MECHANICS.

37

Chap. 2.]

of levers. Required, the weight W, on the other end,to hold the whole in equilibrio.

Then by the rule, 4x8x6x2=384 the product of thepower multiplied into the length of all the driving le-vers, and 2x2x8=32 the product of all the leading levers,and 384-7-32=12 the weight W required.

article 20.

CALCULATING THE POWER OF WHEEL WORK.

The same rule holds good in calculating the power ofmachines consisting of wheels, whether simple or com-pound, by counting the radii of the wheels as the le-vers; and because the diameters and circumferences ofcircles are proportional, we may take the circumferencesinstead of the radii, and it will be the same result. Thenagain, because the number of cogs in the wheels consti-tute the circle, we may take the number of cogs androunds instead of the circle or radii, and the result willstill be the same.

Let fig. 11, Plate II. represent a water-mill (forgrinding grain) double geared.

Numbers The water-wheel,

4 The great cog-wheel,

2 The wallower,

3 The counter cog-wheel,

1 The trundle,

2 The mill-stones,

And let the above numbers also represent the radiusof each wheel in feet.

Now suppose there be a power of 500 lbs. on the wa-ter-wheel, required what will be the force exerted onthe mill-stone, 2 feet from the centre.

The sign + plus, or more, for addition.

— minus, or less, for substruction.

X multiplied, for multiplication.

-7- divided, for division.

= equal, for equality.

Then, instead of 8 more 4 equal 12, I shall write 8+4=7:12. Instead of 12 less4 equal 8, 12—4=8. Instead of 6 multiplied by 4 equal 24, 6 x 4=24 ~Andinstead of 24 divided by 3 equal 8, 24=3=8,