MOTION BY BOLLING CONTACT.

43

necessary to reduce the fraction - to its least terms, and the de-nominator of this reduced fraction will give the number of revo-lutions of the driving wheel as required. Thus let N = 144, and

n — 54, then - = > that is, the driver must make 3

q 144 8-

complete revolutions, or the follower 8, before the same teethcan again come into contact.

60. In a combination of wheels, whose motions are expressed

q N . N

bv the equality — = -4——an indefinite number of values

J Qi «i • n i

may be assigned to the numbers of teeth, which shall producea given synchronal ratio of the first and last axes; but if n 1 andn 2 be given, and n, and n 2 he comprised within certain givenlimits ; then a limited number of values may he found for N,and n 2 .

Thus, for example, let — = 60, n Y = n 2 = 8, and the valuesQi

of Nj and n 2 not to exceed 100 nor to he less than 40.

Here we have—

• ^28x8

= 60:

.-. Nj . n 2 = 60 x 64;

hence, n, may be 60 and n 2 may he 64; but in order to deter-mine all the combinations, we must put the product, 60 x 64,into prime factors, and then distribute these factors into differentgroups answering to the limiting values of rq and n 2 .

Here, 60 x 64 = 2 8 x 3 x 5 ; hence we have —

1st combination, (2 4 x 3) x (2 4 x 5) = 48 x80;

2nd combination, (2 5 x 3) x (2 3 x 5) = 96 x 40;

3rd combination, 2 6 x (2 2 x 3 x 5) = 64 x 60.

61. When all the drivers contain the same number of teeth,and also the followers, then eq. (1), Art. 57, becomes

By means of this formula we may readily determine the least