the bigness of the Circumference of the Circle which the force that turneth it about doth describe be of ten Feet; forafmuch,as ten times. ten are one hundred, one Man alone fhall be able to prefs as ftrongly with this Inftrument, or Screw, as one hundred without it, provided always, that we rebate the force that is required to the turning of it.

gr.

Now I speak here of preffing rather than of Railing, or removing, in regard that it is about this moft commonly that the Screw is employed: but when we would make use of it for the raising of Weights, inftead of making it to advance into a Female Screw, we joyn or apply unto it a Wheel of many Cogs, in fuch fort made, that if v. this Wheel have thirty Cogs, whilft the Screw maketh one entire turn, it fhall not cause the Wheel to make more than the thirtieth part of a turn, and if the Weight be faftned to a Cord, that Rolling about the Axis of this Wheel shall raise it but one Foot in the time that the Wheel makes one entire Revolution, and that the greatness of the Circumference of the Circle that is described by the force that turneth the Screw about be alfo of ten Feet, by Reason that 10 times 30 makes 300, one fingle Man fhall be able to raise a Weight of that bigness with this Inftrument, which is called the Perpetual Screw, as would require 300 Men without it.

Provided, as before, that we thence deduct the difficulty that we meet with in turning of it, which is not properly caused by the Ponderofity of the Weight, but by the force or matter of the Inftrument, which difficulty is more fenfible in it, then in those aforegoing, foral much as it hath greater Force.

CHAP.

I

CHAP. VII.

Of the LEAVER Vectis.

Have deferred to fpeak of the Leaver until the laft, in regard, that it is of all Engines for raising of Weights, the most difficult to be explained.

B

M

E

Let us fuppofe that CH is a Leaver, in fuch manner fupported, at the Point O, (by means of an Iron Pin that paffeth through it across, or otherwife) that it may turn about upon this Point O, its Part C describing the Semicircle ABCDE, and its Part H the Semicircle FGHIK, and that the Weight which we would raife by help of it were in H, and the force in C, the Line CO being fuppofed Triple of OH. Then let us confider, that in the time whilft the Force that moveth this Leaver, defcribeth the whole Semicircle ABCDE, although that the Weight defcribeth likewife the Semicircle F G H IK, yet it is not raised to the length of this Curved Line FGHIK, but only to that of the Line FOK; infomuch, that the proportion that the Force which moveth this Weight ought to have to its Ponderofity, ought not to be meafured by that which is between the two Diameters of thefe Circles, or between the two Circumferences, as it hath been faid before of the Wheel, but rather by that which is between the Circumference of the Greater, and the Diameter of the Leffer. Furthermore, let us confider, that there is a neceffity that this Force needeth not be fo great, at fuch time as it is near to A, or near to E, for the turning of the Leaver, as then when it is near to B or to D, nor fo great when it is near to B or D, as then when it is near to C; of which the Reason is, that the Weights there do mount lefs ; as it is eafie to underftand, if having fuppofed that the Line CO H is parallel to the Horizon, and that A O F cutteth it at Right Angles, we take the Point G equidiftant from the Points F and H, and the Point B equidiftant from A and C; and that having drawn GS Perpendicular to F O, we obferve that the Line F S (which fheweth

how

how much the Weight mounteth in the time that the Force operates along the Line A B) is much Leffer than the Line S O, which fheweth how much it mounteth in the time that the Force operates along the Line B C.

And to measure exactly what his Force ought to be in each Point of the Curved Line ABCDE, it is requifite to know that it operates there, just in the fame manner, as if it drew the Weight along à Plain Circularly Inclined; and that the Inclination of each of the Points of this Circular Plain were to be measured by that of the Right Line, that toucheth the Circle in this Point. As for Example; when the Force is at the Point B, for to find the proportion that it ought to have with the Ponderofity of the Weight which is at that time at the Point G, it is neceffary to draw the Contingent Line G M, and to account that the Ponderofity of the Weight is to the Force which is required to draw it along this Plain, and confequently to raise it, according to the Circle F G H, as the Line G M is to SM. Again, forafinuch as BO is Triple to O G, the Force in B, needs to be to the Weight in G, but as the third part of the Line S M, is unto the whole Line G M. In the felf fame manner, when the Force is at the Point D, to know how much the Weight Weigheth at I, it is neceffary to draw the Contingent Line betwixt I and P, and the Right Line IN Perpendicular upon the Horizon, and from the Point P, taken at difcretion in the Line I P, provided that it be below the Point I, you muft draw PN parallel to the fame Horizon, to the end you may have the proportion that is betwixt the Line IP, and the third part of the Line IN, for that which is betwixt the Ponderofity of the Weight, and the Force that ought to be at the Point D for the moving of it; and fo of others. Where, nevertheless, you must except the Point H, at which the Contingent Line being Perpendicular upon the Horizon, the Weight can be no other than Triple the Force which ought to be in C. for the moving of it: In the Points F and K, at which the Contingent Line being parallel unto the Horizon it felf; the leaft Force that one can Affign, is fufficient to move the Weight. Moreover, that you may be perfectly exact, you must obferve that the Lines S M and PM ought to be parts of a Circle, that have for their Center that of the Earth; and GM and IP, parts of Spirals drawn between two fuch Circles: And laftly, that the Right Lines S M and IN, both tending towards the Center of the Earth, are not exactly Parallels: And furthermore, that the Point H, where I fuppofe the Contingent Line to be Perpendicular unto the Horizon, ought to be fome fmall matter nearer to the Point F than to K, at the which F and K the Contingent Lines are Parallels unto the faid Horizon.

