98 THIRD REPORT — l8So. 



pense of the Frencli Government, from which he has drawn the 

 following empirical formulae, viz. — 



, T iu P/' 11784451 (/•+ -03) « A' 



1. In oak beams -^^ = -f—, 



o o I'o 



2. In fir beams ?Z! = 8161128«A'2. 



o 



where P = half the weight in kilogrammes, a the less, and h 

 the greater sides of the section,/ half the length of the colmnn, 

 and b the versed sine of inflection, the dimensions being all in 

 metres*. 



How far these formulae are to be trusted in practical con- 

 structions is, however, I consider, rather doubtful, because they 

 are drawn from a number of results which differ very greatly 

 from each other ; and in one case in particular the result, as 

 referred to the deflection of beams, has been satisfactorily shown 

 to be erroneous by Baron Charles Dupin, in vol. x. of the Jour- 

 nal de I'E'cole Polytechnique, as also by a carefully conducted 

 series of experiments in my Essay on the Strength of Timber, 

 S(c. I conceive it, therefore, to be very desirable that a set of 

 experiments on this application of a straining force on vertical 

 columns should be undertaken, and it is, perhaps the only 

 branch of the inquiry connected with the strength of materials 

 in which there is a marked deficiency of practical data ; at the 

 same time it is one in which both timber and iron are being con- 

 stantly employed. We see every day in the metropolis houses 

 of immense height and weight being built, the whole fronts of 

 which, from the first floors, are supported entirely by iron or 

 wooden columns ; and all this is done without any practical rule 

 that can be depended upon for determining whether or not 

 these columns are equal to the duty they have to perform. 



I say this with a full knowledge that Mr. Tredgold has fur- 

 nished an approximate rule for this purpose ; but the principle 

 on which it is founded has no substantial basis. The extra- 

 ordinary skill which Mr. Tredgold possessed in every branch 

 of this subject, and the great ingenuity he has displayed in in- 

 vestigating and simplifying every calculation connected with 

 architectural and mechanical construction, certainly entitle his 

 opinion to high consideration; but still on a subject of such 

 high importance, it would be much more satisfactory to be pos- 

 sessed of actual experimental data. The supposition he ad- 

 vanced was made entirely as a matter of necessity, and I am 

 * See Traite Analytique de la Resistance des Solides. 



