34 



NA TURE 



j August 7, 1884 



ible quan- 



the interest and 

 tgin - 



om levoted to it, and 



1 1 'induce it in full 



: 



"CHAPTER XIX 



" Cen ik \i. S 1 \ rn in L11 

 intended to write a long chapter with the above 

 . but, for various reasons, 1 am not yet ■■ 

 o. I have, however, left 111 the heading, for the 

 ence of inserting such a 1 hapter in a future edition 

 10k, should one ever be required." 

 This reminds one of the celebrated chapti 



in Ireland : " There are no snakes in Ireland." 

 > : s- ends with the excellent rules and regulations 

 ention of fire risks prepared by the Society of 

 ih Engineers. Several useful tables are given in 



nol for what it contains but 

 it does not contain. There is in it a strange 

 of the elementary and the advanced. After an 

 al description of the relations that exist between 

 current work and power, we are told by a footnote (p. 19), 

 "The symbol v meai quare root of the quantity 



under it." There is much hasty editing. At p. 30 we are 

 d in a footnote a mathematical proof in the ap- 

 pendix which does not appear there. At p. 25 the symbol 

 lattery is wrong — the poles are reversed. The 

 value of H at Greenwich is given at p. ; is 

 '1794, and at p. 48 as - i8i. The illustrations, it ma\ be 

 remarked, are excellent. 



It is to be hoped that a second edition will soon be re- 

 quired, so that Mr. Gordon may be able to remedy the 

 defects of the present one. A good practical treatise is 

 very much needed. W. H. P. 



OUR BOOK SHELF 



.1 Text-Book on the Method of Least Squares. By 

 Mm field Merriman. (New York: lohn Wiley and 

 Ions, 1SS4.) 



ty almost be looked upon as a second edition of 

 the " Elements " by the same author, which we favour- 

 ably noticed in \\\ 1 1 1 I vol. xviii. p. 299) soon after its 



nee. The sale of the entire edition of the smaller 

 book may lie taken as evidence of its having met a want. 

 The present work, though larger in appearance, covers 

 about the same extent of ground, but, as is pointed out 

 by the author, " the alterations and additions have been 

 so numerous and radical as to render this a new and 

 distinct book rather than a second edition." 



In Chapters I. to IV., which present the mathematical 

 developments of the principles, methods, and formulas, 

 Dr. Merriman gives an introduction, and discusses the 

 law of probability of error, the adjustment of observa- 

 tions, and the precision of observations at some length, 

 and illustrates with numerous (for this subject) examples. 

 In Chapters V. to IX. the application of the above to 

 different classes of observations is made. These chapters 

 are respectively headed : Direct Observations on a Single 

 Quantity, Functions of Observed Quantities, Indepen- 

 dent Observations on Several Quantities, Conditioned 

 i 011s, and the Discussion of Observations. 

 These discussions are likelv to be of u^e to engineers 



and others specially interested in this branch of mathe- 

 matics. In an appendix, inter alia, there is a short 

 I statement on the history and literature of the 



subject, but the fuller list of literature of the earlier book 

 is not reproduced : there are also given here eight handy 

 tables and some other useful material. It is the only 

 work of the kind with which we are acquainted, a: 

 even better adapted, in our opinion, for the end Dr. 



Merriman has in view than his earlier book was. 



Some Propositions in Ge, metry. In Five Parts. By 

 lohn Harris. (London : Wertheimer, Lea, and Co., 

 1884.) 

 WHEN we received the parcel containing this work with 

 some others for review, we speculated upon what the 

 Editor could have sent us, and hope rose within our breast 

 that some magnum opus awaited our perusal. But as we 

 • ard no whisper of such work being on its way, our 

 expectation cooled, and again casting our eyes on the 

 unopened packet, and remembering former works of 

 similar dimensions, a chill seized us, and we thought to 

 ourselves, " Aut 1 1, aut . . ." Shade of De Morgan ! what 

 are we to do witli a work occupying 144 + S quarto pages 

 treating of a subject so thoroughly threshed out, we had 

 hoped, in your immortal " Budget"? 



The title is an attractive one, and much of the work 

 appears to be sound, but when we come across such 

 problems as the trisection of any angle, the inscription of 

 heptagons and nonagons in circles, el id genus oiune, one 

 draws in one's breath, and one's hair stands on end ! The 

 tentative methods given we dare say would enable one to 

 perform these several operations to a very close degree of 

 approximation, but this is not what ordinary mathema- 

 ticians want. But we must be careful here, for Mr. 

 Harris puts the question, " What is a mathematician .' " 

 and in his answer splits the creature up into " sorts." 

 There is, for instance, the very positive and readily in- 

 censed mathematician, the highly exalted mathematician, 

 the profound mathematician, and the exclusive orthodox 

 mathematician. 



It is under this last " sort " that we fear we must be 

 i|. With him "'Mathematics' is a sort of privi- 

 leged religion, having its special articles and technical 

 dogmas. None but the initiated must enter its temple, 

 and woe be to him who dares to do so without a formal 

 certificate from its priests. One of his most valued 

 dogmas is that 7r = 3"I4.1 59 . . . This is called an ap- 

 proximation ; and which if a man do not faithfully believe 



lie will inevitably go Ah, well, never mind where he 



will go to ; but, at all events, no mathematician must 

 hold converse or communication with such a profane 



It will be seen from this extract that Mr. Harris is a 

 man of some humour, but even such oases do not render 

 the vast Sahara of much of his book pleasanter reading. 

 Indeed we have found it very hard work, and so we con- 

 tented ourselves (for review purposes) with the careful 

 reading of one of the " trisection" proofs ; but we gave up 

 in despair, as this proof involved the mastery of a pre- 

 vious proof, and we feared it would be a case of little fleas 

 and lesser fleas, " and so ad infinitum." What did we do 

 next ? Why we applied a trigonometrical test, and found 

 that the method in the text would not give the result at 

 all, except in a special case. Life is really too short for 

 such verification, and we must leave the task to others. 

 The figures, as usual with Mr. Harris, are carefully drawn 

 and very elaborate diagrams. 



We regret more and more that so much labour should 

 be bestowed upon such studies, which, we fear, an unbe- 

 lieving world will never take up. What, then, is the value 

 of n ? It is here said to be (Mr. Harris would say, proved 

 to be) equal to \'8 X \? = 3' 142696 . . . 



We lay down the book more in sorrow and pity than in 

 anger and scorn. 



