Percy gets stuck into the design argument for the Universe. He argues that there is no evidence for a designer of the Universe, therefore there is no Designer:
Until it is clearly proved that the Universe was created, we may reasonably suppose that it has endured from all eternity. In a case where two propositions are diametrically opposite, the mind believes that which is less incomprehensible; it is easier to suppose that the Universe has existed from all eternity than to conceive an eternal being capable of creating it. (page 51)
The system of the Universe then is upheld solely by physical powers. The necessity of matter is the ruler of the world. It is vain philosophy that supposes more causes than are exactly adequate to explain the phenomena of things... (page 52-53)
Percy deals with the same issue Lucretius did in the first chapter of this book but goes one step further. Unlike Lucretius who tried to justify that everything came from nothing, Percy maintains that everything has always existed. He says you can't say God brought everything about, for he must be more "accurate and just" than the Universe, so therefore must also have another creator and that creator must need another creator etc... So here we have the Universe (ie everything) being uncreated and not God.
I'm not sure how much they knew about the Universe back in the 1700's, but today the idea that everything has always existed isn't held too strongly (Check out NASA who have a little time line of the Universe, which of cause starts somewhere (is it even possible to draw a line that doesn't have a beginning?)).
In 1996 Anthony Flew once wrote a short article against some of the arguments of design saying that we can not make the claim that the Universe was designed as we have only a limited experience of things (which is interesting for the atheist to then declare that there is no God from their limited experience of things). In 2004 Flew became a deist as he was convinced by the amount of evidence for design in the Universe that there must be a creator. I find it amazing that a really strong and prominent atheist can be convinced by design because of "following the evidence, wherever it leaves" (see here). I wonder what Percy would have to say if he was born in this century.
You can read a rough draft fragment of Percy's Refutation of Deism here.