1850.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



115 



AVhat Mr. Garbctt has fldiie, sliovvs moreover what may bo done; 

 that art is not without laws, though we do not know tliem all. 

 When the reader has gone through this hook, he has still to read 

 Fergusson and the others, to make up his mind what he will believe 

 and follow out. Nevertheless, we may fairly say Mr. Garbett s 

 book is a step forward. 



Having shown what is the root of the evil, we shall not put tlie 

 book away without a few words as to some of its teachings. Mr. 

 Garbett lays it down, that no building has a right to Ue selfish; but 

 he rides this hobby too far the wrong road, being afraid, as he says, 

 of going on tliat to communism. This is some of the cant ot the 

 day; and is giving a wortli to a name which does not belong to it. 

 If a thing is right, we may stick to it without fear of its name; 

 and we need not wander from the field of building, for a stalking 

 horse on the field of politics. If man is not made to be selfish 

 and live alone, tlien it is his liouiulen duty in a building, as in 

 everything else, to show some feeling for his fc41ows. As he can 

 have no right of himself, but only by the law of the laud, to run up 

 a building, so he can have no riglit to run up a building which is 

 unsiglitly. The least he can do, if only as a reward for the leave 

 given to him, is to l)uild right. 



We may say, by-the-bye, that Mr. Garbett gives his meaning to 

 the word sestbetic — a word wliich is a stumbling-block laid in the 

 way of art by our High Dutch neighbours ; and which the sooner it 

 is got rid of the better, for wliat it means no one knows. ^Ve are 

 sent back to (li.sti'ietilms, and thence to /li.sthaiiomai; then we are 

 brought forward from tlie Greek and (ireek-English to Latin- 

 English; and told that aesthetic means seiisunus, or relating to the 

 sensex, which in English are the feelinirs. Esthetics seems to have 

 been meant by the High Dutch for the knowledge of the laws by 

 which beauty impresses the feelings; but esthetic may mean a 

 number of things, as it is understood in its several Greek, Latin, 

 English, or High Dutch relations. 



REPORT OF THE COMMISSIONERS 



APPOINTED 



TO INQUIRE INTO THE APPLICATION OF IRON 

 TO RAILWAY STRUCTURES. 



The last notice of the Report of the "Iron Commission' 

 referred to the manner in which empirical formula; had been 

 obtained for connecting the longitudinal compression and exten- 

 sion of cast-iron with tlie corresponding el.astic forces. "Tiie law 

 of elasticity," it is said in Appendi.v A, "constitutes the very basis 

 of all s(iund knowledge of the statical and dynamical properties of 

 girders." 



The "revision of that law" is undertaken as one of the subjects 

 of this Appendi.v. The investigation was conducted by one 

 member only of the Coniniission — Mr. Hodgkinson — whose e.vpe- 

 rience and persevering research as an experimenter, render empi- 

 rical deductions obtained by him worthy of the most careful 

 consideration. 



In the preceding number of this Jo tii-n a I (page 92), was given 

 one of his tables for Extension of Cast-iron, showing the relation 

 between different suspended weights, and the extensions produced 

 by them. 



The results of computing the extensions from a certain empi- 

 rical formula are also given, and the errors or deviations from the 

 observed results. These errors, in five cases out of fifteen, 

 deviate from the real result by about one-fiftieth part; tlie smallest 

 of the remaining errors is the two-hundred-and-eighty-fourth 

 part. Now, although these errors may seem small in themselves, 

 they cease to appear so when it is reflected, 1st, that the empirical 

 law assumes the character of "the very basis of all sound know- 

 ledge of the statical and dynamical properties of girders;" 2nd, 

 that the formula is not deduced fi-om abstract theory, but from 

 the experiments themselves, and is in fact no more than a synopsis 

 of their results. 



