1850.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



297 



relation between e and w may be closely expressed as follows : — 

 oe w 



wliich is the equation to a rectangfular iiyperbola of whiob c and w 

 are the co-ordinates. Let ((if?. 1) CA,'CB, be the asymptotes; 

 then referring to the above equation, e and w will be measured 

 along the axes oe, ow, respectively, o being the origin. 



Similarly, the formula «> — Ae— Be is the equation to the para- 

 bola (tig. 2) ; oe, ow, are the axes of e and w; AB the axis of the 

 curve, and A its vertex. 



The formula now proposed may be therefore considered to exlii- 

 bit THE HYPERBOLIC LAW OF ELASTICITY, and the last-meutioued 

 formula the parabolic law, in consistency with tlie nomenclature 

 adopted by James Bernouilli in the 'Acta Eruditorum' of Leipsic, 

 1G94. In the tables accompanying this paper, comparison is made 

 between the two fornmla for cases of extension and deflection; the 

 accuracy of the former is shown to be always the greatest — the 

 error of the parabolic formula being, on the average, between 

 three and four times as great as that of the hyperbolic formula. 



Assuming, then, the proposed expression for the extension of a 

 rod of a unit of length and a unit of sectional area, and the 

 analagous one for compresion ((/), by a weiglit («•), 



yd 



w = 1 



1 + Sd 



It is found that the deflection/, of a rectangular beam of length 



2a, of depth '2d, in the direction of deflection, and width m, by a 



force 2 P, applied perpendicularly at the centre of the beam, is 



/= Pa' 





which is the hyperbolic formula for deflection. 



Hence, an expression is deduced for the ultimate deflection of 

 rectangular beams, from which it follows that tlieir strength is as 

 their thickness and the cube of their de])th directly, and as the 

 length inversely — the law usually adopted in practice hitherto. It 

 is true that this law was not formed to he followed exactly in the 

 experiments above referred to, where tiie magnitude of the beams 

 differed greatly; but the irregularity is explained in the Report as 

 due princi])ally to the superior hardness of small castings. 



Lastly, by substituting in the above formula for the deflection 

 numerical values of/ a and $, obtained from tlie experiments on 

 extension, the numerical co-eflicients are obtained in the formula 

 for com|>ression. Tliis method seems to tend to more correct 

 results than the experiments on direct compression, detailed in 

 the Report. For those results are extremely irregular, and were 

 vitiated by the inclosure of the compressed rod in rectangular 

 tubes, the sides of which were pressed by the rods when they 

 became bent; and tliis pressure bad great efi"ect to resist the com- 

 pressing force at the end of each rod. The numerical values of 

 the co-eflicients of compression iu the hyperbolic formula agree 

 closely together when computed, by the above-mentioned method, 

 from experiments on deflection of difi'erent bars. 



The great desideratum for the improvement of the hyperbolic 

 or any hypothetical law of elasticity is a knowledge of the manner 

 in which the strength of cast metal is influenced by tlie magnitude 

 of tlie casting; and it is to he hoped that this defect of practical 

 knowledge will not long remain unsupplied. 



VALUE OF WASTE GASES FROM BLAST FURNACES. 



On the Value of the Gaseous Escape from the Blast Furnaces at 

 the Ystalfera Iron-works, in Wales. By Mr. Palmer Bldd. 



Mr. Budd stated that, since the meeting of the Association at 

 Swansea, he had continued, and witli increased success, to apply 

 the waste gases th.-it escaped from the top of blast furnaces, to the 

 manufacture of iron; and it was the result of his farther experience 

 applied to the whole of his furnaces (nine in number) since that 

 period, that he now wished to submit to the Section. He con- 

 sidered that he could not have f illen on a better locality for this 

 purpose than Scotland, where tlie iron trade has Iieen developed 

 with a rajiidity that is quite surprising, and quite characteristic of 

 the enterprise of Scotchmen. Twenty-five years ano, Scotland 

 was of no importance in the iron trade, but since then tlie produce 

 of iron iu Scotland had increased to between six and seven hun- 

 dred tliousand tons a-year. In that sliort period Scotland had 

 accomplished a production wliich Staffordshire and other places in 

 England took two hundred years, and South Wales a hundred 



years to accomplish — the make of iron in Scotland being now 

 equal to that of either England or Wales. This great accession 

 to the produce of iron has had a sensible effect on its price; but as 

 lie believed that necessity was the mother of invention, and that 

 nature had in store for us an immense reservoir of riches to be yet 

 developed, he was of opinion that the tendency of all this cheap- 

 ness was to teach us that nothing should be wasted, and that we 

 should look forward to the time when the smoke that at present 

 contaminated the atmosphere, and the filtli that polluted our 

 streets, would be regarded as too valuable to be wasted. 



