THE CUBIC PARABOLA. 63 
The angles for every ten links along the curve are not so easily 
obtained. 
In the computation of their values, the method adopted was a 
mechanical one. After computing the values as above, for dis- 
tances along the axis of X, also the corresponding distances along 
the curve, take the difference (x-s) and interpolate. To be 
more exact, this difference should be multiplied by the cosine of 
some angle, the tangent of which is about equal to 3, before the 
interpolation is commenced. Table 3 has been eccieal in this 
way. 
Table 4 has been calculated, having no regard to the cosine of 
this angle, the angle is small, its cosine is nearly unity, so that it 
can be eliminated, without having much effect on the result. The 
second difference has been taken into account in the interpolation. 
It may be found impossible to locate the whole curve from the 
point 0. In sucha case, the curve may be laid out from the point 
C. Let ZO = 2, OB = x, asbefore. 6 = angle BC O. 
Then we have tan 625, 
let 
m ta ~@,*) 
Appended will be found a list of the formule collated. 
FoRMUL. 
yu me 
1+9 m?2+)? erase ee 2 
p= * cele a yee p = ——.(nearly) 
« 6zuy oy 
R = p at the point C. 
tand = 3mz2,? or tan ace 
PBattn OD = 4 
% = Sin ¢ (os? 4 
= RSind. FEO=2, - x’. 
GT =R-— RCos¢ 
Pape ey OP 
DC = y, Cosec . or DC = EN Te 
tan G= mag. = os 
