A New Century of Inventions. James White
leave an interval of time when they both rise together; during which their valves, respectively, close by their own weight before the column of water falls upon them. In such manner, indeed, that the column never falls at all. By this important arrangement, the work is constantly going on, and no commotion occurs to absorb Power uselessly, or to destroy, prematurely, the Machine; circumstances which constantly attend every Pump Machine acting by merely reciprocal motion.
This non-reciprocity then, I produce by several methods; one of which (perhaps the most easily understood) is that shewn in fig. 2: There, A B are two friction-rollers, made as large as possible, rolling on the curves C X, the ascending and descending parts of which are essentially unequal. For example, the rising part of the curve occupies 2⁄3 of the whole circumference; and the falling part 1⁄3 only; so that both curves recede from the centre at the same time, during 1⁄6 of a revolution, at the two opposite positions, A C and X Y. Applying then, these curves and levers to the Pump-barrels represented in fig. 3, we obtain that continuity of uniform motion, which is necessary to doing the greatest quantity of work with the least power; and to securing the greatest durability of the Machine. Having hinted at a minimum of power, I must add here that this Machine appears to promise that result, much more credibly than any reciprocating pump whatever; especially if to this continuity of motion we add a certain largeness of dimension that shall produce the required quantity of water, with the slowest possible motion of each particle; and even here this continuative principle helps us much; since pistons and valves of the largest dimensions may be used without introducing any convulsive, or (what is synonymous) any destructive effects.
One particular remains to be noticed in fig. 2. It relates to the means by which the perpendicularity of the motion in the Piston-rods is secured. The arcs M are portions of cylinders having the bolts Z, for their centres, and which, rolling up and down against the perpendicular plane O N, secure a similar motion to the bolts. The tenons P, are cycloidal, on their upper and lower surfaces; and work in square or oblong holes in the plane N O, being kept in their holes by the action of the two springs on a pin let through these tenons: and thus is the motion of the point Z of the levers M B, a perpendicular one; and that of the friction rollers A B, very nearly so.
My object in this work, is to make known the principles, and some of the forms of these Inventions, but my limits will not permit their being dilated on; else I could give several more useful forms of this Machine: but, to make room for other subjects, I must hasten forward—reserving to some future period, many hints respecting the adaptation of those ideas to particular cases. Those of my readers who love to speculate on the doctrine of permutations, will anticipate how much may be done by the combination of a hundred Machines with each other: and they will give me credit for detached items of knowledge—useful in themselves, though too minute to be severally brought forward. Should, however, the degree of patronage I have already experienced, be proportionably extended as the work advances, I can and will follow it up with many useful hints, tending to shew the extent of some of my present subjects, and the amplitude of the sphere in which they roll.
It should be observed, in concluding this article, that the present Machine was executed in France, in 1793, and also proposed to the Government, as a substitute for the celebrated Machine of Marly. In the report then published, it was preferred to the whole multitude of former projects; but left in equilibrio with one modern Machine—a competition which prevented it’s adoption for the moment—and indeed till I was glad to escape the notice, instead of courting the favour of the then rapidly succeeding governments.
OF
A SIMPLE MACHINE,
For Protracting the Motions of Weight-Machinery.
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.
To do this, I connect with the jointed rule m d n, another rule like itself but shorter g e f, so as that the figure g d e f shall be a perfect parallelogram: and I then say that knowing the distance of the points d and e, (the distance d f being given) I know the radius of the circle of which g d f is a portion. To prove this, a little calculation is necessary: In the circles A B and a b (fig. 6) draw the lines E D; f d, d g, g f, g e, and g D; and bearing in mind the known equation of the circle, let d n = x, g n = y; and g D = a, the absciss, ordinate, and radius respectively. The equation is 2ax - x² = y²: from which we get