Terms1—2—3—4—5—6—7—8—9—10—11—12
loose; 2⁄2; 3⁄2; 4⁄2; 5⁄2; 6⁄2; 7⁄2; 8⁄2; 9⁄2; 10⁄2; 11⁄2; 12⁄2

or 6 inches for the largest pulley, instead of 12 inches given by the last progression.

So likewise, if we take two loose pulleys, (which will not add much to the complication of the Machine) and make the third term 1 inch, the fourth will become 4⁄3, shewing the ratio of the progression to be 1⁄3, so that the series of 12 terms will stand thus:

Terms,1—2—3—4—5—6—7—8—9—10—11—12
loose; loose; 1; 4⁄3; 5⁄3; 6⁄3; 7⁄3; 8⁄3; 9⁄3; 10⁄3; 11⁄3; 12⁄3;or,

four inches for the largest groove in the concentric part of the System.

Now we saw before, that the first and last pulley were in diameter to each other, as 1 to 12; whereas, here, with only two loose pulleys, these extremes are but as 1 to 4: dimensions much more convenient and manageable. The [5th. figure] of the [Plate 7], is intended to shew graphically, the effect of this modification of the principle. In that figure, if the line a, be the diameter of the first pulley, that of the sixth pulley will be shewn by the line b c; but if the same line a be made the second pulley, the diameter of the sixth will be shewn by the line e d; only 2⁄3 of the former. And in fine, if the same a, be the third pulley, the sixth will have it’s diameter reduced to the line f g, only one half of what it was in the first case. In a word, the more loose pulleys are put before the fixed ones begin, the nearer to cylindrical will the general form become; and the more conveniently may pulleys be used for general purposes. I might even assert, that if one, or at most two loose pulleys had been used in the above-mentioned experiments, the result would have been as favourable to the System, with respect to the weight of the tackle and stress on the ropes, as it was in respect of power; where it’s advantages were important and undeniable.