182 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL, 



[June, 



melancholy exhibition indicates. Engineers incur most serious 

 responsibilities in providinf; for the security of railway travellinf^, 

 which are faithfully discharged by those only who possess sound 

 and scientific knowledge of mechanics— not by those who content 

 themselves with the inaccurate undigested notions which they call 

 practicul knowledge. Until such discussions as that above referred 

 to, have ceased, there will be always a well-grounded apprehension 

 that the assumption of scientific rank is a mere cloak of quackery, 

 enijjincsrn, and presumptuous incompetence. 



Of the two series of experiments upon the dynamical deflection 

 ot girders, those conducted at Cambridge by Professor Willis 

 must be considered the most effectual for the discovery of the 

 mechanical laws of this subject. It is not always the most direct 

 experiments which are the most conclusive. Indeed, the great art 

 1 .^■'fI'""'>efiti'iS consists in abstracting various incidental causes 

 which have no real bearing on the question at issue, but tend 

 merely to comiilicate the results from which laws are to be in- 

 terred. 



Of course tliis abstraction of incidental circumstances, which are 

 ot real occurrence in practice, must be made cautiously and on 

 scientific principles. Unless it be conclusively shown that the 

 causes abstracted are immaterial, an essential link is wanting in 

 the chain of argument deduced from the experimental results. 



In the experiments at Portsmouth the carriage travelled over 

 two trial bars at once; in the Cambridge experiments over only 

 one bar at a time. In the former series, the load during its transit 

 always pressed on two points of each bar at once; in the latter 

 series only on one point. Now, the simultaneous employment of 

 two bars introduces this difficulty— that, because it is impossible to 

 have both exactly of the same rigidity, one will be deflected in a 

 thtterent way to the other; consequently there will be, durincr the 

 transit, a rucking or lateral oscillation of the carriage, which 

 unduly affects the observed deflections. Again, if two wheels of 

 a tour-wheeled carriage press at once on one bar— the bar being 

 9 feet long, and the axles of the wheels nearly 3 feet apart— tlierS 

 IS an inevitable complexity. For at the commencement of the 

 experiment only the fore wheels, at the end of the experiment only 

 the hind wheels, press on the bars— part of the load being at those 

 tjmes borne by the permanent railway beyond the bars: also the 

 theoretical computation of the curves of deflection, on the suppo- 

 sition of a simultaneous pressure on two points of the trial, would 

 be of the most embarrassing nature. Consequently, it ivould be 

 a J but hopeless to attempt an exact comparison betw'een the results 

 of the Portsmouth e.xperiments and the corresponding results of 



Nevertheless, the series of experiments carried on by Captain 

 James and Lieutenant Galto.v were very valuable in themselves— 

 tor they exhibited distinctly the effect of the inertia of the beam 

 in resisting its dynamical deflection. It was shown in the number 

 of ihis. . Journal iw September 1848, in the paper on The D,/,iamical 

 Defleetim and Strain of Rnilway Girders, by Mr. Homersham Cox 

 that wnen the inertia of the load and bridge respectively bear 

 anything like the proportions observed in practice, the increase of 

 deflection due to the ordinary velocities of the load is inconsider- 

 fthle. iiut in the experiments at Portsmouth the dynamical deflec- 

 tions greatly exceeded the statical. The results were, indeed of a 

 nature to surprise those who had not maturely considered the whole 

 question; but this apparent contradiction of the daily experience 

 Of railway travelling ceased when it was reflected that the trial 

 bars were purposely made very light, so that their deflections might 

 be large and easily observed. The relation between the sustainTn.^ 

 and moving masses entirely differed from practical proportions- 

 jind the beam possessed so little resistance of inertia (to adopt 

 loose jihraseology) as to be susceptible, in an e.xcessive degree, of 

 dynamical influence. o "="=? 



In the experiments conducted by Professor Willis, several 

 efnements were introduced, and a beautiful mechanical con- 

 he Xtf-"''/'^'^'' 'T '"";' -"'"."^ *'"^«'l' ^*''t'' g'-e^'t precision, 

 the effects of inertia, and explained " the great and startl ng incre- 

 ments of the deflection" above referred to. The contrivaniehi 

 question was termed by the Professor the In.rtial BaZce 



Themechanism of the Inertial Balance consisted of a loaded lever 



neued by other multiplying levers with the centre of the trial bar- 

 so that for a slight deflection of the bar the loaded lever must neces' 

 sarily turn through a considerable angle. Now, it is apparent tlrU 

 by this contrivance the inertia of the beam was increased but not its 

 elastic strength. For as the balance was poised, it could have no 

 s atical effect, except that due to friction of pivots; and acceptin.^ 

 tlie friction as inconsiderable, a weight at rest on the trial ba? 



would produce the same deflection whether the balance were 

 applied or not. But though the statical strength of the trial bar 

 remained unaffected, its dynamical strength might be increased ad 

 lihtum; the moment of inertia of the loaded balance was easily 

 comparable by known theorems of mechanics, with the effect o'f 



the simple addition of increased mass at the centre of the bar 



such mass acting by its inertia only, and not by its gravity. 



