Chap. 2 . PHILOSOPHY. 79

down above is verified, that the weights equiponderate, whentheir velocities would be reciprocally proportional to theirrefpedtive weights.

4In like manner, if on the fame axis two wheels of dif-ferent fizes are fixed (as in fig. 3 y.) and a weight hung oneach; the weights will equiponderate, if the weight hung onthe greater wheel bear the fame proportion to the weight hung° n the leller, as the diameter of the leffer wheel bears to thediameter of the greater.

4,6. I t is ufiial to join many wheels together in the fameframe, which by the means of certain teeth, formed in the cir-cumference of each wheel, jfhall communicate motion to eachother. A machine of this nature is reprefented in fig. 3 6 . HereA B C is a winch, upon which is fixed a fmall wheel D indent-ed with teeth, which move in the like teeth of a larger wheelEF fixed on the axis G H. Let this axis carry another wheelI> which jfhall move in like manner a greater wheel K L fixed° n the axis M N. Let this axis carry another fmall wheel O,Vv 'hich after the fame manner fhall turn about a larger wheelE Q. fixed on the roller R S, on which a cord fhall be wound,that holds a weight, as T. Now the proportion required be-tween the weight T and a power applied to the winch at AfufRcient to fupport the weight, will moft eafily be eftimated,

computing the proportion, which the velocity of the pointA would bear to the velocity of the weight. If the winch beturned round, the point A will deferibe a circle as A V. Sup-pofe the wheel EF to have ten times the number of teeth, as

the