330 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



fNoVEMBEB, 



the same time be confined to a xinyJe v^ork on each subject. Then, 

 let justice be done to the aiithurn of those works, by the Govern- 

 ment purdiasinf,' the cojiies it expects to require at a fair market 

 price, and lii/ tdkiiif/ tlioxe capies and paying fur thorn at once. At 

 ]iresent, whether in ignorance, or under some more culpable 

 motive, the Council seems to treat an edition of a book like a 

 corfe of coals, or a barrel of train oil, as thins?s to be supplied 

 by contract, — chosen by the lowest tender, and to be supplied 

 at certain stated times, just as they will probably be wanted. 

 They forijet, or at least affect not to know, that copies of books 

 are only to be multiplied at nnce, except at enormous addition^d 

 expense; and that the only ground on which low prices and re- 

 muneration can be combined, is by immediate sale. Wliy is the 

 writer of a good book (and good elementary writing is more rare 

 in all ages of the world than any other class of good writing) to 

 be sent into the Gazette for bis labours — and sent, too, by a 

 Government Board specially appointed for the encouragement 

 and aid of learning .'' Yet sucli is the tendency of the plans 

 adopted by Dr. Shuttleworth, if it have not already been the 

 actual effect. Ami this is called "aiding education"! It makes 

 one blush — aye, till the blue asphyxia takes the place of honest 

 red! 



Nothing short of such a committee will satisfy the public — 

 nothing, indeed, should. An honest compliance with its decisions 

 should replace the present system of underling influence in the 

 selection of books, and in the special recommendation of particu- 

 lar ones from tlie list which is issued by the Committee. On this 

 last phrase, wliich expresses a wide-spread suspicion, we have only 

 to remrtrk that — if an ungarbled report of the prices at which the 

 Committee buys and sells be published, together with liberty 

 granted to the public to inspect all correspondence about the 

 choice and supply of these books; and if we do not find that the 

 suspicion is justified by these documents, we will gladly withdraw 

 the implied censure. \Ve should be amongst the foremost to award 

 the praise of having done well, could we conscientiously believe 

 that such praise was deserved. 



If, on the contrary, such a plan be not adopted, let all works be 

 alike thrown open, so tliat whichever of them be deemed by the local 

 committee of any school tlie best adapted for their own purpose, 

 be supplied with them by the Government, at a certain but fixed 

 per-centage below the price of publication. The Government 

 might without censure, perhaps, demand the trade-advantage; but 

 not a single sous more than any other dealer is regularly allowed. 

 This, indeed, diminishes the author's and publisher's income suffi- 

 ciently — as too many of us know too well. What further reduc- 

 tion the Government may make by the aid of the annual grant, 

 should only be made from these wholesale prices; and not upon tlie 

 sixty per cent, now enforced (upon some books we believe even 

 more) by the Committee, upon authors and publishers. 



But why should even this trouble, and its multiplied costs, be 

 incurred.'' It certainly furnishes a few more opportunities for 

 patronage, by the appointment itf employees in managing the details 

 of the business. Would it not be more simple, economical, and 

 consistent, to allow upon the book-bill of every school that com- 

 plied with the conditions for the grant, a certain per centage in 

 part-payment of the bill? The accuracy and honesty of such bills 

 could be easily guarded by sufficient tests; and even if not, as a 

 false attestation is a misdemeanour at law, we ajiprehend there 

 would be little risk of imposition. 



But to return to Mr. Tate's book : — but here we are again forced 

 back upon the Committee of Council. It appears from the sen- 

 tence quoted as comprising the preface, that any schoolmaster who 

 is master of the first three hooks of Euclid, may otitain a '■'•Govern- 

 ment certificate" of his competency as a teacher. What an exalted 

 idea of the present race of schoolmasters her Majesty's Ministers 

 must have formed! However, the evil will work its own cure; and 

 the ridicule attached to a Government diploma, gained on such 

 grounds as these, will be as great amongst the schoolmasters, as 

 that of a Scotch LL.D. is amongst literary and scientific men. 



What Mr. Tate calls his "edition" comprises only just the half of 

 all modern editions — viz. the first three books. The Privy Council 

 in its superlative wisdom has decreed that these are sufficient, and 

 that the next three are merely curious redundancies which ought 

 to be lopped off: and Mr. Tate, like a well-bred spaniel watching 

 its master's eye, is eager to perform the "fetch-and-carry" orders 

 therein expressed. Tliat tlie fifth book should transcend the 

 comprehension of a minister, or a minister's "managing master," 

 we can well understand; and the sixth has too intimate a relation 

 with the fifth, to be very intelligible without its fellow: but that 

 the fourth, which is the only book that takes a formally practical 

 character, should have been excluded, can only be accounted for 



by the assumption that the question as to the number of books to 

 be required was decided by a throw of the dice, or some equally 

 scientific criterion! 



