uo 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



[Mav, 



tion ? On referrinc: tii liis own way of treatinpj Uie suliject (p. IS), 

 we find an illon-ical atten)])t to exjilain tlie idea of proportion, and 

 to demonstrate the properties of proportionals. It is at best illus- 

 trative. If we must liave similar trian}j;les at an earlier sta)i;e of 

 our frcometrical career, it may be easily accomplished in a much 

 better manner than this ; for instance, as Lejfendre has done, — by 

 assuminfT the doctrine of proportion as one already known and de- 

 monstrated by means of aljjebra. AV'e do not ourselves recommend 

 the method ; hut it has this merit, that it is all fair and open, and 

 does not conceal the difficulty by a series of demonstrative evasions, 

 which merely delude the pupil into a belief that the doctrine is 

 proved, when no real proof^has been f^iven. 



In the last place, Mr. Tate affirms that "Euclid's method of 

 treating the solid geometry is so operose and refined as to place it 

 beyond the reach of persons whose time is limited, and whose ma- 

 thematical talents are not of a superior order." It is known to 

 every one who is acquainted with the 11th and 12th books of 

 Euclid, and the manner in which they are used in this country, 

 that the first twenty-four or five propositions are as simple in their 

 reasoning as the first book of the " Elements ;" and that all the pro- 

 perties of solids which relate to volume or surface, form no part of 

 our systems of academical reading. Mr. Tate must know this as 

 well as we do ; and we cannot consider it ingenuous to represent 

 the difficulties which are inherent in tlie parts which are ditirarded 

 from our usual systems of education, as attaching to those which 

 are retained. Let us look to Mr. Tate's own work as regards these 

 things. We find that with respect to the line and plane, he has 

 nearly followed Euclid's views, leaving out howe\er some essential, 

 steps of i\\e demonstrations, and modifying some others after Le- 

 gendre. Then, with respect to the others, which have in modern 

 times been turned over to the calculus in some of its forms, Mr. 

 Tate settles the question very summarily, by the aid of, we sup- 

 pose, his " common-sense," or his "graphic interest." He settles 

 it, in short, as " common-sense" usually does settle these things, by 

 a gross mutilation of " the arithmetic of infinites." There is, in- 

 deed, no novelty in this : the only novelty is in seeing it done by 

 any man who had previously acquired the title of a mathematician 

 — and in our own day too ! 



We promised a specimen of Mr. Tate's tutorial scheme. Here 

 it is : — 



" Nearly all the geometrical knowledge contained in this work may be 

 conveyed to the pupil in this manner. 



Teacher. What is the hne a b called .' a B 



Pupil. It is called a straight line. 



T. Uf the two straight lines a b 



and D c, which is the greater ? 



P. The line A B is the greater. 



7'. How should you ascertain this with certainty ? 



P. By laying the line d c upon a b. 



T. What sort nf line is a f b 



P. It is a crooked line. 



T. True ; but it is also called a curved line. AA'hether is the curved line 

 A K B or the straight line A B the shorter.' 



P. The straight line a n. 



T. If you wanted to go from Battersea school to the church, in what line 

 should you walk ? 



P. In a straight line. (Why ?) Because a straight line is the shortest 

 distance between the school and the church. 



T, What have you to say relative to the two straight lines a s 



a b and c d ? c d 



P. They appear to be of the same length ; and moreover tliey appear to 

 lie even with each other. 



T, In other words yon might say, c d = a u ; and also c d h parallel to 

 a b. Is c d now parallel to a b ? a b 



P. No; for c D would meet a b on the left side. c^ — --^-^D 



T. On which side would tliey now mtet ? a b 



P. On the right hand side. c ^d 



T, What is therefore the peculiar property or definition of parallel lines.' 



P. That if they he carried out ever so far, on either side, they will never 

 meet. 



A surface is called a plane, or flat even surface, when the line between any 

 two points upon it is straight. Thus the surface of the tahle is a plane if a 

 straight-edge e.\actly fits it when applied in every direction. To ascertain 

 wlien a surface is a plane, bring your eye on a level with it, and if you find 

 (hat every point in the surface can be seen at the same time, it will show 

 that the surface is a plane. Our figures are supposed to be drawn on 

 planes." 



Such is the substitute propounded by Mr. Tate for the artificial 

 verbiat/e of a " technical logic," and '• the tedious verbiage of a rigo- 

 rous demonstration," such as geometers give us ! It is very possi- 

 ble that some readers may consider the substitute to be little else 

 than the vulgar and illiterate verbiage, worthy only of the scientifii: 

 charlatan, rather than of Mr. Tate tand the Battersea Training 

 College. 



