CHAMBERS'S INFORMATION FOR THE PEOPLE. 



toothed-wheels, if we conceive these circles to be, 

 in the first instance, two drums touching at T, 



Fig- 39- 



and the one driving the other by friction. It is 

 obvious that while any portion, as a foot, of the 

 drum hJi supposing it to be the driver passes 

 through the point of contact T, it causes an equal 

 portion of the driven drum, gg, to pass through 

 the same point ; in other words, the driven cir- 

 cumference moves with the same velocity at every 

 instant as the driving one. Now, when a part of 

 the width of each wheel is removed, and project- 

 ing teeth substituted, these teeth must be so con- 

 trived that the primitive or pitch circles shall still 

 move exactly as if they were in contact. Mere 

 straight pegs or blades, like the paddle-boards of 

 a steam-boat, would not answer the purpose. In 

 the first place, the corners of one tooth would 

 have to slide along the face of another, thus grind- 

 ing away the teeth, and wasting the driving- 

 power. Secondly, the motion would not be equal ; 

 during the first portion of the time that two teeth 

 were in contact the driven wheel would move 

 slower than the driver, and during the last portion, 

 faster. The faces or edges of the teeth must, 

 therefore, be curved, so that they shall roll on one 

 another rather than slide ; and the curves must be 

 such that the driven wheel shall move at all times 

 uniformly with the driver. 



Mathematicians have discovered a great variety 

 of ways of satisfying this condition. One way, 

 frequently adopted, is to give the teeth of one 

 wheel the form of the curve called the epicycloid, 

 and those of the other that of the hypocycloid. 

 But the form of teeth that possesses the greatest 

 number of advantages for most purposes is that of 

 the curve called the involute. 



CHANGES IN THE PLANE AND IN THE 

 DIRECTION OF ROTATION. 



When the two shafts to be connected are not 

 parallel to each other, conical or bevel wheels are 

 employed. Fig. 40 represents a horizontal shaft 

 driving a vertical one (or the converse), by means 

 of bevel gearing. The two shafts may have any 

 inclination to each other and to the horizon. 

 When the two wheels are equal and the axes at 



right angles, they are called #V>v?-wheels. A 

 crown-wheel, A, and trundle, B, as represented 



Fig. 40. 



Fig. 41. 



in fig. 41, is another contrivance for effecting the 

 same purpose. 



In the case of two 

 toothed - wheels, the 

 direction of the rotation 

 is always reversed, as 

 shewn by the arrows in 

 n g- 39- ^ n order to 

 preserve the same direc- 

 tion in both, wheels are a\ 

 sometimes geared inter- 

 nally, fig. 42. By inter- 

 posing a third wheel 

 between the driving 

 and driven wheels, the 

 original direction is 

 also retained ; thus, the pinion F, fig. 43, revolves 

 in the same direction as the wheel C. A crossed 

 band (see fig. 38) reverses the direction. 



CHANGES IN SPEED. 



If the wheel C, fig. 43, had three times as many 

 teeth as the pinion G, one revolution of C would 

 evidently cause 

 three revolu- 

 tions of G. If, 



~T 



(T 



Fig- 43- 



instead of being 

 an exact mul- 

 tiple, the teeth 

 of C were, say 

 210, and those 

 of G 90, which 

 is in the propor- 

 tion of 7 to 3, 

 then 3 revolu- 

 tions of C would 

 cause 7 of G. 

 Suppose, again, 

 that C with 101 

 teeth were driv- 

 ing B with 100 teeth. These numbers being 

 prime to one another, the proportion is not ex- 

 pressible in any smaller numbers than the numbers 

 of the teeth themselves ; in other words, if we 

 ' note the two teeth that are at any instant in con- 

 tact, C must make 100 revolutions, causing B to 

 make 101, before the same two teeth will be again 

 in contact that is, before the two will finish 

 together, each an exact number of revolutions. 



In a train of wheels connected, as in fig. 43, the 

 velocity of the last wheel is found by the following 

 rule : Multiply the velocity (or number of revolu- 

 tions in a given time) of the first driver by the 



