 

 duction he says it is not his intention to disclose how he 

 came into possession of the papers ; in the closing pages 

 he is caught in his work of reading and transcribing, 

 and "at length we gained our point, and obtained the 

 full sanction of the late Lady Professor of Girtham Col- 

 lege to publish her papers." " Thus her obedient pupil is 

 enabled to repay his late instructress for all her kindness to 



