946 THEORY AND PRACTICE OF ENGINEERING. Book II.

extract the square root, and subtract 72; then multiply by the square of the length in feet,and the result will be d, or the diameter in inches.

The lateral strain and twisting to which shafts are subjected must be estimated, and itcommonly happens that one of these forces exceeds the other, and therefore the greaterpower is the one to provide against ; the resistance to a lateral strain is measuredby its resistance to resist flexure, and which may be about one-hundredth part of an inchfor each foot in length, before it materially affects the regularity of the motion of themachine.

For the lateral stress on cast-iron shafts, the weight to in pounds, acting in the middle ofthe length l in feet,

v 7

tv X l500

d.

For malleable iron the result must be multiplied by 0-935, for oak 1-83, for fir 1-72, andfor shafts to resist torsion, we have in horse-power h, that the shaft will drive, making turnsper minute,

240 x h

?i

= d for cast-iron.

For malleable iron multiply the result by 0*963, for oak by 2 238, and for fir 206; theseare for shafts of first movers, for second movers multiply the first by 0-8, and for third by0-793. To show the application of the preceding rule, suppose the length of a shaft, fromthe water-wheel to the cogwheel, to be 6 feet, the radius of the water-wheel 9 feet, and thegreatest force it will be exposed to 2000 pounds.

9 x 2000~5-2 x 6 3

= 16 nearly.

V 16+5184 = 72-12subtract 72

-12 : then T2 x 6 8 = 4*32 inches.

Practical men usually estimate the size of shafts or journals by the number of horse-powers,and the speed of the fly-wheels.

Rightly to proportion the shafts of mills to the stress they are subjected to is of greatpractical importance ; timber formerly was entirely used for the axles of mills, and sincethe application of iron to this purpose, machinery has undergone an entire change. Tablesgiving the proportions have been established, so that now the mechanic is guided withgreater certainty in his work. It must always be borne in mind that the stiffness of ashaft or beam is the property it has to resist bending or flexure, and that strength is thatwhich resists breaking or fracture: the stiffness, then, is determined by the force whichcauses it to recede, its transverse strength by the pressure required to break it.

This distinction is expressed when w r e say that beams of equal length have their lateralstiffness as the breadth and cube of their depth, and their lateral strength as the breadthand square of the depth.

Lateral stress, which produces fracture, or which tends to break a body across, is pro-portional to the rectangle of the parts of the beam, and is the greatest when loaded in themiddle ; the rectangle being the product of the parts multiplied into each other. "Whena shaft is loaded exactly in the middle, half the weight is borne on each end, but we maygenerally consider the weight which is spread over any part of a beam as united in itscentre of gravity.

When timber is submitted to a transverse strain, the effect of the weight is greatest in acertain and determinate point, where if sound, defects in other portions are not so important;but if placed in a position to receive pressure endwise, the defective parts at once comeunder its influence; hence it is of the utmost importance in making experiments upon thestrength of materials, that they should be subjected to every species of trial previously totheir application to the purposes of construction, or to machinery of any kind. In thePhilosophical Transactions for 1818, Mr. George Rennie describes the apparatus he usedin his experiments relating to torsion ; it consisted of a wrought-iron lever 2 feet long,having an arched head of about 60°, and 4 feet in diameter, of which the lever representedthe radius; in the centre, round which it moved, was a square hole to receive theend of the bar to be twisted : the lever was balanced, and a scale hung on the archedhead, the other end of the bar being fixed in the square hole in a piece of iron, and thatagain in a vice.

Cylindrical shafts of cast-iron, having the stress applied to them in the middle, and equalto \V hundred-weights, and the flexure not exceeding as many hundred parts of an inch asthe shaft is long in feet, then the fourth root of half the stress in hundred weights, mul-tiplied by the square root of the length in feet, gives the diameter in inches, and it has beenfound, that when the cube of the length in feet is multiplied by 007, the square root of theproduct will be the diameter in inches.