CHAP.

CHAP. VIII.

of Archimedes his Cochlea, or Water Screw, and how a Perpetual Motion hath been attempted to be performed thereby.

I

"Do not think it hit in this place, to pafs over with filence, the Invention of Archimedes to raife Water with the Screw, which is not only Marvelous but Miraculous For we fhall find, that the Water afcendeth in the Screw continually defcending: And in a given time, with a given Force, doth raife an unfpeakable quantity thereof. But before we proceed any farther, let us declare the ufe of the Screw in making Water to Rife: And

in the Figure let us confider the Line ILOPQRSH, being an hollow Pipe of Metal, wrapped or turned about the Columb MIKH, or a hollow Channel, cut in the Columb of Wood, and covered with thin Plate of Brafs or Latten, through which the Water may run. If we shall put the end I into the Water, making the Screw to ftand Leaning, fo

as the Point L may be lower than the firft I, (as the Diagram fheweth) and fhall turn it round about on the two Axes T and V, the Water fhall run thorough the Pipe or Channel, till, that in the end, it fhall discharge forth at the Mouth H. Now I fay, that the water, in its conveyance from the Point I, to the point H, doth go all the way defcending, although the Point H be higher than the Point I: Which that it is fo, we will declare in this manner: We will defcribe the Triangle AC B, which is that of which the Screw H I is generated, in fuch fort, that the Channel of the Screw is reprefented by the Line A C, whofe Afcent, or Elevation is determined by the Angle B AC, that is to fay, if fo be the Angle BAC be one third, or one fourth part of a Right Angle, then the Elevation of the Channel A C fhall be according to one third, or one fourth of a Right Angle alfo: And it is manifeft, that the Rife of that fame Channel AC, will be taken away, debafing the Point C as far as to B, for then the Channel AC fhall have no Elevation: And debafing the Point C a little below B, the water will naturally run along the Channel A C downwards from the Point A towards C. Let us therefore conclude, that the Angle A, being one third of a Right Angle, the Channel A C fhall

B

fhall no longer have any Rise, debafing it on the Point C, for one third of a Right Angle.

→ These things underftood, let us unfold the Triangle about the Columb, and let us make the the Screw BA EFG, &c. which if it shall be pla ced at Right Angles with the end B in the water, turning it about, it shall not this way draw up the water, the Channel about the Columb being Elevated, as may be seen by: the Part B A, but altho' the Columb ftand erect at Right Angles, yet for all that, the Rife along the Screw, folded about the

Columb is not of a greater Elevation, than of one third of a Right Angle, it being generated by the Elevation of the Channel A C: Therefore, if we incline the Columb but one third of the faid Right Angle, and a little more, as we fee I KH M, there is a Tranfition and Motion along the Channel IL: Therefore, the Water from the Point I to the Point L fhall move defcending, and the Screw being turned about, the other parts of it fhall fucceffively difpofe, or prefent them felves to the Water in the fame pofition as the part IL: Whereupon the Water fhall go fucceffively defcending, and in the end fhall be found to be Afcended from the Point I, to the Point H. Which, how admirable a thing it is, I leave fuch to judge who fhall perfectly have understood it.

How it hath been by fome fuppofed, that from this Water Screw a Perpetual Morion may be contrived:

For, fay they, if there were but fuch a Water-Wheel made on this Inftrument, upon which the Stream that is carried up, may fall, in its Defcent it would turn the Screw Round, and by that means convey as much Water up, as is required to move it; fo that the Motion must needs be continual, fince the fame Weight which in its fall does turn the Wheel, is by the turning of the Wheel carried up again.

Or, if water falling upon one Wheel would not be forcible enough for this effect; why, there might be two or three, or more, according as the Length and Elevation of the Inftrument will admit; by which means the Weight of it may be fo multiplyed in the fall, that it fhall be equivalent to twice or thrice that quantity of water which Alcends; as may be more plainly difcerned by the Figure.

1