72 KANSAS UNIVERSITY QUARTERLY. 
fixed by the conditions of the design, as is usually the case, N, the 
number of revolutions of the driving shaft or counter shaft, must be 
made the mean proportional between the extreme speeds. Simply 
multiply the extreme speeds together and extract tlie square root 
and the result is N. 
eh fea See 
And besides this the speeds n,, n,, n,, n, must form a geomet- 
rical series, so that 
n,—nN,, 
ie iio 
n,=n 1,27, 
— 3 
n,—n,a : 
Then when n, and n, are the given extreme speeds 
from which ‘a’ can be found by use of a table of cubic roots, and 
then n, and n, figured. 
Therefore, proceed as follows, there being four steps: Divide 
the fastest by the slowest speed and extract the cube root. If 
there are to be five steps extract the fourth root, if six steps fifth 
root, etc. With this result multipy the slowest speed. This will 
give the next highest. Multiply this now by the same multiplier 
and the result is the next speed in order. And so for all the inter- 
mediate speeds. 
Now multiply the exteme speeds together and extract the square 
root, and this is the N, or number of revolutions the counter shaft 
should make. 
