This experiment shows how the pattern of scattered projectiles can lead to information about the shape of the scatterer. The projectiles (B-Bs) are shot from a gun with a blast of air from a rubber squeeze-bulb. After striking the target (scatterer) they hit the wall of the scattering chamber where they leave a mark on sensitive tape. The following analysis treats the scattering of a point particle from a cylinder of arbitrary shape. It is assumed that the particles scatter in such a way that the angle of incidence is equal to the angle of reflection, called specular reflection. Any sliding of the ball on the scattering surface or change in the rotational state of the ball is ignored.
In the figure, the x axis is always parallel to the path
of the incoming projectiles and the origin of the coordinates is at
the center of the scattering chamber. The scatterer is described
mathematically by some relationship
or 
; a circular scatterer is specified
by 
. The impact point is given by the coordinates
which must satisfy the scatterer equation. The
scattering angle is 
, and 
is the angle between
the line of incidence and the line tangent to the scatterer at the
point of impact. The impact parameter, b, is the distance between
the incident path and the x axis.
From the geometry it can be seen that
, 
, and
. The slope of the scattering surface is
The Law of Sines yields
where S is the radius of the chamber wall. This gives
In a typical situation, 
is less than 0.08; since the sine
function is always less than unity,
Considering this, it is reasonable to neglect 
.
This approximation is equivalent to setting 
.
The above analysis can be applied to a regular cylinder. The equation of a circle centered at the origin is
where R is the radius of the circle. From equations (1) and (2) it can be seen that
Since both y (which equals the impact parameter b) and
are determined
experimentally, equation (3) can be used to determine the
radius of the cylinder.
For the elliptical scattering centers the analysis follows in the same way. The equation for an ellipse is
where A is the semi-major axis and B is the semi-minor axis. The
ellipse is also characterized by its eccentriciy
which is given by
The eccentricity determines the shape of the ellipse but not its size. From equations (1) and (4) it can be shown that
Again, y and 
are
determined experimentally and, using equation
(5), the major and minor axes A and B can be determined.