SHOT -- Charlie and Larry studying the blood under Aquarius. CHARLIE The blood could be a prop, part of the act. Spray some blood on the walls, vanish, and voila, got a pretty good trick. DON And pretty good publicity. So you're thinking it's a hoax? CHARLIE Easy enough to figure out. (off their looks) We can use an application of blood spatter trigonometry to study the correlation of this blood to Talma's probable position within the box.

A moving droplet of blood will eventually hit a surface. At the initial instance of contact, the spherical droplet will be tangent to the intercepting surface. The type of spatter the blood droplet leaves on the surface strongly depends on its direction and speed (its vector). In the diagram, the instance of contact is shown for the red spherical droplet. A Dandelin cone based on the vector approximates the elliptical spatter pattern the blood will leave behind. Note that the initial tangent point is one of the foci of the underlying ellipse. The speed and viscosity will further deform the elliptical pattern.

CHARLIE (cont'd) We were able to analyze the pattern of the blood droplets, along with the angle and velocity of impact to determine, with high probability that Talma suffered a real injury. It could have been accidental, or it could have been the result of a struggle... (takes out Penn's card) I'd like to consult a couple of experts who might have an idea which it was.

Two eigenvectors and their corresponding eigenvalues (taken from the length of the vectors) can determine the deformation of a circle into an ellipse. The image shows how a linear transformation, uniquely determined by these eigenvector/eigenvalue pairs, transforms points on the unit circle.

Charlie punches up the glass cylinder on the monitor. LARRY Witnesses from the performance report that it was full. Charlie presses a key, the cylinder fills. CHARLIE (quick calcs in his head) Okay, we're looking at approximately 50 cubic feet of water... AMITA 400 Gallons. CHARLIE Water weight 3,300 Pounds. AMITA A little over one and a half tons.

This Demonstration shows the volume of a cylinder.

Charlie's laying on his stomach where Aquarius would have sat, digging around in the guts of the machinery. CHARLIE I count three input pipes. Larry brings up 'Figure 2 - Water System.' LARRY Only three? Reconstruction of the apparatus indicated at least four.. AMITA Six if they were playing it safe. CHARLIE To fill the cylinder with three pipes in five seconds...

A hydraulic press is a machine made of two pistons with different cross-sectional areas (*A* and *a*), which is used
to lift large weights or compress material. The ratio of the distances moved and the ratio of the forces are both equal to the ratio of the areas of the pistons.