There is no use in entering upon detailed explanations of what a learner has before him. Shafts are seen wherever there is machinery; it is easy to see the extent to which they are employed to transmit power, and the usual manner of arranging them. Various text-books afford data for determining the amount of torsional strain that shafts of a given diameter will bear; explain that their capacity to resist torsional strain is as the cube of the diameter, and that the deflection from transverse strains is so many degrees; with many other matters that are highly useful and proper to know. I will therefore not devote any space to these things here, but notice some of the more obscure conditions that pertain to shafts, such as are demonstrated by practical experience rather than deduced from mathematical data. What is said will apply especially to what is called line-shafting for conveying and distributing power in machine-shops and other manufacturing establishments. The following propositions in reference to shafts will assist in understanding what is to follow:—

1. The strength of shafts is governed by their size and the arrangement of their supports.

2. The capacity of shafts is governed by their strength and the speed at which they run taken together.

3. The strains to which shafts are subjected are the torsional strain of transmission, transverse strain from belts and wheels, and strains from accidents, such as the winding of belts.

4. The speed at which shafts should run is governed by their size, the nature of the machinery to be driven, and the kind of bearings in which they are supported.

5. As the strength of shafts is determined by their size, and their size fixed by the strains to which they are subjected, [45] strains are first to be considered.

There were three kinds of strain mentioned—torsional, deflective, and accidental. To meet these several strains the same means have to be provided, which is a sufficient size and strength to resist them; hence it is useless to consider each of these different strains separately. If we know which of the three is greatest, and provide for that, the rest, of course, may be disregarded. This, in practice, is found to be accidental strains to which shafts are in ordinary use subjected, and they are usually made, in point of strength, far in excess of any standard that would be fixed by either torsional or transverse strain due to the regular duty performed.

This brings us back to the old proposition, that for structures which do not involve motion, mathematical data will furnish dimensions; but the same rule will not apply in machinery. To follow the proportions for shafts that would be furnished by pure mathematical data would in nearly all cases lead to error. Experience has demonstrated that for ordinary cases, where power is transmitted and applied with tolerable regularity, a shaft three inches in diameter, making one hundred and fifty revolutions a minute, its bearings three to four diameters in length, and placed ten feet apart, will safely transmit fifty horse-power.

By assuming this or any other well-proved example, and estimating larger or smaller shafts by keeping their diameters as the cube root of the power to be transmitted, the distance between bearings as the diameter, and the speed inverse as the diameter, the reader will find his calculations to agree approximately with the modern practice of our best engineers. This is not mentioned to give proportions for shafts, so much as to call attention to accidental strains, such as winding belts, and to call attention to a marked discrepancy between actual practice and such proportions as would be given by what has been called the measured or determinable strains to which shafts are subjected.

As a means for transmitting power, shafts afford the very important advantage that power can be easily taken off at any point throughout their length, by means of pulleys or gearing, also in forming a positive connection between the motive-power and machines, or between the different parts of machines. The capacity of shafts in resisting torsional strain is as [46] the cube of their diameter, and the amount of torsional deflection in shafts is as their length. The torsional capacity being based upon the diameter, often leads to the construction of what may be termed diminishing shafts, lines in which the diameter of the several sections are diminished as the distance from the driving power increases, and as the duty to be performed becomes less. This plan of arranging line shafting has been and is yet quite common, but certainl............