turn. In the mechanical powers, in general, one-third of power must be added for the loss sustained by friction, and for the imperfect manner in which machines are generally constructed. Thus, if by theory you gain a power of 600: in practice, you must reckon only upon 400. In those pulleys which we have been describing, writers have taken notice of three things, which take much from the general advantage and convenience of pulleys as a mechanical power. The first is, that the diameters of the axes, bear a great proportion to their own diameters.

second is, that in working they are apt to rub against one another, or against the side of the block. And the third disadvantage is the stiffness of the rope that goes over and under them.

The first two objections have been, in a great degree, removed by the concentric pulley, invented by Mr. James White: B (Plate IV. Fig. 27.) is a solid block of brass, in which grooves are cut, in the proportion of 1, 3, 5, 7, 9, &c. and A is another block of the same kind, whose grooves are in the proportion of 2, 4, 6, 8, 10, &c. and round these grooves a cord is passed, by which means they answer the purpose of so many distinct pulleys, every point of which moving with the velocity of the string in contact with it, the whole friction is removed to the two centres of motion of the blocks A and B ; besides it is of no small advantage, that the pulleys being all of

one piece, there is no rubbing one against the other.

Emma. Do you calculate the power gained by this pulley, in the same method as with the common pulleys?

Father. Yes, for pulleys of every kind, the rule is general, the advantage gained is found by doubling the number of the pulleys in the lower block: in that before you there are six grooves, which answer to as many distinct pulleys, and consequently the power gained is twelve, or one pound at P will balance twelve pounds at w.

Father. We may now describe the inclined plane, which is the fourth mechanical power. Charles. You will not be able, I think, to reduce this also to the principle of the lever.

Father. No, it is a distinct principle, and some writers on these subjects reduce at once the six mechanical powers to two, viz. the lever and inclined plane.

Emma. How do you estimate the advantages gained by this mechanical power?

Father. The method is very easy, for just as much as the length of the plane exeeds its perpendicular height, so much is the advantage gained. Suppose A B (Plate IV. Fig. 28.) is a plane standing on the table, and C D another plane inclined to it; if the length cD be three times greater than the perpendicular height; then the cylinder E will be supported upon the plane c D, by a weight equal to the third part of its own weight.

Emma. Could I then draw up a weight on such a plane with the third part of the strength that I must exert in lifting it up at the end?

Father. Certainly, you might; allowance, however, must be made for overcoming the friction; but then you perceive, as in other mechanical powers, that you will have three times the space to pass over, or that as you gain power you will lose time.

Charles. Now I understand the reason why sometimes there are two or three strong planks laid from the street to the ground-floor of warehouses, making therewith an inclined plane, on which heavy packages are raised or lowered.

Father. The inclined plane is chiefly used for raising heavy weights to small heights, for in warehouses situated in the upper part of build

ings, cranes and pulleys are better adapted for the purpose.

Charles. I have sometimes, papa, amused myself by observing the difference of time which one marble has taken to roll down a smooth board, and another which has fallen by its own gravity without any support.

Father. And if it were a long plank, and you took care to let both marbles drop from the hand at the same instant, I dare say you found the difference very evident.

Charles. I did, and now you have enabled me to account for it very satisfactorily, by showing me that as much more time is spent in raising a body along an inclined plane, than in lifting it up at the end, as that plane is longer than its perpendicular height. For I take it for granted

that the rule holds in the ascent as well as in the descent.

Father. If you have any doubt remaining, a few words will make every thing clear. Suppose your marbles placed on a plane, perfectly horizontal, as on this table, they will remain at rest wherever they are placed: now if you elevated the plane in such a manner that its height should be equal to half the length of the plane, it is evident from what has been shown before, that the marbles would require a force equal to half their weight to sustain them in any particular position suppose then the plane perpendicular to the table, the marbles will descend.

with their whole weight, for now the plane contributes in no respect to support them, consequently they would require a power equal to their whole weight to keep them from descending.

Charles. And the swiftness with which a body falls is to be estimated by the force with which it is acted upon?

Father. Certainly, for you are now sufficiently acquainted with philosophy to know that the effect must be estimated from the cause. Suppose an inclined plane is thirty-two feet long, and its perpendicular height is sixteen feet, what time will a marble take in falling down the plane, and also in descending from the top to the earth by the force of gravity?

Charles. By the attraction of gravitation, a body falls sixteen feet in a second (see p. 41.) therefore the marble will be one second in falling perpendicularly to the ground; and as the length of the plane is double its height, the marble must take two seconds to roll down it.

Father. I will try you with another example. If there be a plane 64 feet perpendicular height, and 3 times 64, or 192 feet long, tell me what time a marble will take in falling to the earth by the attraction of gravity, and how long it will be in descending down the plane?

Charles. By the attraction of gravity it will fall in two seconds; because, by multiplying the sixteen feet which it falls in the first second, by