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CALCULATIONS OF THE STRENGTH

in the course of a day or two, when I will endeavour further to elucidatethe subject, by reference to Mr. Ilodgkinson’s inquiries into the strengthof cast-iron beams, which bear directly upon that part of the question,and refer also to the distribution of the material in other parts of the tube.

My present object is to deduce from the experiments the strongestform of section in the middle of the beam, which, once attained, the othermust follow as a matter of course.

I am, my dear Sir, sincerely yours,

Robert Stephenson, Esq. William Fairbairn.

Time had now become of great importance, and finding itimpossible to remain any longer inactive, it was decided toproceed with such formula; and calculations as could be deducedfrom the experiments already made. In my next letter, I en-deavour to complete the calculations and practical conclusionscommenced in my last communication.

My dear Sir, Manchester, April 6, 1846.

In my letter of the 3rd you had the characteristics deduced from ex-periment, as to the properties and shape, of the material forming theupper and lower sides of the tube. From that statement, it is obvious,that in order to obtain the section of greatest strength, -Ajths morematerial was requisite on the top, to prevent “ crimping,” than what waswanted on the bottom side, to resist tension. In these computations,you will please to observe, that the proportions between the resistingforces had reference to every point in the beam ; but the thickness of theplates applied exclusively to the middle part, which is subject to thegreatest strain. In these calculations, it must be borne in mind, thatthe plates, or rather the sections of double plates, must be considerablymore at the centre than any other part of the tube; from that point theywill diminish in certain definite proportions, as they approach the pierson each side, following the same law (as nearly as possible) as laiddown in Mr. Hodgkinson’s treatise on cast-iron beams. In effectingthis diminution, it will be necessary to do so with caution, and here weshould have to deviate from theory so far as to retain rigidity and pre-vent crimping, which is the chief and almost only difficulty we have hadto contend with.