When we ctuisidered the utility of iron. Us low price, and its 

 general distribution in the deposits of every age, we could not but 

 look upon it otherwise than as the great agent in modern civil- 

 isation. 



Mr. Budd then referred to liis mode of ajiplying the gaseous 

 escape, and said it was well known that there were two descrip- 

 tions of furnaces used for metallurgic purposes. The one was the 

 blast furnace, into whidi air was injected, by mechanical means, 

 at a great density, so as to penetrate upwards of forty feet of dense 

 materials; and the other the reverberatory furnace, where the lire 

 was produced by means of the draught of a chimney stack. What 

 be had accomplished was by combining tliese two, so that the gaseous 

 products of the furnace, instead of escaping through the funnel 

 head, were drawn sideways by a high stack, and passing through 

 the stoves and boilers, leave behind the necessary temperature of 

 the blast and of the steam. In a blast furnace the ores are smelted 

 before the tuyeres by the conversion of the solid carbon into car- 

 bonic acid, which, passing up through the middle region of the fur- 

 nace into a bath of carlion, was reconverted into carbonic oxide, 

 capable of combining with a farther dose of oxygen. It would be 

 thus seen that the whole of the carbon of the fuel should be present 

 at the top of tlie furnace in a gaseous form. When the British 

 Association met at Swansea, be had not used the gaseous escape 

 at any great distance from the furnace, his stoves and boilers being 

 very closely contiguous. Furtlier experience, however, had proved 

 that by the aid of a stack at the end of the chain of suflicient 

 dimensions, the gaseous escape from the furnace might be made to 

 travel in the most tortuous directions, descending to the stoves 

 built for heating by the usual (ire-places, and traversing the boil- 

 ers ; the only condition absolutely necessary being that tliere 

 should be an unbndven communication with the high stack at the 

 end, into which the gaseous escape miglit at last pass, and by 

 which it was drawn fn-ward, instead of passing oft' wastefuUy at 

 the funnel-liead. AV'hen, however, the draught was carried down- 

 ward, and to long distances, he had found it necessary to drop 

 into the top of tlie furnace a hopper or funnel, made of sheet-iron, 

 which acted as a shield at the mouth of the horizontal flues, and 

 jirevented them from either being affected by high winds, or from 

 being choked np by the materials thrown into the furnace. 



The reason, no doubt, why this funnel was not applied before 

 was the great apparent temperature at the funnel-head. In 

 practice, however, it was found that until the gaseous escape 

 mingled with the atmos])here, its heating power was not such as 

 to injure sheet-iron, or even to make it red hot. In fact, so long 

 as there was an escape upwards, the iron funnel would not he in- 

 jured. The damage arose during and after stoppages of the fur- 

 nace, when the blast was obstructed in its passage upwards by the 

 settlement of the materials in the furnace, so that the atmosphere 

 ruslied down to meet the ascending gases, and of course, caused a 

 very high local temperature. His practice was to exclude the 

 atmospheric air as much as possible. The afl^nitv of the gases for 

 oxygen was so great that the air leakage raised the temperature 

 quite sufficient for safety, whilst the full combustion of the gaseous 

 escape w(uild melt down the liricks in the flues, and destroy the 

 texture of the irmi tube. It was not possible for him to say what 

 combinations took place at high tenijierature, where carbonic 

 oxide, carbonic acid, hydrogen, and nitrogen, were mixed in such 

 proportions. At any rate, he found a smothered combustion to ba 

 the most suitable and economical for the purposes in view. 



He was happy to say that, at length, the application of the 

 gaseous escape had been tried in Scotland ; and that at Dundyvan 

 and elsewhere it was now in successful operation. The peculiar 

 (piality of the furnace coal of Scotland being what was called in 

 South Wales "free buriiing," vvhich, when put into the furnace 

 raw, coked sufficiently in its dei^tent, gave out an enormous escape, 

 so much so that, upon a rough estimate, he calculated that the 

 waste from one furnace in Scotland was sufficient to heat the 

 blast, and to raise the steam for three. With anthracite coal, the 

 minimum effect was obtained, as it was a dense fuel of nearly 95 

 per cent, of solid carbon; but in Scotland there would be aa 

 enormous surplus at the funnel-head. 



40 



