For all three scatterers take your values of
y and 
and plot values of 
versus 
. The theory says they are related by
Both of these have the form of a straight line
y=mx+b, with a slope m and intercept b.
Thus the plot for the circular scatterer
should yield a straight line with a slope of -1 and intercept equal
to 
. The elliptical scatterers
should have slopes of 
and intercepts of
. These values allow you to determine A and B
independently.
In making the plots, plot 
on the horizontal or x axis.
The straight line will have an intersection on both axes: the
intercept b is the intersection of the plot line with
the vertical or y axis, but the other intersection also yields
useful information. In the case of the circular scatterer, the
theory says the two intersections should be the same since the
slope should be -1. Check it out. For the elliptical scatterers,
it can be shown from Eqn. 5a that the other intersection
(on the horizontal axis) occurs at 
.
Determine the values of A, B, and R and compare them to the measured values. NOTE: Since the projectiles are not point particles, their centers actually scatter from a surface which is larger than the scatterer by an amount equal to the radius of the projectiles. Be sure to measure the projectiles and add this correction to the measured size of the scatterers. For the elliptical scatterers, the axis set parallel to the x axis is the semi-major axis for purposes of the analysis. Depending on how the ellipse is oriented, the major axis can be greater than or less than the minor axis. The ellipses are not very accurately made near the ends with the greatest curvture. Data points for B-B's scattering off the ellipses near the ends may not fit the straight lines very well.