Were this book merely thrown on the market for those who may 

 wish to purchase it, our concern would be less than it is about sucii 

 a work : but we have heard that all the schools in England which 

 are under the control of the Govenmient Board of Education, are 

 likely to have it forced upon them, as the condition of their re- 

 ceiving any part of the sums voted by the House of Commons in 

 aid of those schools. The dedication of the work to Ur. Kav 

 iShuttleworth is ominous ; and the rumours which have reached us 

 since we sat dowti to write, appear in jierfect consistency with such 

 a suspicion. Yet we can scarcely credit the rumour ; and we be- 

 lieve that such an adoption of it would create a degree of dissatis- 

 faction with that decision of that Board amongst scientific men and 

 the friends of real education, which would be very disagreeable to 

 the Government, and which might endanger its possession of the 

 patronage which it is the policy of the Government to e.xtend in all 

 directions. 



Oh, no! despite the misrepresentations and perversions with 

 which the "Elements" is assailed, let us keep to the good old 

 Euclid of our earlier days — unmutilated, and in his own venerable 

 costume. The true sjiirit of geometry will be lost in England as it 

 is elsewhere, if Euclid shall cease to be our text-book for the 

 Elements of Geometry. 



A Treatise on Practical Surveying, as particularly applicable to Nein 

 Zealand and other Colonies, containing an account of the Instrument.-i 

 most useful to tlie Colonial Surveyor and Engineer, iijc. By Arthuii 

 AVhitehead, late Civil Engineer to the New Zealand Company. 

 London: Longman, 1848. 8vo. pp. 19B, with plates. 



The title of this work sufficiently explains its object. The 

 author, acquainted by experience with the particular difficulties 

 and exigencies of colonial surveying, has here recorded a large 

 amount of useful knowledge, which has probably been acquired 

 amid many toils and hardships. To the English surveyor, accus- 

 tomed to well-cleared country, the task of mapjiing-out the un- 

 trodden wilds of New Zealand must be a new and formidable un- 

 dertaking. The greatest difficulties of surveying at home, sink 

 into insignificance in the colonies. Here we have open country, 

 and the use of the instruments is little impeded by obstructions 

 to vision — there the thick forest closes in on every side, impene- 

 trable to the eye and almost to foot of man. Here there are well- 

 known way-marks and boundaries, of which every particular is 

 already accurately ascertained and delineated — there everything is 

 new and uncertain ; the endless, unvaried scene presents nothing 

 but intertangled thicket, without mark or vestige beyond the rare 

 and fading traces of the hatchet of the savage. Here we have 

 liigh-ways and bye-ways for chariots and horsemen — there the 

 pioneer forces his way through a fence which is as thick as it is 

 long. Or else his journey lies over the treacherous morass. Or 

 he must swim the unbridged, nnfordable torrent. Or his path 

 mounts up the steep hill-side, witli some 1 10° of Fahrenheit, and J-A" 

 of angular acclivity against him. No cheerful hostel for him where 

 he may turn in to tarry for the night. He must not ask, with 

 Falstaff, " May I not take mine ease in mine iiiu ?" His inn is 

 his blanket. His kitchen and larder are the basket which accom- 

 panies him at every steji. To hap on a ]ilace where food might be 

 obtained by barter, would be as surprising to liiiii as to meet a po- 

 liceman or postman. He pioneers without a road, and thinks him- 

 self fortunate if his course be along the mazes and I'apids, the 

 rocks and shoals, of a mountain stream. 



It requires no ordinary energy to face such difficulties. And we 

 may congratulate ourselves that the spirit of our nation renders 

 Englishmen especially fit for occupations so arduous. The mania 

 for enterprise which renders the English tourist the wonder or 

 annoyance of the untravelled German or Italian, is turned to use- 

 ful account when the wilds of the antipodes are to be marked out 

 and plotted into farms and townshijis. A\'itliout this spirit there 

 could be no sufficient inducement to begin this first attack upon 

 nature. For these colonial surveyors are not civilizers, but the 

 pioneers of civilization. They lead the forlorn hope. VVlien they 

 have made the breach practicable, others enter in and gather the 

 spoil. 



The first chapter of the work before us gives descriptions and 

 accounts of the methods of adjusting the instruments chiefly em- 



