no 



Tin: CIVIL KNGIXEER AND ARCHITECT'S JOURNAL. 



fApBir,, 



Tlip framp w:is m.ulc in t'fo pnr.illol pieces, which were screwed 

 tofretlier, .iml tlms adjusted, as nearly as possilile, to tlie si/e of the 

 bar; so that it "had thepower of lieinfj moved by tlie hand, but 

 no power of deviatioji from tlie rif^ht line of its position." In 

 other words, tliorc was a pood fit. hut not a tij^ht one. 



Unfortunately, however, thoui,'li the bars were intended to have 

 no power of deviation from the rifjlit line, they assumed it for 

 themselves. \\ liether that tlie frame was not screwed up suHi- 

 ciently sit first, or that it was not strong' enoufjh, or that the 

 screws yielded, certain it is, that this bending of the bars, which 

 it was ail-important to avoid, actually took place. At page 64 we 

 find the following: — 



"Remark. — The great difficulty of obtaining accurately the decrements and 

 sets from the small Heights in tlie comnienceraent of tlie experiments, ren- 

 dered those decrerueiits and sets, particularly the latter, very anomalous ; it 

 was found, too. that some of the bars which had been strained by 16 or 18 

 tons had become very perceptibly undulated. It has not been thouicht pru- 

 dent, therefore, to draw any conclusions from bars which have been loaded 

 with more than 14 to IG tons ; and it may be mentioned that the results 

 from 2 to 1 1 tons are those only which ought to be used in seeking for 

 general conclusions." 



Now, if the bar '■'■very perceptihh/ undulated" in some cases, it 

 is reasonable to suppose that it undulated in less dejrree in others. 

 A flexure (|uite inappreciable by the naked eye would altogether 

 vitiate any inferences from the experiments as to the law of el.is- 

 tieity. The contraction of the rod after it has been bent, is no 

 longer measured solely by compression in the direction of its 

 length, hut partially by the diminution of the chords of certain 

 curves — the curves of flexure. .\nd it is to be remarked, that 

 the diminution of these chords affects more especially those 

 very terms in the formula which are principally sought for — the 

 terms after the first, which exjiress the defect of elasticity. 



.Moreover, leaving the geometrical consideration, in a mechanical 

 point of view the c.ise jiresents great difficulties. The external 

 compressing force is no longer resisted by direct compression alone, 

 but by compression aiul transverse pressure compounded. Again, 

 if the bar closely fitted the interior of the frame originally, it 

 must have bulged the sides of the frame when it got bent. Con- 

 sei|iiently, at tliose points where the bar most deviated from the 

 right line, it must have pressed strongly against the frame. 



Now, the effects of the pressure in question may be illustrated 

 as follows: — Let a thin, flat rod of wood, whalebone, or steel, be 

 placed on a table, and abut at its two etuis against fixed points, so 

 a- to curve slightly upwards from the t;ible. It will be seen that a 

 very slight pressure on the summit of this c\irve will produce 

 a very greatly multiplied pressnie on the points of abutment; 

 also tlie multijilicntion will be greater as the rod is less bent. 



It is oIi\ious from this, that the bent cast-iron rod, by pressing 

 against the sides of the inclosing frame, must have derived great 

 suiiport to resist the e.xternal force to which the ex]ierimenter 

 subjected them. Obviously, serious errors would arise from sup- 

 posing the only external forces acting upon the bar to be those 

 ajiplied at its ends. 



These considerations lead to the anticijiHtion that the experi- 

 ments would present anomalies: and this certainly appears to be 

 the case. M'ithout minute reference to the actual figures of the 

 tables, the whole of the anomalies could not be specified: their 

 general nature may, however, be briefly indicated. 



1st. The ratio of the compressing weight to the compression 

 (^ in the tables), instead of regularly decreasing in each set of 

 experiments, alternately increases and decreases in an irregular 

 manner. There are four kinds of iron — Low Moor, Blaenavon, 

 (iartslierrie, and a mixture of Leeswood and (Hengarnock — for 

 which the ratio is given (pp. Ci and (ifi). The first three sets of 

 exjieriments consist of thirteen results each, and the last set of 

 twelve results. Let us suppose the results numbered in their 

 numerical order, 1, 2, ."J, &c., and let -f or — indicate that the 

 ratio for one result is greater or less, respectively, than that which 

 follows it. Then, for the results on each iron, the fluctuation of 

 the ratio will be expressed as follows : 



1. H. X 4. ,1. B. 7. 8. 9. 10. 11. 12. 



Low UToor — + — — + + + — ~ + +■ + 



Blncniivon + — + + — + + + + — + + 



GnrtBheirlB + + - + + + + + - + + + 



Leegwood & Glengarnock . + + — 4- — — + + + + + 



The plus sign occurs 34 times, and the minus sign 13 times, in the 

 above synopsis; consequently, as the plus sign indicates a descend- 

 ing ratio, the number of ascending ratios is more than one-third 

 the number of descending ratios. Now, in the formula of the 

 Report, it is assumed that the ratio constantly descends; accord- 



ingly, the abnormal are more than one-third of the normal results. 

