164 KANSAS UNIVERSITY QUARTERLY. 
primary radius, along OL, gives the ("em part of OA. Or 
conversely, if setting to the (= )un part ot-OA Rte ( A en 
part of OB will be determined on OL. And for the (~)m part 
: - 3 nN 
of AB, along OL, the ratio of intercepts is fae For the 
nN 
(*)mn part along OD, the ratio 1s ( } And for a desired 
n 
(elas 
. a : a 
ratio, (=). the intercept on OD must be ( Hf and that on 
n 
n— 
OL, ( 
a ; : 
times the primary radius. 
Or, otherwise, calling the intercept on OL, x, and the corre- 
sponding intercept on OD, y, we have from the preceding the 
equation 
relating the two intercepts, for any setting, and any angle, whers x 
and y are expressed in terms of the primary radius. Or we have 
oe Rx 
ay REx 
when x and y are the actual length of the intercepts, and R is the 
length of the primary radius. 
| Application: So if we should have an equation of the form 
ax 
a--x’ 
where a is any constant term it can be solved at once, as follows: 
Set the instrument to any straight line, as OL, Fig. 8, marking the 
pole and striking a spiral arc. Witha radius —a inches, strike a 
circle arc, thus determining OD for thiscase. Then take the value 
of x to. be substituted in the equation, and lay it off from O, along 
OL, and set the instrument to it. Then the intercept on OD is 
the value of y sought. 
Reyersing the equation we have 
Noa 
