trary, by making the middle prominent; the other wheel is described by the same the reason of this may be understood, by curve revolving within the circle. It has examining the manner in which a tight been supposed by some of the best austrap running on a cone would tend to thors, that the epicycloidal tooth has also run towards the thickest part. Sometimes the advantage of completely avoiding also pins are fixed in the wheels, and ad. frictinn; this is however by no mitted into perforations in the straps; a true, and it is even impracticable to in. mode only practicable where the motion vent a form for the teeth of a wheel, is slow and steady. A smooth motion which will enable them to act on other may also be obtained, with considerable teeth without friction. In order to di. force, by forming the surfaces of the minish it as much as possible, the teeth wheels into brusles of hair. More com must be as small and as numerous as is monly, however, the circumferences of consistent with strength and durability; the contiguous wheels are formed into for the effect of friction always increases teeth, impelling each other, as with the with the distance of the point of contact extremities of so many levers, either ex. from the line joining the centres of the actly, or nearly, in the common direction wheels. In calculating the quantity of of the circumferences; and sometimes the friction, the velocity with which the an endless screw is substituted for one of parts slide over each other has generally the wheels. In forming the teeth of been taken for its measure. This is a wheels, it is of consequence to determine slight inaccuracy of conception, for it is the curvature which will procure an certain, that the actual resistance is not equable communication of motion, with at all increased by increasing the rethe least possible friction. For the equa. lative velocity ; but the effect of that reble communication of motion two me sistance, in retarding the motion of the thods have been recommended; one, wheels, may be shown, from the general that the lower part of the face of each laws of mechanics, to be proportional to tooth should be a straight line in the di. the relative velocity thus ascertained. rection of the radius, and the upper a When it is possible to make one wheel portion of an epicycloid, that is, of a curve act on teeth fixed in the concave surface described by a point of a circle rolling on of another, the friction may be thus dimi. the wheel, of which the diameter must be nished in the proportion of the difference half that of the opposite wheel; and in of the diameters to their sum. If the face this case it is demonstrable, that the plane of the teeth, where they are in contact, is surface of each tooth will act on the too much inclined to the radius, their mucurved surface of the opposite tooth, so tual friction is not much affected, but a as to produce an equable angular motion great pressure on their axis is produced ; in both wheels; the other method is, to and this occasions a strain on the machi. form all the surfaces into portions of the nery, as well as an increase of the friction involutes of circles, or the curves describ on the axis. If it is desired to produce ed by a point of thread which has been a great angular velocity with the smallest wound round the wheel while it is un. possible quantity of wheel-work, the di. coiled ; and this method appears to an. ameter of each wheel must be between swer the purpose in an easier and sim- three and four times as great as that of pler manner than the former. It may be the pinion on which it acts. Where the experimentally demonstrated, that

pinion impels the wheel, it is sometimes equable motion is produced by the action made with three or four teeth only; but of these curves on each other; if we cut it is much better in general to have at two boards into forms terminated by least six or eight; and considering the them, divide the surfaces by lines into additional labour of increasing the numequal or proportional angular portions, ber of wheels, it may be advisable to al. and fix them on any two centres, we shall lot more teeth to each of them than the find, that as they revolve, whatever parts number resulting from the calculation : of the surfaces may be in contact, the so that we may allow thirty or forty teeth corresponding lines will always meet each to a wheel acting on a pinion of six or other.

eight. In works which do not require a Both these methods may be derived great degree of strength, the wheels have from the general principle, that the teeth sometimes a much greater number of of the one wheel must be of such a form, teeth than this; and, on the other hand, that their outline may be described by an endless screw or a spiral acts as a pithe revolution of a curve upon a given nion of one tooth, since it propels the circle, while the outline of the teeth of wheel through the breadth of one tooth VOL. XII.



only into each revolution. For a pinion of wheel travels round it. If the central six teeth, it would be better to have a wheel be fixed, and the exterior wbeel wheel of thirty-five or thirty-seven than be caused to turn on its own centre dur. thirty-six; for each tooth of the wheel ing its rovolution, by the effect of the would thus act in turn upon each tooth contact of the teeth, it will make in of the pinion, and the work would be every revolution one turn more, with remore equally worn than if the same teeth spect to the surrounding objects, than it continued to meet in each revolution. would make if its centre were at rest, The teeth of the pinion should also be during one turn of the wheel which is somewhat stronger than those of the fixed; and this circumstance must be rewheel, in order to support the more fre. collected when such wheels are employ. quent recurrence of friction. It has been ed in planetariums. proposed, for the coarser kinds of wheel Wheels are usually made of wood, of work, 1o divide the distance between the iron, either cast or wrought, of steel, or middle points of two adjoining teeth into of brass. The teeth of wheels of metal thirty parts, and to allot sixteen to the are generally cut by means of a machine; tooth of the pinion, and thirteen to that the wheel is fixed on an axis, which also of the wheel, allowing one for freedom carries a plate furnished with a variety of of motion.