 It may be shown, by simple analytical reasoning, that if the for- 

 mula include only two terms, the ratio of the weight to the C(mi- 

 pression must be either always ascending or always descending; that 

 if the formula extend to three terms, the ratio may be asceniling to a 

 certain point, and then descending, or conversely; and tliat if the 

 ratio be ascending and descending several times alternately, there 

 must be more terms in the formula. 



2nd. The experiments for different sorts of cast-iron indicate 

 widely-different physical properties in them. The ratio of the 

 weight to the coni]iressioii diflers greatly for corresponding expe- 

 riments in tlie four difl'erent sorts of iron: and not only is the ratio 

 difl^erent absolutely, but its fluctuations are different also. This 

 is shown in the foregoing synopsis, and a remarkable instance 

 occurs in the tiibles on the two last kinds of iron, of which the fir.-t 

 is represented as much less easily compressible than the latter ;.t 

 the beginning of the two sets of experiments, and more easily com- 

 pressible at the end of those experiments. This may be possible, 

 but it is not ])r(d)able. At all events it renders invalid all general 

 inferences taken from collecting (as at page 07) the means of the 

 results for materials exhiliitingsuch different properties; just for 

 the reason tliat it winild he improper to collect in one table the 

 experiments on marble and ivory, and deduce a single formula for 

 the elasticity of both, liut tliis is precisely the way in which the 

 formula for compression of cast-iron has been obtained. 



It is to be observed, however, that in the table in which the 

 mean results of compression of all Jhur sorts of iron are given, the 

 ratio of the weight to the compression is generally a descending 

 one. This circumstance removes the impossibility of expressing 

 the elasticity by a formula of two terms. It is barely possible also, 

 that in thus collecting the means, the errors of the original ex- 

 periments might destroy each other. But when the errors inse- 

 parable from the methods of those experiments, and the discre- 

 jiancies among them, are considered, such a compensation appears 

 extremely improbable. 



The formula is obtained only from the mean results of all the 

 irons — no formyila> are given for each iron separately. The fore- 

 going considerations explain this circumstance. In the experiments 

 of tension^ however, where the results are much more trustworthy, 

 and the ratio is a deacendiiuj one in evert/ case vith a si»fj!e exception — 

 formnlje are given for each iron. The omission of formula; for 

 each iron compressed cannot, therefore, be considered accidental: 

 if attempts to sujiply such formulie have been made and omitted 

 from the Report as unsuccessful, the failure must le attributed 

 to the analytical principles which we have above enunciated. 



Doubtless, experiments on compression of long bars present 

 great difficulties; liut we can conceive of no metbod of insuring 

 their accuracy while the inclosing frame is retained. The fact of 

 such a frame being reipiired manifests that the experiments are not 

 what they profess to be — experiments on direct compression — but 

 experiments on compression and flexure combined. 



If the subject be taken up anew, some means must be devised of 

 compressing the bars without the chance of lateral support inter- 

 fering with the accuracy of the results. But to compress the bars 

 in this way, they must have such a section- — the cruciform, for 

 instance — -as of itself has great power to resist flexure. If the 

 compressing force be applied by a lever, the angle through which 

 it moves in the course of the compression might be read off by the 

 microscope. We offer these suggestions by no means confidently, 

 but in the hope that they may stimulate endeavours to solve a most 

 important practical ])roblem. 



In the case of tension, the experiments seem comparatively free 

 from difliculty. It might perhaps h:ive been worth while to have 

 given a correction for the effect of the weight of the rods them- 

 selves, and the couplings, which were heavy masses of metal: and 

 this correction might have been applied without much difficulty. 

 In other resjiects, the results of experiments on tension appear 

 exempt from general causes of error. 



We have somewhat minutely examined the subject, because of 

 its gi-eat practical importance, and because we have questioned 

 the validity of the formula; for compression and extension pro- 

 posed as the basis of theory of girders. But as tliese formulie are 

 given on the authority of an able experimenter, who has the 

 highest claims to respect, we shall be glail to hud that the views 

 here expressed have been reviewed, and if need be, revised, by 

 investigators of higli scientific repute. 



