Number of teeth in driver is 66, which divided by the number in the driven, 48, gives 1.375. This multiplied by the number of teeth in the driver of the other pair = 36 gives 49.5, which divided by the number of teeth in the driven wheel of the first pair gives 2.75, which multiplied by the pitch of the lead screw 4 gives 11 as before.
Taking now the second example as in [Fig. 1240], and beginning from the first pair of gears, we have, according to the rule, 36 ÷ 48 × 66 ÷ 18 × 4 = 11 = pitch the gears will cut; or proceeding from the second pair of gears, we have by the rule, 66 ÷ 18 × 36 ÷ 48 × 4 = 11 = the pitch the gears will cut. It is not often, however, that it is required to determine what threads the wheels already on a lathe will cut, the problem usually being to find the wheels to cut some required pitch. But it may be pointed out that when the problem is to find the result produced by a given set of wheels, it is simpler to begin the calculation from the wheel already on the lathe spindle, rather than beginning with that on the lead screw, because in that case we begin at the first wheel and calculate the successive ones in the same order in which we find them on the lathe, instead of having to take the last pair in their reverse order, as has been done in the examples, when we began at the wheel on the lead screw, which we have termed the second pair.
The wheels necessary to cut a left-hand thread are obviously the same as those for a right-hand one having an equal pitch; all the alteration that is necessary is to employ an additional intermediate wheel, as at i in [Fig. 1241], which will reverse the direction of motion of the lead screw. For a lathe such as shown in [Fig. 1235], this intermediate wheel may be interposed between wheels d and i or between i and s. In [Fig. 1236], it may be placed between d and i or between i and s, and in [Fig. 1238] it may be placed between a and c or between d and s.
Fig. 1242.
Here it may be well to add instructions as to how to arrange the change wheels to cut threads in terms of the French centimètre. Thus, an inch equals 254⁄100 of a centimètre, or, in other words, 1 inch bears the same proportion to a centimètre as 254 does to 100, and we may take the fraction 254⁄100 and reduce it by any number that will divide both terms of the fraction without leaving a remainder; thus, 254⁄100 ÷ 2 = 127⁄50. If, then, we take a pair of wheels having respectively 127 and 50 teeth, they will form a compound pair that if placed as in [Fig. 1242] will enable the cutting of threads in terms of the centimètre instead of in terms of the inch.
Thus, for example, to cut 6 threads to the centimètre, we use the same change wheels on the stud and on the lead screw that would be used to cut 6 threads to the inch, and so on throughout all other pitches.
