Letter from Charles Bage to William Strutt [no date]
Concerning the strength of Beams
If ABCD Fig 1 be the section of a beam where the strength is to be ascertained, it is not difficult to conceive that the strength may be represented by the contents of a solid figure ABCDEF. _ For the strength or cohesion of the particles in the line CD, are in proportion to their number, that is, to the length of the line multiplied by its distance from the line AB; that is, multiplied by AC. An in like manner the strength of the particles cd, is equal to Ac x cd. But AD x CD = Area of ECDF and Ac x cd =ecdf. An as the strength of all the Lines cd added together gives the whole strength of the beam; so the areas of all the ecdfês added together give the contents of the solid. The dimensions of the solid must of course be FD and BD (Fig 2) = AC Fig 1 _ And CD Fig 1 = EF = AB = CD Fig 2. Because FD represents the distance of the particles from the top of the beam, and BD Fig 2 the Number of the particles in the perpendicular line; or in other words the Number of cdês.
In my last I troubled you with an account of an experiment on Spherical Arches with Hexagon Bricks. I now present you with the latest improvements that have occurred to me. In the former description, the pillars were tied together by wrought Iron Bolts, and rib arches were thrown from pillar to pillar to support the Spherical Arches. Instead of the Rib Arch and Iron Bolt, I propose connecting the pillars by Arched plates of Cast Iron 5/8 thick. The under edge to have projections thusÄ from which the Spherical Arches may spring. These plates properly attached at C.C. to the pillars by dove tail joints will answer the purpose of wrought Iron bolts, and properly bedded against the pillar at D.D. by iron wedges will have great strength as arches to support the weight of the spherical Arches. I also propose flat pillars AAAAAA bedded in the brick work and therefore not necessary to be more than 4 Inches by 1. They will serve to take the weight off the walls and enable us to attain greater accuracy in the workmanship. _ To the flat pillars, the bond timber in the walls to be attached. You said you would find as many faults with my stove as you could _ I hope you will not only do this, but send me a letter. The final arrangement of our plans is delayed till we have your approbation on censure, and therefore if a few lines in the course of a post or two would not be inconvenient I should esteem them a favour. In a short time afterwards I hope to pay my respects to you in person in my way to Leeds. _
I am dear sir yours respectfully.