3i8 



THE CIVIL ENGINEER AND ARCIIITECrs JOURNAL. 



QNoVElIBEB, 



(A) is least in the sections Ar/i and./V, and greatest in the sections ae 

 and dh. As the contraction may Filt. i 



he considered as a force acting f 



perpendicularly to the axis of the a. ^^ ^-^ ft 



stream, it follows that the parti- 

 cles of wiiter in a^\i^t\d, are moved 

 hy a greater force, and more 

 nearly ap])roach the centre than 

 the particles /; A, 7, A, on which 

 smaller force acts; these must 

 therefore he deflected from the 

 centre to a certain point while 

 the others approach the centre. 

 Hence arise by degrees different 

 fcn-ms of the column, as Poncelet 

 and others have described, and as 

 the section is represented in fig. 

 (H). When the points /, A, (. A-, 

 have extended to their maximum, 

 they again approach the centre; 

 and when, finally, these recurring 

 undulations aro gradually de- 

 stroyed, the column approaches 

 the circular form (C), when the 

 acceleration of gravity and the 

 resistance of the air separate the 

 particles of water, and render the 

 precise form indeterminable. 



For similar reasons, the column from a rectangular orifice of 

 which the greatest side is horizontal, at different distances from 

 the orifice will have the form of section represented in fig. 2. 

 A^hen the greater side is vertical, the sections are as in fig. 3. 

 The section for an elliptical orifice will also he elliptical, as re- 

 presented in figs, t and 5, These forms are given in the experi- 

 ments of Weisbach.* 



Berlin, August 1846. 



* * Experiments upon the Dischirne of Water,' &c. Versiiche (ll)er der AuB flusa des 

 Wassera durch Schrcber, Hahtie, Klappen unci Ventile. Leipsig, lb42. 



Substitute for the Crank. — Professor Frazer lately exhibited at the Frank- 

 lin Institute, a model of a contrivance hy Mr. G. W. Risdon, intended as a 

 substitute for the crank in converting rectilinear into rotary motion. The 

 model consisted of two cylinders, the pistons of which were connected by a 

 cross-head, to which were attached two vertical racks, passing one on each 

 side of tlie first axis of the machinery, upon which is placed a toothed semi- 

 circle, so adjusted that during the descent of the pi!,tuns it is driven by one 

 rack, and during the ascent by the other; the circular motion is tims con- 

 tinually preserved. A shifting catch at one exteniity of the toothed segment 

 allows the motion to be reversed with rapidity and ease. 



The First Three Books of Euelid's '■Elements of Geometry^' from the 



text of Dr. Robert Simson, together with various useful Theorem:! 



and Prohtems, as Geometrical E.rerei.s-es on each Book. By Thomas 



Tate, &c. &c. &c. London: Longmans, 18t9. 12mo. 



Mr. Tate is a genuine Proteus! It was only /«.«< year that 

 Mr. Tate most heroically denounced the 'Elements' of Euclid, as 

 altogether unfitted for the purposes of education. He then spoke 

 of the work as, the "artificial verbiage of a technical logic" — as, full 

 of the "tedious verbiage of rigorous demonstration" — as, having 

 "defects as an initiatory system too apparent to admit of even an 

 apology." These statements were, of course, believed by Mr. Tate 

 true then: hut why has one short year made them false now? Is sci- 

 entific truth so mutable as this implies it to be.'' If it be not, why is it 

 that Mr. Tate conies forward now with an edition of that very book 

 which he last year consigned to the "tomb of the Capulets"? We 

 should at least have expected, were it only for the sake of his 

 reputation, that he would have offered some kind of apology 

 for this strange inconsistency; either by attempting to explain 

 away the harsh language he had applied to Euclid's work; by a 

 candid acknowledgment of having become more enlightened on 

 the merits of that book; or, at least, to show that in his present 

 undertaking nothing of mercantile purpose was the moving 

 cause. Mr. Tate, however, can "blow hot and cold," according as 

 his hands are too cold or his broth too hot, with sufficient nonchal- 

 ance to astonish the Educational satyrs of Battersea and the Com- 

 mittee of Council — to say nothing of those still more plastic 

 satyrs, "the schoolmasters who may be desirous of obtaining a 

 Government certificate." 



This last quotation is from Mr. Tate's new preface; but we will 

 give tliat manifesto entire, as it is but a single sentence:— 



"This edition of Euclid has been published in a cheap form, with the hope 

 that it may tend to advance the mathematical education of this country, and 

 with an especial reference to the instruction of schoolmasters who uiuy l>e 

 desirous of obtaining a Goveinment certificate." 



"Least said — soonest mended." Mr. Tate has left off writing 

 dissertational prefaces, which in a man whose opinions on science 

 vary with the development of the understanding of the Committee 

 of Council, is, to say the least, very prudent. He, however, adopted 

 this "canny" course too late: his preface to the 'Principles of 

 Geometry' should never have been written — or at least never pub- 

 lished. His present book would have come before the world with 

 a better grace, did it not always remind us of the menial, time- 

 serving, and purpose-serving spirit in which he so evidently writes. 

 It is utterly impossible that .Mr. Tate's real opinions on these sub- 

 jects can have honestly veered round to the opposite point of the 

 compass since last year. He must think, in the main, as he thought 

 then; antl we cannot but ask how any man, to serve a temporary 

 purpose, can become accessory to the enforcement of a system of 

 education diametrically opposed to his own honest convictions? 

 The "Sir Archy Mac Sycophants" may enforce constant "boo-ing 

 to the great mon"; but it is very degrading to the man of science 

 to "boo" his scientific convictions to the caprices of an ofticiiJ 

 Board — of a Board, too, which from its composition must be to- 

 tally incompetent to form a trustworthy opinion upon any subject 

 connected with the practice of popular education. Indeed, it 

 appears that the introduction of anvthing having the name of 

 Euclid attached to it, into the Council's list of books, was rather in 

 compliance with the urgent representations of the press, than from 

 any conviction on the minds of the Committee that Euclid was the 

 only proper work for the purpose. What should we s.iy of the 

 physician or the divine who wrote books on medicine or theology 

 in subservience to the views entertained by a medical or theolo- 

 gical Committee of the Privy Council.-" — condemning a nostrum or 

 a dogma last year with the severest vituperations, and this yeat 

 coming fcnnv.ird with a patent to vend the self-same nostrum, and 

 to profit by the sole right of preaching the self-same dogma.'' The 

 physician would be branded as a quack and a charlatan — the divine 

 as a hypocrite and impostor. \Vill Mr. Tate tell us wherein his 

 case differs from these suppositious ones.'' 



Short as the preface to Mr. Tate's Euclid is, he could not help 

 compromising himself, in stating that the cause of his publishing it 

 "in a cheap form" was "the hope that it may tend to advance the 

 mathematical education of this country." The "mathematical edu- 

 cation of this country" can he "advanced" by a book which has 

 so recently been described hy Mr. Tate as "a highly artificial 

 system, which can only be read, thoroughly, hy a person who is 

 already a mathematician, and who can enter into its metaphysical 

 Bubtilties and operose demonstrations"! Who can fail to see 



