in the opposite direction. Since the two bevel gears (G and H) are fixed on the shaft with F, they also turn. These bevel gears, meshing with the horizontal bevel gears (I and J), cause I and J to swing the front ends of the telescopes to the right. Thus with a simple system of gears, it is possible to keep the two telescopes pointed at a moving target. In this and many other applications, gears serve one purpose: to change the direction of motion. GEARS USED TO CHANGE SPEED As you’ve already seen in the eggbeater, you use gears to change the speed of motion. Another example of  this  use  of  gears  is  in  your  clock  or  watch.  The mainspring Slowly unwinds and causes the hour hand to make  one  revolution  in  12  hours.  Through  a  series-or train-of  gears,  the  minute  hand  makes  one  revolution each hour, while the second hand goes around once per minute. Figure  6-9  will  help  you  to  understand  how  speed changes are possible. Wheel A has 10 teeth that mesh with the 40 teeth on wheel B. Wheel A will have to rotate four times to cause B to make one revolution. Wheel C is rigidly fixed on the same shaft with B. Thus, C makes the same number of revolutions as B. However, C has 20 teeth and meshes with wheel D, which has only 10 teeth. Hence, wheel D turns twice as fast as wheel C. Now, if you turn A at a speed of four revolutions per second,  B  will  rotate  at  one  revolution  per  second. Wheel  C  also  moves  at  one  revolution  per  second  and causes D to turn at two revolutions per second. You get out two revolutions per second after having put in four revolutions   per   second.   Thus,   the   overall   speed reduction  is  2/4—or  1/2—that  means  you  got  half  the speed out of the last driven wheel you put into the first driver  wheel. You can solve any gear speed-reduction problem with this formula: Figure 6-9.-Gears can change speed of applied motion. Now use the formula on the gear train of figure 6-9. To obtain any increase or decrease in speed you, must choose the correct gears for the job. For example, the turbines on a ship have to turn at high speeds-say 5,800  rpm—if  they  are  going  to  be  efficient.  The propellers, or screws, must turn rather slowly—say 195  rpm—to  push  the  ship  ahead  with  maximum efficiency.  So,  you  place  a  set  of  reduction  gears between the turbines and the propeller shaft. When  two  external  gears  mesh,  they  rotate  in opposite directions. Often you’ll want to avoid this. Put a third gear, called an idler, between the driver and the driven gear. Don’t let this extra gear confuse you on speeds. Just neglect the idler entirely. It doesn’t change the gear ratio at all, and the formula still applies. The idler merely makes the driver and its driven gear turn in the same direction. Figure 6-10 shows you how this works.  where       =        =       =      = speed of first shaft in train speed of last shaft in train product of teeth on all drivers product of teeth on all driven gears Figure  6-10.-An  idler  gear. 6-5