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March I, 1868.] THE CIVIL ENGINEER AND ARCHITECT’S JOURNAL. 87 ’—sin-’ r- so also p ~ • 3 Calling x and y the lever arms of P and N about E, we have ®=?/2— s =v / ’' 2 —« 2 2 —J/=R— N=P- y X., Taking the example of R=11 ft., and r=10 ft., and calculating N for several values of x D I find that N is greatest when aq = 4 ft., x,=3'5 ft., which give, sin- 1 ^ = T179w, sin- 1 ^2-=-113827r K r and these quantities will be constant whatever the dimensions of the dome, provided R and r bear the same proportion to each other as in this example : that is to say, the weakest point on a £ dome of this form is at a height of ~^R above the springing line. In the above example, the span being 20 ft., we have N=55-78 lbs. or To form the Equation of Stability for calculating the thick ness of the pier, we find F the weight of the portion between E F and A B, and z' the distance from the axis of its centre of gravity, by means of the foregoing integrals, putting F=F X —F 2 Fi-F 2 4 and the limits of integration are x=Q to x= —R for F x and F^, 1 7 and x=— -aq to as= -x 1 for F 2 and F 2 2„ F. c being the moment 8 8 of F about-S, c=r-|-f—z'; N. b being the moment of N (supposed to act at F) about S, b=H-j- ^R ; H being the height of pier. We can thence form the Equation of Stability 2Nb = P . u-j-F . c+Q . q. P . a being the moment of P (supposed to act at E) about S, and a=4-|--06324r. In the above example the equation becomes 4 3 + 304 2 +8.5354—130-82=0, 4=1'9 ft. In the dome of uniform thickness of 1 ft. I found N = 921bs., 4=2-45 ft., so that the difference between the two is very con siderable. The foregoing papers were read at the Royal Society, and partly published in the “ Proceedings,” No. 85, 1866. Errata.—In the Fig. 4, Plate 4, the letter e should have been marked at the bottom of the perpendicular from E. Also in Fig. 8, Plate 4, the letter I should be marked at the end of the horizontal line drawn from X. Statistics of Coal.—An interesting blue-book has just been issued, containing reports from her Majesty’s Secretaries of Embassy and Legation, respecting the production of coal in different countries. According to these reports, the production of coal in Belgium in 1866 from 286 mines was 12,774,662 tons; the quantity exported in the year was 3,938,768 tons, nearly all of which was sent to France. With reference to the exhaustion of the coal mines, a subject to which public attention has been directed in Belgium, it appears that in Hainhault alone, of a coal producing surface of 54,173 hectares, only 23,423 hectares had been explored in 1860. It is estimated that there were about 4,700 millions of tons yet to be worked at an easily workable depth, and the exhaustion of the Hainault coal-fields above a depth of 1,000 metres would not take place before the expiration of a century and a half. In Brazil, large coal fields have been discovered in the province of St. Catherine’s. In China, coal has been discovered at Ponghou, the chief island of the Pescadores. It is reported that no coal useful for steam purposes has yet been found; a judicious miner, however, could alone settle the question as to the extent of these mines, and the quality of the coal. At Iwa- nai, in the Island of Yeddo,'in Japan, coalmines have been discovered. An experiment was made with some of the coal picked out from the surface of the seams, in the galley fire of her Majesty’s ship Salamis; 791b. of coal yielded 17’27 per cent, of ash, 1’5 per cent, of clinker, an average volume of smoke, and a strong durable flame. THE INSTITUTION OF CIVIL ENGINEERS. March, 1868.—The Paper read was “ On the Manufacture and Wear of Rails]' by Mr. C. P. Sandberg, Assoc. Inst. C.E. This communication was divided into three parts. First, as to the best method of manufacturing rails out of common iron, and as to the time they would last. Secondly, as to the disposal of the iron rails when they were worn out. And thirdly, as to whether iron or steel, or a combination of the two materials, was the most economical to use for rails. The mode of manufacturing iron rails for Sweden, as carried out in South Wales between the years 1856 and 1860, was described; and it was stated that, with a view of ascertaining the best method, it was decided to submit a number of sample rails, made from five different kinds of ‘ piles,’ to actual practical trials. These experimental rails were laid down at the Camden Town station, by permission of the London and North Western Railway Company; and the following table showed the number of tons passed over each description of rail before it was crushed, and also before the rails were taken up :— Mark of Rail. T Y H E N Crushed. Tons. 3,680,000 4,140,000 3,220,000 6,900,000 3,220,000 Worn Out. Tons. 5,060,000 5,290,000 5,060,000 8,970,000 5,520,000 A table calculated from the above, showed how long the rails would last, supposing them to be passed over by three thousand trains yearly, each train being composed of an engine weighing 30 tons, and of twenty wagons of 10 tons each, or a gross load of 230 tons. From these tables it was ascertained, that the five different descriptions of rails were on the average crushed in six years, and worn out in nine years. The conclusion was thus arrived at, that hammering after the first welding heat, for this particular kind of iron, did not improve the endurance of the rails, but that the simplest mode of manufacture had also the material advantage of being the best. These trials at the same time established the fact, that it was not the wear or the di minished sectional area caused by abrasion, which produced the un satisfactory results in the endurance of iron rails, but the lamination caused by imperfect welding. This explained the great difference between the wear of rails made in exactly the same way, the welding in the one case being perfect, whilst in the other it had been very im perfect. These experiments also confirmed the rule laid down in Mr. R. Price Williams’s Paper, ‘ On the Maintenance of Permanent Way,’ viz., that the endurance of rails might be measured by the product of the speed and of the passing weight. Trial rails, of the same kind of manufacture as those marked £ in the previous table, but of a heavier section, laid on the Great Northern Railway, might thus be said to have borne 276 million tons at a speed of 1 mile per hour. The en durance of the rails tried at Camden Town, under unusual conditions, where the wear was occasioned principally by the frequent use of the breaks and by continual shunting, was much less, and might be repre sented by 120 million tons at a speed of 1 mile per hour. These ex periments seemed to indicate that 220 million tons might be carried over rails, of the section and make referred to, at a speed of 1 mile per hour ; so that any railway company, knowing the load which yearly- passed over their line and the speed, might by multiplying the one into the other, and dividing this product by 220, ascertain the life of iron rails in years. The conclusions the Author had arrived at were, that no rule could be laid down for the manufacture of rails that would apply to every manufacturing district; but that in the case of Welsh iron, to which he had more particularly referred, it had been proved that the best method of manufacturing the rail was that now most commonly prac tised, viz., rolling the iron into bars, piling these, and repeated rolling to the finished rail, without hammering. The Author assumed that the prejudicial result from hammering was owing to the large amount of sulphur in the Welsh iron. Where the iron contained more phos phorus, and less sulphur, as, for instance, in the Cleveland, Belgian, and French iron districts, hammering had proved beneficial, and rails had been made direct from puddled bars, without the intermediate process of piling—this being, in fact, the method generally adopted in those places, and being found to answer best. As to the disposal of the rails when worn out, and as to the possi bility of re-rolling old rails with advantage by companies far removed from the seat of manufacture, such as the British Colonies, the countries round the Mediterranean or the Baltic, the Author thought that for railways near the seat of rail manufacture, the best way would be to continue to sell the old rails to the rail mills. For other countries, situated like Sweden, for instance, it became important to ascertain whether it would not be more advantageous to re-roll them. On this subject precise and detailed calculations were entered into, which led the Author to think, that the manufacture might be carried on in that country with advantage, using Swedish Bessemer Steel for
