immediate object of his research being to determine by calculation the strength and deflexion of beams that were to be experimented upon, previous to being applied to their intended purpose.

The difficulty of obtaining suitable formulæ, or modes of calculation for any particular case, induced the Author to peruse the above-named work with some attention, and from this perusal the plan of his own performance was suggested. It occurred to him that the theory, as delivered in Mr. TREDGOLD's work, might be more simply developed, and the formulæ arising therefrom, collected and arranged in such a manner as to enable practical persons to refer at once to an expression applicable to the very case proposed: this is the chief object to which the writer's attention has been directed, and he flatters himself that he has in some measure succeeded.

The mode of comparison here employed for establishing the theory, cannot, it is presumed, from its simple and obvious nature, be easily misunderstood; the principle is not new, but it does not appear to have hitherto been adopted as the ground-work of a similar

doctrine the theory of strength, of deflexion and stiffness, as delivered in the following pages, depends entirely upon it; and by using the same experimental results as the author `above-named, we have in every instance arrived at the same conclusions. This is so far satisfactory; for, admitting the material on which the experiment was tried to be perfectly free from defects, and uniform in every part, the formulæ deduced from the experimental numbers may be applied in other cases, where the material is the same, with mathematical certainty; and even in cases where the material

different, the results will be sufficiently accurate to apprise the engineer of its fitness or unfitness for the intended purpose.

The Author thinks it not amiss to remark that, during the progress of the work he has consulted no other writer on the strength of materials but Mr. TREDGOLD, and, consequently, according as the principles of his prototype are true or false, the theory here sought to be established must stand or fall. The manuscript was submitted to the inspection of THOMAS TELFORD, Esq., President of the Institution of Civil Engineers; and, but for the

encouragement which he held out, aided by the liberality of the publisher, the attempt would have been entirely abandoned.

Having said this much respecting the plan and circumstances attending his work, the Author submits it to the public eye, with a sincere hope that his labours will be useful to those persons inquiring on the subject; and should the reception of the work be such as to occasion the demand for another edition, it may experience further improvements.

29, Hertford Street, Fitzroy Square. November 1831.

PAGE

ERRATA.

21-11th line from bottom, for 1885, read 942; and for 8915, read 9858. 23-4th line from top, for 4, read 6.

7th line from bottom, for 1080, read 1620.

5th line from bottom, for 1080, read 810; and for 80082, read 80352.

118-6th line from top, for √6.208=2·49, read √6·3947=2·52.

133-13th line from top, for 7, read '7.

'167-13th line from top, for fourth part, read fourth power.

Α

TREATISE

ON

CAST IRON BEAMS,

WHEN EXPOSED TO A TRANSVERSE STRAIN.

THE doctrine of the strength of materials originated with the illustrious Galileo, and since his time many eminent mathematicians and philosophers have laboured to perfect the theory and to reduce its principles to numerical calculation; but their endeavours have chiefly been directed to the discovery of rules for calculating the ultimate strength, or the force excited in the material at the instant of fracture, and hence have determined the dimensions of beams that will just break with a given strain: to those, however, who consider the subject with a little attention, it will soon appear, that this limit of strength ought never to be reached in practice, for beams should not be exposed to a strain capable of producing this effect.

It has been found, that when a material is loaded beyond a certain point, its elastic force is impaired, and it loses the power of restoring itself to its

B

natural state when the load is removed; and Dr. Young has justly remarked, that when this is the case, the value of the material is destroyed for bearing purposes, because a small addition to the straining force is sufficient to increase the deflexion or bending of the beam till fracture takes place: hence it appears, that rules designed to assist the mechanic in the proper construction of beams, should be so framed as to give results within the elastic power of the material, for in that case, the load to which they are exposed will be sustained with safety.

The subject chosen is cast iron, a material almost universally employed in works where strength and durability are objects of consideration; the strain on which we have treated is transverse; the data are derived from experiment, and, consequently, the rules which we are about to establish must partake of the accuracy or inaccuracy of the results from which they are derived.

The forms of beams most commonly exposed to transverse strains in practical cases are, the rectangular, the square, the cylindrical, the tubular, the grooved, or that which has its transverse section in form of the letter I, and the open,* or that whose

* This is a particular case of the rectangular beam, its longitudinal section is