there is a small one making near you by Mr. Vivian. I hope they have corresponded with Trevithick about the proportions of it; if they have not, I shall be particularly obliged to you to desire them to do so, for by his experience of what he has done they may be benefited, for it would be a shocking thing to have a bad engine put up for the first time in his native county. "Mrs. Homfray unites with me in best compliments, and wishing you many happy returns of the season. "I remain, dear Sir, "Your most obedient servant, "SAMUEL HOMFRAY. "_To Mr. Davies Giddy._" The evidence in this contest between the Watt low-pressure steam vacuum engine and the Trevithick high-pressure steam-puffer engine is in favour of the new principle; for the steam-engine with an 18-inch cylinder did fifty per cent. more work than the vacuum engine with a 24-inch cylinder with an equal quantity of coal, though the latter was seventy-five per cent. larger than the former; and a still greater economy was expected from the larger boiler to be built, 26 feet long, 7 feet in diameter, with internal fire-tube 4 feet 4 inches diameter at the fire end, tapering to 21 inches at the chimney end. Thus in 1804 the cylindrical boiler in Wales had nearly reached its present form, and Homfray thought that none but idiots would prefer the Watt engine; forgetting that Trevithick's near friends and neighbours were carrying on a similar contest at Dolcoath Mine. "PENYDARRAN PLACE, _January 2nd, 1805_. "MR. DAVIES GIDDY, "Dear Sir,--I have duly received your favour enclosing a letter for Mr. Trevithick, and which I, according to your desire, forwarded to him at Manchester, where he now is; and a letter directed to him, to the care of Mr. Whitehead, Soho Foundry, Manchester, will find him, as he will stay a little time there, being very busy. I had lately the pleasure of writing to you, and gave you the account of our engine working, and the satisfaction it gives; I have nothing more to add on the subject, but that it is now at work, going on as usual, and I should be happy for you to have a sight of it. "We are beginning another of a larger size, and I have no doubt but by making the cylindrical boiler larger, so as to take a longer tube withinside it, by which means the fire will spend itself before it leaves the tube to go up the chimney, that we shall work to much better advantage in point of fuel than we do at this present one, as this boiler is so short that a great deal of the flame of the fire goes up the chimney. We are now better acquainted with the different proportions than we at first were, for which reason I am anxious that one now making by Mr. Vivian should be made according to the directions of Mr. Trevithick. "I beg leave to offer you the compliments of the season, and many happy returns, and "Remain, respectfully, dear Sir, "Your most obedient servant, "SAMUEL HOMFRAY."