Perhaps some one of the "rising generation" of Pettys may 

 enlighten their grandpapa, the Marquis; or some of Dr. Shuttle- 

 worth's Cambridge friends, sorry to see so great a man committing 

 such strange blunders, remonstrate with him on the absurdities of 

 his doings. In due time, the fourth book may get amongst the 

 conditions for the "Government certificate;" and to save appear- 

 ances, even the fifth and sixth may be inserted in the list, though 

 nut enforced as a condition. In these cases, Mr. Tate's eye will be oa 

 Dr. Shuttleworth's; and the signal being understood, Mr. Tate's 

 edition will expand in the indicated ratio. 



As Mr. Tate's edition is professedly printed verbatim from 

 Simson's, this is no place for remark upon any of its details. A 

 few pages of problems and theorems, mostly unsolved, constitute 

 the whole of Mr. Tate's labours — with the exception of a treatise 

 on 'Geometrical Analysis,' which occupies, with its illustration, 

 almost a whole page! These "various useful theorems and pro- 

 blems" are so familiar to our eye (mere "stock-problems," the pro- 

 perty of everybody), and the whole, either in the same or slightly- 

 modified forms, have been so often given, that we wonder what 

 peculiar merit belongs to Mr. Tate for their transfer from Mr. 

 Potts's edition of Euclid into his own. To bring them together 

 for the first time is very meritorious, for it costs an immense 

 amount of disagreeable labour: but to mark a few of an already 

 collected set for the use of the printer, involves so little labour, 

 that if fame is to be thus obtained, fame ought to be as cheap as 

 "blackberry tarts." Mr. Tate has earned thin fame at least. But 

 there yet remains the "analysis." 



In a foot-note at p. 88, we find the following : — " Should the 

 student fail in solving any of these problems by the ordinary synthe- 

 tic method, let him employ the method of analysis given at p. 107." 

 We have to ask whether the words ordinarg and synthetic are to be 

 understood as synonymous, and the phrase itself as a pleonasm? 

 or whether we are to understand that there are more synthetic 

 methods besides the ordinary one ? We look in vain for an ante- 

 cedent definition of synthesis, and the student would naturally go 

 to Johnson to be enlightened — with what success we need not say. 

 However, we proceed to the page referred to, viz. p. 107, and we 

 begin by placing Mr. Tate's and Sir John Leslie's definitions of 

 analysis in juxta-position. 



Tate. 

 Geometrical Analysis* 

 In the method of analj'sis we as- 

 sume the proposition advanced, and 

 then proceed to trace the conse- 

 quences which follow from this as- 

 sumption, till we arrive at some 

 known or admitted relation. The 

 reverse of this process constitutes 

 Synthesis or Composition, which is 

 the method employed in the pre- 

 ceding pages. In the solution of 

 geometrical prolilems of more than 

 ordinary difhculty, it is necessary 

 that we should adopt the method of 

 analysis, in order to discover the 

 different steps which must be pur- 

 sued in the construction. ''Analysis," 

 observes an eminent geometer, "pre- 

 sents the medium of invention j 

 while synthesis naturally directs the 

 course of instruction." 



Leslie. 



Geometrical Analysis, 

 Analysis is that procedure by which 

 a proposition is traced up, through a 

 chain of necessary dependence, to 

 some known operation, or some ad- 

 mitted principle. It is alike applic- 

 ahle to ihe investigation of truth con- 

 templated in a theorem, or to the dis- 

 covery of the construction required 

 for a problem. Analysis, as its name 

 indeed imports, is thus a sort of in- 

 verted form of solution. Assuming 

 the hypothesis advanced, it re-mounts, 

 step by step, till it has reached a 

 source already explored. The reverse 

 of this process constitutes Synthesis, 

 or Composition, which is the mode 

 usually employed for explaining the 

 elements of science. Analysis, there- 

 fore, presents the medium of inven- 

 tion, while synthesis naturally directs 



the course of instruction. 

 The wonderful originality of Mr. Tate will now be apparent 

 enough: but the intelligibility of these very general modes of 

 defining analysis, to any but an experienced analyst, will be more 

 doubtful. What is said is not false : yet it is only vaguely true ; 

 and no one, we are confident, that attempted to form an idea of 

 geometrical analysis from such definitions, could form a correct and 

 definite, and still less a working, idea. In truth, there is no portion 

 of geometry that requires so much careful instruction and ampli- 

 fied illustration to become intelligible, as the doctrine of geo- 

 metrical analysis — not even the doctrine of ratio or the method of 

 exhaustions. In this nearly all writers have alike failed. Brevity 

 leads to obscurity — as Horace intimated long ago. Mr. Tate was 

 not then very likely to succeed where so many have failed: but most 

 writers (and Leslie amongst them) have made some atonement by 

 furnishing an adequate number of examples, from which thepraetict 

 of the method of analysis and its related synthesis might be learnt. 

 Here, however, we are shuffled off with the analysis and syntheii* 



