On the subject [of]1 your hempbreak a thought occurr’d to me since I received your letter which I submit to your judgement. On the axis of the wallower instead of arms 15 in long, suppose a cast iron wheel 15 in diamr with cogs only half way round & on the face of the head block instead of a horn, a curved piece of cast iron 30 in long & 4 broad, with cogs corresponding in number &c with those on the cast wheel, the upper cog on this curved iron should be one half inch longer than the one next it, for it will then more certainly be taken by the upper cog on the wheel, this will facilitate the introduction of the following cogs to their respective places & prevent butting, There would be some danger when the head block recoils, that the long cog in the upper part of the curved iron would strike the lower cogs of the wheel, to prevent which, the cogs of the wheel should gradually shorten till the last cog should be half an inch shorter than the first, a corresponding shape must be given to the cogs of the curved iron, that is, if the first cog is 3½ inches, the 2nd will be 3 i, & every following cog must be gradually longer till the last cog is 3½ in. The wheel & head must then run free, great exactness is necessary in the forms for the castings they should be made at home & experimented on till they are exactly adjusted, a Mill wright would make them in 2 days & the irons would cost 5 or 6$.

The arms at first view appear to have one advantage over a Wheel, they give 2 strokes for one revolution of the wallower, this but one, but the power of this wheel 15 i diar is to the power of an arm 15 i long, inversely as the semi diar of the wheel is to the length of the arm, ie. as 15 is to 7½ or 2 to 1. or presenting but half the resistance the velocity doubles. It will also raise the weight much higher & as the velocities of falling bodies are uniformly accelerated thr’o their whole descent, the effect of the stroke must be augmented by that cause, to show this, The arm of 15 i long cannot I think with advantage take the horn at an angle greater than 30° below the horizontal plane passing thr’o the axis, if so, it must drop the horn at the same angle above that plane, the arm must then have described an arc of 60° & while doing so it must have raised the head block to a height equal to the chord of that arc, but the chord of 60° is equal to Radius, therefore the break will be raised 15 i high by an arm 15 i long.—The whole circumference of the cog wheel 47.124 [i] the half or part with cogs is 23.562 i this acting on the curved iron must make the head block describe an arc exactly the same length, let the moving part of the break be 12 feet, this arc 23.562 is the measure of an angle whose quantity may be found a Rad 12 f gives a circumfe 904.7808 i then say as the circle is to this arc so is 360° to 9.°22. The chord of this arc is the measure of the breaks ascent, but as the chord of every arc is double the sine of half the angle it measures, the length of that chord (ie) the perpendicular ascent of the break may be found, bisect that angle 4.°41 & say as Rad is to the sine 4.°41 so is the length of the break 12 f. to half its ascent 11.7 × 2 = 23.4 in. I once projected a thing for this use 2 fluted cast iron cylinders deriving motion from a small water wheel spur cog & trundle, the dispatch would have been rapid, the hemp well broke but this is better I think.—

Nothing can be more simple than the construction of a steam engine for all, perhaps more domestic purposes than your letter requires, recollect the figure I sent to you, a strong iron bar connects the steam & water pistons, an arm is fixed in that bar for the purpose of turning the cocks, let a horizontal shaft be connected with that arm, let this shaft go thr’o the kitchen, & let the other end play on a hinge in the wall 7 or 8 feet from the floor, let a hominy pestle a dough pestle & a churn staff be appendant to that shaft with a small contrivance to turn the spit, it [is]2 obvious as the piston bar goes up & down the whole machinery is at work, pipes for raising the water need not be larger in the bore than a musket, the power of steam necessary to do all this is trifling, the boiler may be worked into & even with the back of the fireplace or it may be of a rectangular form the perpendicular in the fire back the horizontal into & even with the hearth, thus a greater surface is exposed to the heat, no room is lost, nor an atom more of fuel consumed than without it,—In 2 or 3 Months if I can I shall go to Phila to have the model of my projet executed. Be pleased to accept my gratefull acknowlegements for your polite attention to my last & believe me to be as I have ever been most respectfully & sincerely Yrs

Geo. Fleming