Chap. 7.] AEiion of Wheels. 71 



by the number of teeth in the wheel D ; then multiply 

 the number of cogs of the nut If by the number of 

 cogs in the nut c ; this firft product by the number of 

 cogs in the nut d; and the fecond product, by the 

 number of cogs of the laft nut e : the iaft products of 

 the teeth of the wheels and the cogs of the nuts, will 

 give the proportion required. 



It may then be eftablifhed as a general rule, that 

 the number of the revolutions of the firft wheel A, is 

 to the number of the revolutions of the laft nut, as the 

 product of the cogs of the nuts is to the product of 

 the teeth of the wheels. Hence it follows, that it is. 

 not necefiary to determine the number of cogs and 

 teeth which each rrut and wheel fliould have in parti- 

 cular ; it fuffices that the proportion of the product of 

 all the cogs to the product of all the teeth, (hall be 

 fuch as is required. 



By means of this kind of wheels, the action of a 

 power may be tranfmitted to a diftance, the direction 

 of the movement may be changed, and the velocity of 

 the powers may be varied. 



Firft, if inftead of applying the nut (fig. 3.) im- 

 mediately upon the wheel H, a nut D is fixed to the 

 other extremity of the prolonged axle as far as is ne- 

 ceflary, then the power which acts by the handle G 

 may be tranfmitted to a certain diftance by means of 

 the nut D fixed at the extremity of the axle. 



Secondly, If this nut D catches with another wheel 

 E, which has teeth parallel to its axle, the movement 

 which will be tranfmitted to it will change the direc- 

 tion, and become horizontal inftead of vertical. 



In fine, if the wheel E has four times as many teeth 

 as the nut D has cogs, fmce the nut cannot move 

 without the vertical wheel H, it follows that the lat- 

 ter muft turn four times round while the horizontal 

 F 4 wheel 



