finish of the up-stroke the steam should only be about the pressure of the atmosphere, or say from 1 to 10 lbs. on the inch, having commenced it with steam of from 100 to 200 lbs. on the inch, and cutting off the supply from the boiler when the pole had gone but a very small part of its upward stroke, more or less as the mine requirements admitted of it. The principle of expansive working and momentum of moving parts was of necessity modified in its application to pump-work. "DEAR TREVITHICK, "EASTBOURNE, _February 15th, 1816_. "I have been called here by the decease of my wife's uncle, and consequently your letters of the 11th did not reach me till this day. "The account you give me of your new engine has been extremely gratifying. The duty performed by the engine in giving a velocity of 8 feet in a second, thirty-six different times in a minute, to 24 tons of matter, by the consumption of 2 bushels of coal in an hour, is indeed very great, amounting to about fifty-seven and three-quarter millions. So that when you obtain a proper burden, and the extraordinary friction arising from the too close fitting of the plunger-pole and case is reduced, there seems to be no doubt of your engine performing wonders. "I am of opinion that the stronger steam is used, the more advantageous it will be found. To what degree it should be applied expansively must be determined by experience in different cases. It will depend on the rate at which the engine requires to be worked, and on the quantity of matter put into motion, so that as large a portion as possible of the inertia given in the beginning of the stroke may be taken out of it at the end. "Some recent experiments made in France prove, as I am told, for I have not seen them, that very little heat is consumed in raising the temperature of steam. And if this is true, of course there must be a great saving of fuel by using steam of several atmospheres' strength, and working expansive through a large portion of the cylinder. I have really been impatient for a week past to receive some account of your machine, having learned nothing about it, except from a paragraph dated Hayle in the Truro paper of last Saturday week, and somehow or other the next paper has not reached me, "I hope to be in London about Tuesday next, but at all events direct to me there, as my letters are regularly forwarded. "Believe me, dear Sir, "Yours ever most faithfully, "DAVIES GIDDY." [Rough draft,] "MR. JOHN ADAMS, "BROMSGROVE, _8th March, 1816_.