Under the first head, we observe that any error in the empirical 

 law becomes enormously multiplied when it is ajiplied to the 

 theory of girders. The'result of integration and other analytical 

 processes involved in that theory, is that the magnitude of the 

 original error is not at all commensurate with the magnitude of 

 those it induces. We are to remember that the old law of elas- 

 ticity (that of direct proportion of the longitudinal forces to the 

 extension or compression) led to the inference, that in a girder 

 the central deflection and transverse pressure were in direct pro- 



portion also. This result, however, was not guite true. A small 

 increase of deflection above that due to the proportional increase 

 of jiressure was observed; and the former increase was due to a 

 6))«(// error in the assumed law of elasticity. It may easily be sup- 

 posed that this "small increase" and "small error ' (though small 

 considered separately with reference to the results from which they 

 were respectively derived) are not small with respeel to each other. 

 This is the best way in which we can put the argument, without 

 aid of mathematical language: that would show that the "defect 

 of elasticitv" of the deflected girder is a quantity of the same 

 order as the "defect of elasticity" of the longitudinally compressed 

 or extended rod. 



In tlie table above referred to, the "enors" or deviations of the 

 formula from experiment, are given "in parts of the real weight 

 stretching the rod: but if the errors had been given in parts of 

 the much smaller quantity — "the defect of elasticity" — they would 

 have appeared much larger. 



The second head of our remarks is this, that the formula is 

 essentially empirical. It depends on no abstruse investigation; 

 and all that is required is a method of representing observed 

 results in the short-hand of mathematics. The way in which this 

 has been done, appears unscientiric in its principle as well as 

 unsatisfactory in its results. Two empirical coelhcients a and 6 

 were to be obtained in a formula 



w::::^ae — be'', 

 where «• is the tensile force and e the extension. 



If the formula were absolutely exact, and experiments could 

 be made which were absolutely exact also, two experiments would 

 sulfice to determine a and i. But, because that accuracy is prac- 

 tically unattainable, it was of course the case that any pair of 

 experiments would give values of a and b differing from those of 

 another pair of experiments: we have a remarkable instance of this 

 at page 58, where it is stated that by one pair of experiments, the 

 value of b obtained was 177290-03, and by another pair, the value 

 of i was2211fi;M7. 



Now, in selecting the pairs of experiments for this computation, 

 no sort of system or scientific method appears to have been 

 adopted — the selection was made entirely at random. This process 

 mhjht have produced satisfactory results, but the chances were 

 immeasurably against its success. At all events, the accuracy of 

 the final formula so obtained could not but rest on a much lower 

 kind of evidence than that in favour of a formula formed in accor- 

 dance with the mathematical laws "in that case made and pro- 

 vided." 



The mathematical laws of combination of observations are 

 definite and exact. Practical astronomy is almost made up of 

 such combinations, in which several results are to be represented 

 by a formula which shall give the closest possible approximations. 

 The importance of the subject in physical science long ago led 

 matliematicians to perceive tliat they must combine tlieir results by 

 fixed principles, and not by taking averages indiscriminately. 

 Gauss, the author of the Theoria Combinatiorns Obsereatiunam, 

 proposed the celebrated rule of Least Squares, which has been 

 independently discussed by Legendre, Laplace, Poisson, Ivory, and 

 others. 



'I'o the kindness of 'Sir. Adams, Fellow of St. John's College, 

 Cambridge, we have been jirivately indebted for copious examples 

 of tlie application of the method to the case before us; he has also 

 pointed out a very simple method of extending the formula, to 

 include the nibe of the extension. The agreement of the theo- 

 retical and computed results then becomes extremely close and 

 accurate: when two terms only are taken by the method referred 

 to, though the formula is considerably improved, it still falls short 

 of the required degree of accuracy. This systematic method of 

 comjiutation has the advantages not only of superior accuracy but 

 of superior facility — the labour which it involves is far less than 

 that required by taking averages without regularity of order. 



AV'e may quote the same high authoj-ity for the opinion that the 

 experiments on Co.mpression, given in the Report, cannot be 

 represented accurately by a formula involving even the third 

 power, still less by one extended only to the second power. A 

 very careful consideration has led us to the conviction that the 

 irregularities arise in the experiments thenuelues, and that 

 the errors of observation are probably much greater than in the 

 experiments on tension. 



The experiments on compression were made in this way: — a bar, 

 10 feet long by 1 inch square, was inclosed in a strong iron frame, 

 open at both ends, to permit the free compression of the bar lon- 

 gitudinally, but to pre\ent, as far as possible, its lateral flexure. 



