318 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



[Oct. 



only cbanie was in the ratio of the rihs, the rlepth and every other dimension 

 in the model remaining the same. Finding that all these beams had been 

 broken by the bottom rib being torn asunder, and that the strength by each 

 change was increased, I had the bottom rib successively enlarged, the size of 

 the top rib remaining the same. The bottom rib still giving way first, I had 

 the top rib increased, feeling that it might be too small for the thickness of 

 the middle part between the ribs. The bottom rib was again increased, so 

 that the ratio of the strengths of the bottom and lop ribs was greater than 

 before ; still the beam broke by tlie bottom rib failing first, as before. As 

 the strength continued to be increased more than the area of the section, 

 though the depth of the beam and the distance between the supports re- 

 mained the same, I pursued, in the future experiments, the same course, 

 increasing by small degrees the size of the ribs, particularly that of the 

 bottom one, till such time as that rib became so large that its strength was 

 as great as that of the top one, or a little greater, since the fracture took 

 place by a wedge separating from the top part of the beam. I here discon- 

 tinued the experiments of this class, conceiving that the beams last arrived 

 at, were in form of section nearly the strongest for cast iron." 



The form of the strongest section thus ascer- 

 tained was, as shown in the adjoined diagram ; 

 the ratio of the sectional area of the top and bot- 

 tom was as 1 : 6 ; so greatly does the compres- 

 sive strength of cast iron exceed its tenacity. The 

 depth of this beam was uniform throughout, but 

 thickness lessened towards each end, so that the 



plan of each flange was lens-shaped, the curves 

 being portions of a parabola. This form has been shown theoretically to be 

 that which makes a beam of uniform depth equally strong in every part. 



The omissions in Mr. Hodgkinson's inquiry, or rather the subjects in 

 which he has left room for further inquiry, appear two-fold. In the first 

 place, the object of his experiment was confined almost entirely to ascer- 

 taining the proper proportion of the two flanges to each other ; and secondly, 

 the flanges were always thin, compared with their width, and of a rectan- 

 gular section, '"'he proper form and dimensions of the vertical rib, seem to 

 have been comparatively neglected ; and it was not ascertained whether for 

 a given quantity of material, additional strength might not be attained by 

 making (he bottom flange of greater vertical depth in proportion to its 

 width. 



The strongest beam is that of uniform strength, or that which when it 

 tends to break has that tendency in every part ; consequently the best form 

 is that for which the beam tends to give way in both flanges, and the Ter- 

 tical rib simultaneously. Moreover, the tendency to give way must be 

 equally exhibited in every part of each of these members : the beam when 

 the load is placed at its centre, must not tend to give way sooner in the 

 middle than towards the ends, nor to fail in the flanges sooner than in the 

 rib. Now Mr. Hodgkinson's beams always broke in the middle, and the 

 failure was aluays in one of the flanges. 



It is a great mistake to suppose that the vertical rib ought to be as thin 

 as possible. Where nearly the whole strength is contained in the flanges, 

 the rib need not usually possess much strength towards the centre, but it 

 ought to be increased in streugth towards the extremities ; and the law of 

 increase has been clearly shown in a former page of this Journal {ante p. 174). 

 The consideration of the exact nature of the forces acting on the vertical rib, 

 seems to have been overlooked in our theoretical books ; and it ought to be 

 made the subject of an altogether new c'ass of experiments. 



The next question on which it appears to us further experiments are 

 wanted, relates to the possibility of improving the sectional form of the 

 flanges themselves. It has been usually considered that they ought to be 

 two thin wide lamina;, and the object for adopting this form is, that tlie iha- 

 terial may have the greatest possible leverage about the neutral axis. Mr. 

 Hodgkinson evidently falls in with this notion, which, as we think, arises 

 from erroneous conceptions of the action of the vertical rib. Wc are 

 strongly inclined to pronounce the bottom flange in the section given above, 

 too thin for its width, It does not seem very hazardous to predict that, all 

 other things remaining the same, the strength would be greatly increased by 

 doubling the thickness of this flange. 



It seems clear that the part of the metal in the immediate neighbourhood 

 of the vertical rib will be more acted upon than the outer or more project- 

 ing parts of tlie flange. These are comparatively incrticient ; for to suppose 

 that all parts of the flange, because nearly at the same distance from the 

 neutral line, therefore exert the same elastic force — what is this but assuming 

 in another form the old exploded notion of the incompressibility or inex- 



tensibility of the material .' The parts projecting the greatest distance be- 

 yond the vertical rib will be least acted upon, and consequently the great 

 object ought to be to collect the material of the flanges as closely about the 

 upper and lower edges of the rib as is compatible with other considerations. 

