3 6

Of the mechanical Powers .

The pulley.

and the winch being no longer than the sum of the semidiametersof the great axle and rope, the trundle could have no more power onthe wheel, than a man could have by pulling it round by the edge,because the winch would have no greater velocity than the edge of thewheel has, which we here suppofe to be ten times as great as the ve-locity of the rising weight: so that, in this case, the power gainedwould be as io to i. But if the length of the winch be 12 inches,the power gained will be as 20 to 1 : if j 8 inches (which is longenough for any man to work by) the power gained would be as 30 to 1 ;that is, a man could raife 30 times as much by such an engine, as hecould do by his natural strength without it, because the velocity of thehandle of the winch would be 30 times as great as the velocity of therising weight; the absolute force of any engine being in proportion ofthe velocity of the power to the velocity of the weight raised by it.—But then, just as much power or advantage as is gained by the engine,so much time is lost in working it. In this fort of machines it is re-quisite to have a ratchet-wheel G on one end of the axle, with a catchH to fall into its teeth; which will at any time support the weight,and keep it from defcending, if the workman should, through inadver-tency or carelefnefs, quit his hold whilst the weight is raising. Andby this means, the danger is prevented which might otherwiie happenby the running down of the weight when lest at liberty.

3. The third mecbanical power or engine consists either of onemoveable pulley , or a fyflem of pulley s ; forne in a block or case which isfixed, and others in a block which is moveable, and rifes with theweight. For though a single pulley that only turns on its axis, andrifes not with the weight, may ferve to change the direction of thepower, yet it can give no mecbanical advantage thereto; but is only asthe beam of a balance, whofe arms are of equal length and weight.

f ig. 6.

Thus, if the equal weights W and P hang by the cord B B upon thepulleys, whofe block b is fixed to the beam HI, they will counter-poife each other, just in the fame manner as if the cord wer e cut inthe middle, and its two ends hung upon the hooks fixt in the pulley atA and A, equally distant from its Center.

But if a weight W hangs at the lower end of the moveable block pof the pulley D, and the cord GF goes under the pulley, it is plainthat the half G of the cord bears one half of the weight IV, and thehalf F the other 3 for they bear the whole between them. Therefore,whatever holds the upper end of either rope, fustains one half of theweight: and if the cord at F "be* drawn up fo as to raife the pulley D to C,the cord will then be extended to its whole length, all but that part

which