Any Dodge fans (or people who know about engines?)

I can remember the big deal about the car in the film Vanishing Point was that it was a Dodge Charger Hemi - Which apparently stood for hemispherical combustion heads which fired the bhp way up.
I know that a gas in a perfectly spherical container pushes against every point on the inner surface of the container with an equal force. Does this have something to do with the bhp boost that this gave the engines? Would pushing against the top of the combustion chamber with equal force at all points somehow give it a boost?

The force on the piston is strictly a function of the area of the piston, not its (nor the cylinder’s) shape.

The shape of the combustion chamber does affect some other variables, notably the flow of the gases through the cylinder. I’m not competent to speak in detail, but one of the primary considerations in engine performance, particularly at high RPMs, is volumetric efficiency, i.e., how well can you get a new fuel-air charge into the cylinder and exhaust the old one. (Obviously any leftover gases from the previous cycle are of no value.) The shape of the cylinder head, the number and locations of the valves, the valve movement (governed by the camshaft) all impact volumetric efficiency. My guess is that there was something special about the “hemi” engine in this area.

FWIW, the gas in any container pushes against every point with equal force. We call that pressure.

Nope. Different idea.
The “Hemispherical” chamber simply improved airflow into and out of the combustion chamber.

In a typical “wedge” shaped chamber, all the valves are arrayed in a fairly straight line, in line with the length of the cyclinder head. Because of this, and the fact that the valves are typically lightly canted towards the “intake” side, the intake and exhaust passages are pretty well “L” shaped. IE, the air has to make a pretty radical downward turn to get into the chamber, then an even more radical turn to get out through the exhaust passage.

In the Hemi head, the intakes are canted quite a bit more radically towards the intake side, plus the exhausts are canted wildly in the opposite direction. This “straightens” out the passages, which leads to freer breathing (the ingestion and expulsion of the fuel/air mixture) which leads to more horsepower.

The arrangement of the valves creates a semispherical combustion chamber (there’s also a little benefit to the centrally located sparkplug) rather than the “wedge” shaped chamber of the more typical engine, so they called it a “Hemispherical Head”.

Doc.

Also, the arraingement of the valves in the hemi allows for maximum size of the valves themselves, and thus maximum airflow.
And this is just TWO valves.
A Four valve cylinder design moves more airflow than even a hemi

One of the reasons Hemi heads are no longer commonplace is that they can be more prone to detonation. The high octane fuel such an engine needs is no longer available at the corner station, not since the days of Ethyl™. Wedge shaped chambers with the plug toward the narrow side are less prone to detonation but don’t have the flow characteristics of a hemi.
I just flashed on a Simpsons episide, where Homer buys Snake’s car at a police auction. Homer is blasting around town, abusing the car and Snake hears from inside the jail exercise yard. “That’s Li’l Bandit, and she’s in pain! She needs premium dude! Premium!”

Doc pretty well covered The Hemi question already.

But I must point out that the VP car was a Hemi Challenger.