 Under this head also new experiments might be advantageously insti- 

 tuted. 



In the theoretical investigation of the transverse strength of beams, Mr. 

 Hodgkinson does not adopt the theory of John Bernoulli, Mariotte, Prof. 

 Moseley, and others, that the elastic forces of the fibres are proportional to 

 their distance from the neutral axis, but represents those fores by an expres- 

 sion ax — (p(x') where q>(jr) is " a function representing the diminution of the 

 force in consequence of the defect of elasticity." He is disposed to conclude 

 from experiment that for cast iron tliia function would be of the form b x'. 



The present treatise shows clearly enough that the old assumption leads 

 to erroneous results. We may furnish the following proof in addition to 

 those given by him. We recently had the curiosity to apply the formulae 

 given by Professor Moseley (p. 507 & il'i) for the deflection of beams to 

 several cases of the experiments relative to the Menai Bridge, detailed in this 

 Journal, p. 147, and found the deflections so calculated six or seven times as 

 great as those actually observed. This seems to us quite suflicient proof that 

 the old theory is not to be trusted ; it is indeed founded on an assumption 

 which it would be very difticult to prove, that the centre of curvature for all 

 the filaments of the beam, and for the bounding surfaces, coincides with the 

 centre of curvature of the neutral line. 



But although Mr. Hodgkinson has probably made an improvement in the 

 theory in the particular here alluded to, we by do means assent to one of the 

 assumptions on which this theory proceeds, namelv, that the parts of the 

 section will be extended or compressed according to their distance from the 

 neutral. We think that enough has been said to show that the bottom flange 

 cannot be in a state of uniform tension throughout at equal distances from 

 the neutral axis. At all events this ought to be proved before it is 

 assumed. 



It should be mentioned that the works before us contains a large portion 

 of the results already communicated in reports to the British Association. 

 The theory of the strength of materials is daily assuming a more complete 

 form ; in fact there is scarcely any branch of the philosophy of engineering 

 of which so much is known. The subject is one which has been illustrated 

 by the splendid talents of Euler, Bernouilli, and many others of almost equal 

 celebrity : but the merit must undoubtedly be awarded to Mr. Hodgkinson, 

 of having realised the investigations, and of having given to them that cer- 

 tainty and method which alone can render them useful to the practical 

 engineer. 



WILLIAM OF WYKEHAM. 



The annual volume of the Archoeological Institute is just published. It 

 refers almost exclusively to the architecture of Winchester. The following 

 extract, from a paper by Mr. Cockerell, wdl show that we are not singular 

 in our notions of the necessity of faithfulness in architecture. The extract 

 refers to the artistic merits of one who, if worthier notions of the funda- 

 mental principles of art were generally entertained, would be esteemed in- 

 comparably the greatest of English architects:^ 



" The chief expression of Wykeham's architecture is its constructive cha- 

 racter ; throughout we trace the sound builder, the able mason, the inge- 

 nious carpenter, whose well-designed operations satisfying the mind, carry 

 with it the fancy, by natural consequence, in harmonious consent; and an 

 unsought felicity follows as a matter of course. He wrought out his design 

 through the model, and an intimate knowledge of the materials, and careful 

 consideration of the wants and requirements on the spot. His cornices and 

 labels and watertables explain their purposes of carrying off the wet; the 

 buttresses are never for ornament alone, but proportioned to the support 

 and durability of the edifice. No parasitical excrescences obtrude them- 

 selves ostentatiously, no parts and prettiuesses are indulged which may not 



be accounted for by a natural grace and logical fitness He 



was one of the first to recognise the utility of the four-centred arch, and to 

 employ its depressed form where a superincumbent floor made it convenient. 

 It is probable that he did not encourage that fashionable adoption of it, 

 which introduced it (under Edgiugton, his predecessor in the see of Win- 

 chester) into the cathedral itself, for we find uniformly the two-centred arch 

 in his halls and chapels; while the four-centred was confined to situations 

 of limited elevation. He was one of the first to condemn the tenuity, elon- 

 gation, and weakness, real and apparent, of the Lancet and Decorated style, 

 and to introduce the so-called Perpendicular, which, fortified by its muUions 

 or constructive subdivision of skeleton framing, or network, the enormous 



