Let A, [Fig. 4] [Plate 8], be the barrel-wheel of a Clock, or other Machine, already in use, and driven by a weight; and let the similar barrel B be added to the former; the motion of both being connected by the unequal wheels C D. The rope or chain E F, is then led from the barrel A under the pulley P to the barrel B: By which arrangement, when the weight has occasioned one revolution of the barrel and wheel A C, those B D, will have made a lesser portion of a revolution in the ratio of the wheel C and D; (namely as 22 to 24,) and that motion will have taken up 11⁄12 of the line which the barrel A has given off. By these means, the motion of the whole may be prolonged almost indefinitely. This System may appear to some persons open to the objection that the friction of the wheels C D, will absorb so much of the power, as to leave the rotatory tendency too feeble for it’s intended purpose. But I again take refuge in the well proved property of my patent geering,—of not impeding (sensibly) the motion of any Machine in which it is used.
Should it further be suggested, that this is only an awkward parody on the differential wheel and axle, ascribed by Dr. Gregory (in the introduction to his work, page 4,) to the celebrated George Eckhardt: I would answer, that I made that invention also; though doubtless after Mr. Eckhardt; and especially after the date of the figure given by the Doctor, as coming from China, “among some drawings of nearly a century old;” Of course then, I do not pretend to priority of invention: but truth herself authorises me to say, that I did invent this Machine also, in the night between the 17th. and 18th. of January, 1788, and drew it in bed by moonlight, that it might not escape me! It was the result of a previous fit of close thinking: and of the conclusion I then drew, that in whatever way, slowness of motion is obtained by the connection of two movements, power is invariably gained for the same reason, and in the same proportion. The fact is, that all my ideas respecting differential motions, have flowed from this source; as will be evident to the attentive reader of these pages.
OF
AN INSTRUMENT
For drawing Portions of Circles, and finding their Centres by inspection.
It is a known property of an angle such as g d f ([plate 9] [fig. 1]) when touching two fixed points g f, and gliding from one of these points to the other, to describe a portion of a circle g d f. My object in this instrument is to determine, by inspection, the radius of such circle in all cases.