IS 50.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



171 



From Stations being now so far from eacli other, miicli local 

 traffic is lost, lor many a man iinds it better to ride or dri\e, 

 than go some miles to a station, and afterwards have a furtlier 

 journey to make from the arrival station to tlie place of his des- 

 tination. We may confidently assert that, throughout, much rail- 

 way traffic is at present lost, and that railway traffic is still in its 

 infancy. .Vlthough there are traffic managers and goods managers, 

 there is not one line which has a statistical department; whereas 

 a com])etent statician should be engaged by each company to see 

 what traffic there is in the district, how it is carried, what 

 goes on the railway, what does not, and why not. The occasional 

 exertion of a chairman or superintendent of traffic can never 

 keep up with all the minutiae of the many items constituting the 

 carrying trade; for it is quite as much as such officials can do to 

 attend to the daily working of the traffic under their control, 

 which is their legitimate business. 



Nothing but the light-engine system will diminish the margin 

 of waste now constituting the expenditure of railways under the 

 head of way and works, locomotive power, carrying, and stations ; 

 and the sooner the able men engaged in railway administration 

 direct their attention to this, the sooner shall we have a diminished 

 expenditure and increased traffic, and be able to do witlu)ut those 

 impolitic and pernicious expedients of raising fares and limiting 

 the accommodation of travellers. Railway directors, who have 

 generalh' risen from the ranks, nevertheless forget the circum- 

 stances of those classes who are not blessed with a superfluity of 

 wealth. Every tradesman knows better than a railway director, 

 and proceeds upon the principle of getting as much as he can from 

 his customers by suiting his charges to their means in articles of 

 daily necessity. The business of a railway director is to make as 

 large a profit as he can, to carry on as large a trade as lie can, and 

 if he has not got trade to make it: but it is seldom he finds 

 this out. The Metropolitan and Dublin Railways without suburban 

 residences, Southampton without packets, Fleetwood without a 

 harbour, the Midland Railway without coal and lime-pits, would 

 fare but badly; and yet, in the teetli of this, how is railway de- 

 velopment neglected! The Brighton steamboats have been 

 burked, Suiulerland Docks starved, tlie southern coal traffic kept 

 back, the fish trade left to shift for itself, no attention paid to the 

 carriage of building-stone and lime, and manure generally ne- 

 glected. Horse traffic flourishes, the canals are in fu'l vigour, and 

 if railways have a large traffic, it is thanks to themseh'es, and not 

 to their managers, who leave the trade to look after itself. 



A Practical Treatise on the Construction of Oblique Bridges, with 

 Spiral and Equilibrated Courses. By Francis Bashporth, M.A., 

 Fellow of St. John's College, Cambridge. London: Bell. 1850. 

 Although works on oblique bridges are numerous, still one from 

 the pen of Mr. Basliforth is welcome, as that gentleman is well 

 known for liis high mathematical attainments. The nature of the 

 work, and the principles on wliich it is founded, are sufficiently 

 described by the author. He says the metliods in his first part are 

 substantially the same as those of Messrs. Nicholson and Buck, 

 but he has introduced numerous variations in the details. He 

 prefers spiral courses for oblique bridges, because altliough grave 

 objections may be urged, yet the accuracy of form which can be 

 given to the archstones renders it advisable, under proper limita- 

 tions, to adopt them in preference to a better arrangement of the 

 courses, which does not admit of like exactness in the execution of 

 the work. 



In Part II. Mr. Bashforth has endeavoured to give information 

 on equilibrated courses in oblique arches, suited to tlie practical 

 man; but we doubt if it be possible or desirable to initiate those 

 concerned in carrying out the details in the elaborate analysis 

 exhibited by the author. Mr. Adie, it will be remembered, was 

 the first to construct oblique bridges of tliis kind, and Dr. WheweLl 

 and Mr. Sang have likewise written upon it. 



The work is accompanied by numerous diagrams. 



Railways in Ireland. — A return is just printed of all the moneys 

 lent to railway ompanies in Ireland by the Exchequer Bill Loan 

 Commissioners, and the amounts repaid. It appears that, from 1832 

 to 1842, the amount advanced to Irish railways was 157,200/., and that 

 tlie interest on such advance has been duly paid. Of the priocipal, 

 99,595/ has been repaid, and the remainder is in regular course of 

 payment. From 1842 to 1849, there has been advanced to Irish rail- 

 ways, 834 000/, chiefly withiu the last three years. There is no in- 

 stance in which any arrears of interest are due. Of the principal, 

 51,179/. being the whole amount which has faliea due. 



METHOD OF SQUARING A CIRCLE. 



Sir — I send, subject to your approbation, the following descrip- 

 tion of a novel and ready geometrical method of squaring a circle^ 

 at once easy of application, and more approximate to the truth 

 than any method yet proposed. The resulting square is only in 

 excess of the true area TfTjAimth part; and the side of the square is 

 in excess of the true side only ,.,„', g,| th part; therefore being, for 

 practical purposes, as accurate as the ordinary rule; side of square 

 =V-7854'X square of diameter of circle. The process is as follows. 



(on AB) FG = ,^ , 

 produced in H, and I. 



Let ADBE be the given circle. Find DE, the side of a penta- 

 gon inscribed in this circle, and produce DE both ways to H and I. 

 Let C be the centre of the circle, and AB be a diameter perpen- 

 dicular to DE From F (the intersection of AB, and DE,) set ofl; 



; and with centre G, and radius GC, cut DE 



Then HI is the side of the square GEF. 



I have assumed that the side of the pentagon can be readily 

 found, either by angles, or by geometry. In the first case, make 

 the arcs DB, BE, eacli equal to 36°; in the second case, I have 

 employed a geometrical method wliich I have not met in any trea- 

 tise or mathematical work, and which I find very useful. At B 

 erect BL perpendicular and equal to the radius BC. Bisect the 

 radius BC at K ; and with centre K, and radius KL, cut AB pro- 

 duced in M; then, with centre B, and radius BM, cut the circle 

 ADBE in D, and E. Join DE, which is the side of the pentagon 

 required. 



Demonstration.— "Hat to enter tinnecessarily into a long explana- 

 tion, it will suffice to state that if the diameter of the gi\en circle 



be considered=l, then CF: 



a/5+1 



and HI — 0-8862337014.45a ; 



in 

 th 



But the true side is = 0-886226925452 g ; 

 .•. the resulting side is 6775992 



parts in excess in 886226925452; more concisely represented by 

 the fraction, TTirr^^th part. 



It may also be shown that the excess of area is nearly double 

 that of the side, for HP = 0-785410196624.a ; 

 But the true area is = 0-7853 98163397 a ; 



.-. the resulting area is 12033227 parts in e.xcess 



785398163397 ; more concisely represented by the fraction, ,j^^ 

 part. 



I think that I have succeeded in showing that this new and 

 simple method is quite as ]iractically accurate as the ordinary 

 numerical rule, with which it also agi-ees to four decimal places. 

 Numerical calculations are always troublesome to working-men, 

 and a good geometrical method of reducing squares and circles has 

 been long desired. As the method I now propose is easier, and 

 more accurate than any previous ones, I shall be happy, through 

 the medium of your Journal, to make it known. 



J. B. HUNTIMGTON. 



24* 



