_Mrs. B._ They are, I believe, generally connected as described in figure 4, both for nautical, and a variety of other purposes; but in whatever manner pulleys are connected by a single string, the mechanical power is the same. The third mechanical power, is the wheel and axle. Let us suppose (plate 6. fig. 5) the weight W, to be a bucket of water in a well, which we raise by winding round the axle the rope, to which it is attached; if this be done without a wheel to turn the axle, no mechanical assistance is received. The axle without a wheel is as impotent as a single fixed pulley, or a lever, whose fulcrum is in the centre: but add the wheel to the axle, and you will immediately find the bucket is raised with much less difficulty. The velocity of the circumference of the wheel is as much greater than that of the axle, as it is further from the centre of motion; for the wheel describes a great circle in the same space of time that the axle describes a small one, therefore the power is increased in the same proportion as the circumference of the wheel is greater than that of the axle. If the velocity of the wheel is twelve times greater than that of the axle, a power twelve times less than the weight of the bucket, would balance it; and a small increase would raise it. _Emily._ The axle acts the part of the shorter arm of the lever, the wheel that of the longer arm. _Caroline._ In raising water, there is commonly, I believe, instead of a wheel attached to the axle, only a crooked handle, which answers the purpose of winding the rope round the axle, and thus raising the bucket. _Mrs. B._ In this manner (fig. 6;) now if you observe the dotted circle which the handle describes in winding up the rope, you will perceive that the branch of the handle A, which is united to the axle, represents the spoke of a wheel, and answers the purpose of an entire wheel; the other branch B affords no mechanical aid, merely serving as a handle to turn the wheel. Wheels are a very essential part of most machines; they are employed in various ways; but, when fixed to the axle, their mechanical power is always the same: that is, as the circumference of the wheel exceeds that of the axle, so much will the energy of the power be increased. _Caroline._ Then the larger the wheel, in proportion to the axle, the greater must be its effect? _Mrs. B._ Certainly. If you have ever seen any considerable mills or manufactures, you must have admired the immense wheel, the revolution of which puts the whole of the machinery into motion; and though so great an effect is produced by it, a horse or two has sufficient power to turn it; sometimes a stream of water is used for that purpose, but of late years, a steam-engine has been found both the most powerful and the most convenient mode of turning the wheel. _Caroline._ Do not the vanes of a windmill represent a wheel, Mrs. B.?