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Backwards. Backwards this doing I'm. I should have done this bit first. Because it gives general instructions that are referred back to in some of the other beer types. Sorry about that.

As it's rather long, I'm splitting it into two parts. I understand how short attention spans are.

"Practical Instructions by Mr. Richardson.

Art, I.—For Mild Ale In General.

1.—Heat of the Liquor.

This being an ale which requires early purity, the first heat of the liquor must therefore scarcely ever be under, and is not seldom above, 180°, to which 5º are to be added for the second mash, and 5° more for the third, where three mashes are made for strong ale; but where there are two only, the addition may be 10°; that is, 180° and 190°. If, however, you find by experience that a lower heat of the liquor will produce purity, this will be a preferable practice, as producing a more mucilaginous wort, and it is better calculated for making small beer after it. It is therefore advisable that you begin with the heat of the liquor just mentioned, and then try 175° for the first mash, varying 5º at a time in different brewings, for the sake of practice and experience. Sometimes, indeed, when I take my first heat at 180°, or higher, I only increase 5° for my second, though I have but two mashes for strong ale, in order to avoid that thinness on the palate, which too high a heat is sometimes apt to produce.

§ 2.—Time of Infusion.

If there be only one mash for strong ale, as is sometimes the case for ale of great strength, the time of infusion should be four hours. If there be two mashes, allow three hours for the first, and two or two and a half hours for the second; and if three mashes/ allow two and a half or three hours for the first, two for the second, and one and a half or two hours for the third; it being intended to allow as much time as is consistent with the proper forming of the extract, and the necessary expedition of the process.

$ 3.—Quantity of Hops.

To ale made from worts whose average specific gravity is about thirty pounds (which answers to about two barrels from a quarter of malt), not less than two pounds of hops should be used in winter, and more as the season advances, even to four pounds in a great heat of the atmosphere; or it is perhaps more rational to apportion the hops to the malt used, in which case eight pounds per quarter are allowed, for the more certain preservation of the ale. This being adapted for the climate of England, a greater portion ought to be allowed where the heat of the air is greater.

§ 4. —Time of Boiling. This in general, should be only till the wort breaks pure, in order to extract only the finer parts of the hops; but in great heats of the air, a longer time in boiling, as well as a greater portion of hops, is necessary for the preservation of the ale. For this purpose, also, (having in view a finer flavour in the ale,) it is advisable to boil the wort for an hour or more, before the hops are added, which renders it more preservable, at the same time that it avoids the rank extract of the hops. If, however, those produced in Worcestershire be used, the mildness of their flavour renders this precaution unnecessary.

What is meant here by breaking pure, is that state of the Wort when the hops subside to the bottom, and the mucilaginous parts of the malt are coagulated into large lumps, and float up and down in it, very rapidly, leaving the interstices of the wort perfectly pure. This generally happens (when the wort is boiled briskly, as it ought always to be) in about twenty or twenty-five minutes in the first wort, but is somewhat longer in the others. The mode of observing it is, to take a little wort in a bowl or dish, after having boiled about a quarter of an hour, and let it stand steady to observe the effect; and, by doing so every five minutes after, for two or three times, you will note the difference, and soon become a competent judge. Without making this observation, you cannot err much in boiling the first wort about three-quarters of an hour, and an hour or an hour and a half the second; or if you boil altogether, the whole time may be allowed. This, however, respects the extract of the hops rather than the effect it is to have on the wort; and ;is intended only for the winter season, and when the ale is for present use."
"The art of brewing" by David Booth, 1829, pages 40 - 41. (Copy of text from Richardson's "Philosophical Principles of the Science of Brewing." 1798.)
Let's start with the mashing temperature. First mash 180º, second 185º, third 190º. That seem a bit warm to you? Let's have a look and see what I can find in my brewing log bag. Here's three lots. From Barclay Perkins, Truman and Whitbread:

Whitbread 1837 XX XXX XXXX 1st mash 165º 165º 170º 2nd mash 184º 184º 184º 3rd mash 184º 184º 184º Source: Whitbread brewing records held at the London Metropolitan Archives. Document LMA/4453/D/01/001
Barclay Perkins 1838 X X X 1st mash 172º 166º 164º 2nd mash 190º 186º 193º 3rd mash 200º 194º 194º Source: Barclay Perkins brewing records held at the London Metropolitan Archives. Document ACC/2305/01/550
Truman 1831 XXX XXX XXXK 1st mash 177º 178º 176.5º 2nd mash 184º 185º 185º 3rd mash 183º Source:

Truman brewing records held at the London Metropolitan Archives. Document B/THB/C/115

What does that tell us? That they mashed at all sorts of temperatures. A couple of those Barclay Perkins ones are even higher than Richardson's recommendation for the second and third mashes. But all of the first mashes are below 180º F.

Now to the hopping. Eight pounds per quarter? Sounds pretty reasonable to me. Here's a mixed bunch of London Ales from the 1830's:

Hopping rates of London Ales Date Year Brewer Beer lbs hops/ qtr hops lb/brl 15th Mar 1837 Whitbread X 6.05 1.87 15th Mar 1837 Whitbread XX 6.05 2.35 13th Mar 1837 Whitbread X 7.64 2.41 3rd Mar 1837 Whitbread X 8.07 2.65 27th Feb 1837 Whitbread XX 6.11 2.38 23rd Dec 1836 Whitbread XXXX 7.00 3.64 22nd Nov 1838 Barclay Perkins X 9.47 3.54 29th Nov 1838 Barclay Perkins X 6.53 2.38 13th Dec 1838 Barclay Perkins X 6.32 2.30 10th Jan 1839 Barclay Perkins X 7.14 2.52 1st Dec 1831 Truman XXX Ale 8 4.00 2nd Dec 1831 Truman XX Ale 8 2.77 3rd Dec 1831 Truman X Ale 7 2.33 24th Dec 1831 Truman XX Ale 6 2.63 26th Dec 1831 Truman XXX Ale 7 3.54 27th Feb 1832 Truman XXXX Ale 8 4.32 Sources: Brewing records held at the London Metropolitan Archives Documents: LMA/4453/D/01/001, ACC/2305/1/550, B/THB/C/115

Between 6 and 9.5 lbs per quarter. Eight is about bang in the middle of that range.

Boiling times. 90 minutes is a good average. Don't add the hops at the start of the boil. If I understand him correctly, Richardson is saying boil for 90 minutes, adding the hops after 60.

Almost forgot. The strength: 30 lbs per barrel, drawing 2 barrels from a quarter of malt. Sorry, but that is just rubbish extract. 60 lbs from a quarter? They should be getting closer to 80. 30 lbs per barrel is, in case you're wondering, 1083º.

Next instalment: fermentation and cleansing.