WATfiR. 



of that axis, and in fuch manner that the loweft point of the 

 demi-fpire on which the ball prefTes becomes elevated, then 

 the bJl falls neceflarily from this point upon that which 

 fuaceeds, and becomes loweft ; and as this fecond point is 

 more advanced towards the fecond extremity of the cylinder 

 than the former one, the ball will be advanced towards that 

 extremity by this new defcent, and fo on, that it will at 

 length arrive at the fecond extremity. Moreover, the ball, 

 by conftantly following its tendency to defcend, has ad- 

 vanced through a right hne, parallel and equal to the axis 

 of the cyhnder ; and this diftance is horizontal, becaufe the 

 fides of the cylinder were placed horizontally. 



But fuppofe the cylinder had been placed oblique to the 

 horizon, and turned on its axis continually in the fame di- 

 reftion, it is eafy to fee that the ball will move from the 

 lower end of the fpiral tube towards the upper end, al- 

 though it is aftuated folely by gravity, for this caufes it to 

 occupy the loweft point of the firft demi-fpire ; and when it 

 is abandoned by this point, as it is elevated by the rotation, 

 and will roll by its weight upon that point which has taken 

 its place, this fucceeding point is further advanced towards 

 the elevated extremity of the cylinder than that which the 

 ball occupied juft before ; confequently the ball, while fol- 

 lowing its tendency to defcend, will be always more and 

 more elevated, by virtue of the rotation of the cyhnder. 

 Thus it will, after a certain number of turns, be advanced 

 from the lower extremity to the upper, or through the 

 whole length of the fpiral ; but it will only be raifed 

 through the vertical height, determined by the obHquity of 

 the polition of the cylinder. 



Inftead of the ball, let us now confider water as entering 

 by the lower extremity of the fpiral canal, when immerfed 

 in a refervoir. This water defcends at firft in the canal 

 folely by its gravity ; but the cylinder being turned, the 

 water moves on in the canal to occupy the loweft place, 

 and thus, by the continual rotation, is made to advance 

 further and further in the fpiral, till at length it is raifed to 

 the upper extremity of the fpiral, where it is expelled. 

 There is, however, an effential difference between the water 

 and the ball ; for the water, by reafon of its fluidity, will 

 adapt itfelf to the form of the fpiral, and, after having de- 

 fcended by its heavinefs to the loweft point of the demi- 

 fpire, will rife up on the contrary fide to the original level ; 

 on which account, more than half one of the fpires may be 

 filled with the fluid. 



The moft fimple method of tracing a fcrew or a helix 

 upon a cyhnder is well known to be this : — Take the height 

 or length of a cyhnder for the perpendicular leg of a right- 

 angled triangle, and make the bafe or horizontal leg equal 

 to as many times the circumference of the cylinder as the 

 fcrew is to make convolutions about the cylinder itfelf; 

 then draw the hypothenufe to complete the triangle. Sup- 

 pofe this triangle to be enveloped about the furface of the 

 foUd cylinder, the perpendicular leg being made to he 

 parallel to the axis of the cylinder, and the horizontal leg 

 or bafe to fold upon the circumference of the cyhnder, even 

 with its bafe ; then the hypothenufe or floping fide of the 

 triangle will form the contour of the fcrew. If a tube be 

 formed according to the direftion of this fpiral, and a fmall 

 ball put into it when the cyhnder is placed upright, the 

 ball would roll to the bottom with the fame velocity, and 

 the fame force, as it would have defcended upon a plane 

 furface, inchned in the fame degree as the hypothenufe of 

 the triangle which we have fuppofed, when the bafe thereof 

 ia-horizontal. But fuppofe the cyhnder be inclined in fuch 

 degree, that the hypothenufe of the faid triangle would be 

 horizontal inftead of the bafe, as the angle which the 



threads of the fcrew make conftantly with the bafe of the 

 cylinder is juft equal to that incUnation, the tlireads at 

 their point of fmalleft inclination will be parallel to the ho- 

 rizon ; fo that there being nothing to occafion the ball to 

 roll towards either end, it will remain immoveable, fup- 

 pofing the cyhnder to be at reft ; but if the cylinder be 

 turned on its axis in one direftion, the ball (abftrafting 

 from friftion) will move the contrary way, in conformity 

 with the firft law of motion. The inclination which we 

 have juft aflTigned is the leaft we can give, fo that the ball 

 fhall not defcend of itfelf ; but if we augment this inchna- 

 tion, then, by turning the cylinder, the ball will always have 

 a defcent on one fide, and will in confequence roll towards 

 the elevated end of the fame, and will mount by defcending. 

 The reafon is very fimple : the plane which carries it makes 

 it rife more, in confequence of the rotatory motion, than it 

 defcends by virtue of the force of gravity. It is obvious, 

 from what has been remarked, that this fcrew can never 

 raife water, when the angle which the central line of the 

 fpiral makes with the bafe of the cyhnder is larger than 

 the angle which the bafe of the cylinder makes with the 

 horizon. 



The ratio of the weight of the ball to the force which is 

 neceffary to make it rife by turning the fcrew, is as the ver- 

 tical fpace through which the weight is raifed to the fpace 

 paffed through by the power in moving it. Suppofe the 

 moving force afts at the circumference of the cylinder, the 

 fpace paffed over by that force will be equal to as many 

 times the circumference of the cyhnder as the number of 

 convolutions of the helix. Let the diameter of the cylin- 

 der be 14 inches, the vertical altitude of the upper end of 

 the cylinder above the lower end 12 feet, or 144 inches, and 

 12 convolutions of the fpiral : let the cylinder he fo placed, 

 that the inclination of the axis is greater than the inclination 

 of the fpiral to the axis, and let the weight to be raifed be 

 a 48 lb. ball. The circumference of the cylinder will be 

 nearly 44 inches, and the 12 turns equal to 12 x 44 = 

 528 inches, for the fpace the power muft move through. 

 Hence we have 528 inches : 144 inches :: 48 lbs. : 133- lbs. ; 

 the meafure of the requifite force to be apphed at the fur- 

 face of the cyhnder. If the moving force defcribes a circle 

 whofe diameter is three times that of the cylinder, or afts 

 at a winch whofe diftance from the axis of motion is 21 

 inches, that force will then be rednced to j of 133- or 44 lbs. 

 which is lefs than one-tenth of the weight of the ball. In 

 this inveftigation, no notice is taken of the friftion upon the 

 pivots, or of the effefts of the air included in the fpiral : 

 yet if the fpiral had been folded upon a cone inftead of a 

 cyhnder, or if it had been formed of a flexible tube of va- 

 rying diameter, thefe effefts would have been important : 

 fome of them are confidered in our account of the ipiral 

 pump. 



The Archimedes' fcrew is a machine fo frequently em- 

 ployed in hydrauhc architefture, as to deferve particular di- 

 reftions for conftrucEting it. The fimple pipe wrapped 

 round a cylinder will not afford any confiderable fupply of 

 water, and therefore a hollow barrel muil be made with one 

 or two fpiral partitions running in it, hke the fpiral ftair 

 cafes ufed in church fteeples. 



Vitruvius has given minute direftions for the conftruftion 

 of the water-fcrew, and Mr. Smeaton's direftions, which 

 are very fimilar, are as follow : — For a fcrew of i8 inches 

 diameter, ufe a fohd cyhnder of fix inches diameter as an 

 axis, upon the furface of which cut a double helix, form- 

 ing two feparate grooves round the axis of about three- 

 quarters of an inch wide and deep, fo that the grooves in 

 going once round will advance about fixteen inches, and in 



confequence 



