In this case the falling of either weight would not effect the leverage, because the distance of both weights would remain the same from the centre of the shaft. The leverage of the 12 lbs. is denoted by the line a, and that of the 6 lbs. by b.
So far as the transmission of power is concerned, therefore, pulleys are in effect revolving levers, which may be employed to concentrate or to distend power, but do not vary its amount.
Fig. 3354.
Suppose we have two shafts, on the first of which are two pulleys, b and c, [Fig. 3354], while upon the second there are two pulleys d and e. A belt h, connecting c to d. Let the pulleys have the following dimensions:
If we take the first pair of wheels b and c, we have that the velocity will vary in the same ratio or degree as their diameters vary, notwithstanding that their revolutions are equal.
| Radius. | Diameter. | Circumference. | |||||
| B | = | 51⁄8 | inches. | 101⁄4 | inches. | 32.2 | inches. |
| C | = | 101⁄4 | „ | 201⁄2 | „ | 64.4 | „ |
| D | = | 75⁄8 | „ | 151⁄4 | „ | 47.9 | „ |
| E | = | 151⁄4 | „ | 301⁄2 | „ | 95.8 | „ |
The velocity is the space moved through in a unit of time, and as it is the circumference of the pulley that is considered, the velocity of the circumference is that taken; thus, if we make a mark on the circumferences of the two pulleys, b and c, [Fig. 3354], the velocity of that on c will be twice that upon b, or in the same proportion as the diameters.
Let there be suspended from the circumference of b 10 lbs. weight, and let us see the degree to which this power will be distended by this arrangement of pulleys, supposing the weight to rotate b, and making no allowance for the friction of the shaft.