Chap. 2. PHILOSOPHY.

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

4.5. In 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 hungon the lesser, as the diameter of the lesser wheel bears to thediameter of the greater.

4 6 . I t is usual to join many wheels together in the fameframe, which by the means of certain teeth, formed in the cir-cumference of each wheel, shall communicate motion to eachother. A machine of this nature is represented in fig. 3 6 . HereA B C is a winch, upon which is fixed a small wheel D indent-ed with teeth, which move in the like teeth of a larger wheelE F fixed on the axis G H. Let this axis carry another wheelI, which shall move in like manner a greater wheel K L fixedon the axis M N. Let this axis carry another small wheel O,which after the fame manner shall turn about a larger wheelP CL fixed on the roller R S, on which a cord shall 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 Asufficient to support the weight, will most easily be estimated,by 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 describe a circle as A V. Sup-pose die wheel E F to have ten times the number of teeth, as

the