The balance was provided with two shifting " bobs,"' of equal 

 weight which, as they were always placed at equal distances from 

 tiie fulcrum, counteracted each other's weight, but increased at 

 pleasure the moment of inertia. 



It would require too much space to describe all the other refined 

 and ingenious contrivances which were applied by Professor Willis 

 to secure the correct registration of the results. We must refer 

 to the Report itself for an account of his methods of determining 

 precisely the velocity of transit, and of applying tracing pencUs at 

 different points of the trial bar, so as to show the simultaneous 

 deflections at those points during the whole transit. 



We have no little gi-atification in finding that the practical 

 results, deduced by the combination of his labours with the beautiful 

 investigations of Professor Stokes, agree identically with those 

 predicted in this Journal two years and a half ago, in' the paper on 

 The Dynamical Deflection of Girders. In the ' Cambridge Transac- 

 tions for the year 184.9, Professor Stokes, after giving an analytical 

 series for expressing the relation of the dynamical to the statical 

 deflection, in terms of a quantity 0, expressing the effect of centri- 

 fugal force, adds, "In practical cases this series is reduced to 



1 +"6 • The latter term is the same as would be got by taking 

 into account the centrifugal force, and substituting in the small 

 term involving that force the radius of curvature of the equilibrium 

 trajectory for the radius of curvature of the actual trajectory. 

 The problem has been already considered in this manner by others 

 by whom it has been attacked." The method here explained is pre- 

 cisely that which was given in this Journal, which contained the 

 only other investigation of the problem published. 



Professor Willis also gives numerical results for comparing the 

 two kinds of deflection, which agree exactly with our own, except 

 that he has given the ratios in decimals which we gave as vuVar 

 fractions. " 



Both Professors M^illis and Stokes object, however, to one 

 conclusion in the "able paper by ilr. Cox." In the 'Cambridge 

 Transactions,' Mr. Stokes s liberality of feeling towards other 

 labourers in the fields of science, induces him to speak of the paper 

 as one in which "the subject is treated in a very striking and 

 original manner;" but he adds, that "among the sources of labour- 

 ing force which can be employed in deflecting the bridge, Mr. Cox 

 has omitted to consider the vis viea arising from the horizontal 

 motion of the body:" and proceeds to show that taking the 

 horizontal acceleration into account, it is theoretically possible that 

 the deflection may be under certain circumstances more than 

 double that which could be maintained statically. 



Of this theoretical truth there can be no dispute, nor of the 

 accuracy of the argument alleged in its support. A single observa- 

 tion however will be sufficient to remove the apparent discrepancy 

 between the two independent investigations. That of Professor 

 Stokes treated the subject in all its theoretical generality with the 

 aid of all his analytical powers, and was addressed to a mathematical 

 audience. The investigation of Mr. Cox was intended for practical 

 engineers, and therefore regarded the subject with those limita- 

 tions respecting the inertia of the beam which practice imposes. 

 When these limitations are introduced, the results of both papers are 

 identical. The opinion of Professor AV'illis is conclusive on this 

 point: speaking of the paper in this Journal, he says:— "The 

 author has employed methods of approximation which, although 

 they have not apparently vitiated his results as far as real bridges 

 are concerned, would cause tliem to fail utterly if applied to the 

 interpretation of experiments such as those contained in the present 

 volume."— That is, experiments in which the ratios of the mass of 

 the beam and load altogether differ from those ordinarily adopted. 

 Moreover, it is to be observed that the object of the paper in this 

 Journal was the discussion of the deflection of the girder at the 

 centre; and for that point the conclusions of the paper still 

 holds, even when the additional consideration of horizontal ac- 

 celeration is introduced. 



The observations are made not merely from personal feeling — for 

 tliat would be amply gratified by the acknowledgment made of our 

 labours — but also to show how materially the whole question is 

 affected by the relation of the moving and' sustaining masses. 



