956
THEORY AND PRACTICE OF ENGINEERING.
Book 11.
tween the threads is greater or less than the other; into it is introduced a nut n, inwhich is fixed the thread of the micrometer; this nut cannot turn at the same time withthe axis, for it is prevented by the bar mm; but at each turn of the axis it passes over aspace equal to the distance between the threads of the screw ; it participates consequentlyin two opposite movements, that of the absolute change of this axis, and that round the axisitself, so that it only advances by the difference of these two motions. Let a be the dif-ference between the threads of the screws, ab, cf; g that of the screw erf; after n revolu-tions of the axis, the support n will have gone over a space equal na — nd, equal n (a —d) ;but a —a may be as small as we please, a and a also as large as circumstances require.
A spiral enveloping a cylinder presented to a current of airor water changes the rectilinear motion of these fluids into acircular one, and the screw of Archimedes may be consideredas the inverse of the problem. The simplest method of pro-ducing a rectilineal alternating motion from a circular con-tinuous one consists in raising a beam or stamper vertically, asthat of an oil mill, by wheels formed into an irregular outline,or carrying on their circumference wipers or spirals. 'I hestamper is thus raised to a certain height, and descends through 1334 .
the same height by its own weight, when the succeeding wiper begins to act upon it, andraises it a second time. In the vertical wheel with floats, in the undershot, breast, andovershot bucket wheels, we have at once an example of rectilinear converted into circularcontinuous motion.
s'
Fig. 1335. UNDERSHOT WHEEL.
Horizontal Windmills are composed, first, of awheel formed by six sail-beams, fixed tothe axle c ; secondly, of vanes, a,b,d } e,fg fixed to these sail beams by their pivots, placed insuch a manner that their surfaces are divided into two unequalparts by the axis of rotation. If we place in the sail-beamsthe obstacles r, formed by vertical cords, in such a manner thatthe distance between each obstacle and the pivots of the vanesbelonging to the same sail-beams are smaller than the largestvane, so that they can freely turn, without being able topass beyond the direction of the sail-beams, which is performedby stops, and other cords placed between those we have men-tioned and the points of rotation, it will be seen that in whateverposition the vanes are in calm weather, immediately the windblows, they present themselves to it, so as io turn ihe axis c alwaysin the same direction — a circumstance which would give adecided advantage to this kind of sail over vertical sails, but forgreat inconveniences which have thrown discredit on them : ofthese the chief is the resistance resulting from the action betweenthe wind and the part of the wheel which moves in a contrarydirection to it. The continual friction of the vane against thecords also diminishes the effect of these machines, and tends todestroy it: it has been attempted to obviate this by multiplyingthe number of vanes on the same sail-beam ; but the incon-veniences from the sails of the horizontal mill are greater than
the advantages. fie-1337.
Windmill with a vertical Wheel. — These mills are composed of a turning axle b inclinedto the horizon from 8 to 15 degrees: second, of four pieces of wood, c,d,e.f, each 40 feetlong, perpendicular to the axle b; they are fixed to the axle at its upper extremity: third,by four sails sustained by these four pieces of wood : each sail commences at 6 feet 6 inchesfrom the turning axle b , and terminates at the extremity of the arms which sustain it;consequently it is 32 feet long, their breadth rather more than 6 feet 6 inches. Accordingto Monge and Haehette, each sail may be regarded as an irregular surface engendered bythe motion of a right line perpendicular to the piece which sustains the sail, and which atthe commencement of the sail, viz. nearest the turning axle, would form with it an angle of