... what you are supposed to do is quote me the passage in OoS that gives the actual theory.
Well, that's a big ask, and you know it is. The theory as Darwin put forward is described in the book, the entire book. He didn't write his theory on page one and then go on to write "the wind in the willows" to fill-up the remaining pages. I could sit and transcribe the entire book but that would be pointless. What you are asking-for is the sound-bite version of it, the theory as put forward in say 20 or fewer words. There are very few theories that you can actually do that with. The example that you cited earlier is only a part of the theory of gravitation, it is nowhere near the complete theory as BluegrayV pointed-out.
Okay, so I can oblige with something of a sound bite version and with a few carefully selected pieces of "the origin". The first (and most famous) sound-bite came from Herber Spencer, who, on reading "the origin", coined the term "Survival of the fittest". Now personally I see that as a perversion of the theory, that would imply a measure of fitness based on a goal - when in actual fact the not-quite-fitter-only-a-bit-different also survive and later on prove to be better in a completely unexpected scenario. But I digress...
So when Spencer coined the phrase in 1864, two years after the first edition of the book, it was brought to Darwin's attention by a friend Thomas Huxley. Darwin was drawn to the way that this phrase could be accepted by the masses and incorporated it into "the origin" in later editions. The one online at gutenberg or Google Books is the sixth edition and chapter four has the subtitle "The survival of the fittest".
Again, I wouldn't use this sound-bite myself. So what would I say?
In chapter four, many discussions and scenarios are laid-out for the reader to explain the theory, and from the last line on page 118 until the the end of the first paragraph on page 119 he states ... and I so hate having to leave-out so much of the rest of the book ...
We shall best understand the probable course of natural selection by taking the case of a country [ecosystem] undergoing some slight physical change, for instance, of climate. [...] We may conclude, from what we have seen of the intimate and complex manner in which the inhabitants of each country are bound together that any change in the numerical proportions of the inhabitants, independantly of the change of climate itself, would seriously affect the others. [...] we should then have places in the economy of nature which would assuredly be better filled up if some of the original inhabitants were in some manner modified [...] In such cases, slight modifications, which in any way favoured the individuals of a species, by better adaptating them to their altered conditions, would tend to be preserved; and natural selection would have free scope for the work of improvement.
Recall that I pointed-out earlier that the modern theory of evolution incorporates natural selection as a piece of the theory, and NS actually can't exist on its own. Darwin couldn't explain where variation came from or how traits are passed from generation to generation.
Several writers have misapprehended or objected to the term Natural Selection. Some have even imagined that natural selection induces variability, whereas it implies only the preservation of such variations as arise and are beneficial to the being under its conditions of life.
Some laughable explanations did come up in the past (most notably
Lamarckism), but fortunately in this age of genetic science whe can provide better answers to those questions for Darwin and NS within evolution is now a better theory.
where exactly is this much vaunted Theory of Evolution that explains inverted pendulum control in all birds as they pivot and balance on a branch.
Well, the inverted pendulum control for balance is a
designed system, and seeing as you have asked us to demonstrate this design in nature you are asking us to prove Intelligent Design. I'm not going to say that I won't do that, I'll just point out that I
can't do that because nature doesn't conform to designs that humans dream-up. There are no references to bird balance in any scientific study of inverted pendulum control, these are all studies of robots balancing a pole on a "finger" or similar scenario. It has nothing to do with birds and the neuro-muscular system of birds doesn't even come close to the wiring and computer programming that goes into these robotic demonstrations.
I also thought that you might like to read "the origin" on page 118 where the dear departed Darwin refutes your original argument from the grave. I guess this "natural selection is a gramatical gargoyle" thing is
that predictable...
Others have objected that the term selection implies conscious choice in the animals which become modified; and it has even been urged that, as plants have no volition, natural selection is not applicable to them! In the literal sense of the word, no doubt, natural selection is a false term; but who ever objected to chemists speaking of the elective affinities of the various elements? --and yet an acid cannot strictly be said to elect the base with which it in preference combines. It has been said that I speak of natural selection as an active power or Deity; but who objects to an author speaking of the attraction of gravity as ruling the movements of the planets? Everyone knows what is meant and is implied by such metaphorical expressions; and they are almost necessary for brevity.