circles, divided into different numbers of The wheel and pinion may either be equal parts, marked by small excavasituated in the same plane, both being tions; these are brought in succession commonly of the kind denominated spur. under the point of a spring, which holds wheels, or their planes may form an an the axis firm, while the intervals between gle; in this case one of them may be a the teeth are expeditiously cut out by a crown or contrate wheel; or both of revolving saw of steel. The teeth are them may be bevelled, the teeth being afterwards finished by a file; and a macut obliquely. According to the relative chine has also been invented for holding magnitude of the wheels, the angle of and working the file. It is frequently the bevel must be different, so that the necessary in machinery to protract the velocities of the wheels may be in the time of application of a given force, or to same proportion at both ends of their ob reserve a part of it for future use. This lique faces; for this purpose, the faces is generally effected by suffering a of all the teeth must be directed to the weight to descend, which has been pre. point where the axes would meet. In viously raised, or a spring to unbend it. cases where a motion not quite equable self from a state of forcible flexure, as is is required, as it sometimes happens in exemplified in the weights and springs of the construction of clocks, but more fre- clocks and watches. The common kitchquently in orreries, the wheels may either en jack is also employed for protracting be divided a little unequally, or the axis and equalizing the operation of a weight; may be placed a little out of the centre ; in the patent jack the same effect is proand these eccentric wheels may either duced by an alternate motion, the axis act on other eccentric wheels, or, if they being impelled backwards and forwards, are made as contrate wheels, upon a as in clocks and watches, by means of an lengthened pinion. An arrangement is escapement, and the place of a balance sometimes made for eparating wheels spring being supplied by the twisting and which are intended to turn each other, untwisting of a cord. and for replacing them at pleasure; the In these machines, as well as in

many wheels are said to be thrown by these others of greater magnitude, the fly operations out of gear and into gear wheel is a very important part, its veloagain. When a wheel revolves round city being increased by the operation of another, and is so fixed as to remain near any part of the force which happens to ly in a parallel direction, and to cause the be superfluous, and its rotatory power central wheel to turn round its axis, the serving to continue the motion when the apparatus is called a sun and planet wheel. force is diminished or withdrawn. Thus, In this case, the circumference of the when a man turns a winch, he can excentral wheel moves as fast as that of the ert twice as much force in some positions revolving wheel, each point of which de as in others, and a fy enables him in scribes a circle equal in diameter to the some cases to do nearly one-third more distance of the centre of the two wheels; work. In the pile engine, also, without consequently, when the wheels are the help of the fly, the horses would fall equal, the central wheel makes two re for want of a counterpoise, as soon as the volutions, every time that the exterior weight is disengaged. Such a fly ought



to be heavy, and its motion must not be ed by electrical experiments and disco. too rapid, otherwise the resistance of the veries. air will destroy too much of the motion ; WHISPERING places, are places but in the kitchen-jack, as well as in the where a whisper, or other small noise, striking part of a clock, where the super. may be heard from one part to fluous force is purposely destroyed, the ther, to a great distance. They depend fly is made light, and strikes the air with on a principle, that the voice, &c. be. a broad surface. An effect similar to that ing applied to one end of an arch, of a fly and a spring is sometimes pro- easily passes by repeated reflections to duced in hydraulic machines by the in the other. troduction of an air-vessel, the air con Hence sound is conveyed from one side tained in which is compressed more or of a whispering gallery to the opposite less according to the intensity of the one, without being perceived by those force, and exerts a more uniform pres who stand in the middle. The form of a sure in expelling the fluid which is forc. whispering gallery is that of a segment ed irregularly into it. See Young's Lec of a sphere, or the like arched figure ;

and the progress of the sound through it Wheel, in the military art, is the word may be illustrated in the following manof command, when a battalion or squa ner: Let A B C (Plate XVI Miscel. fig. dron is to alter its front either one way 12.) represent the segment of a sphere; or the other. To wheel to the right, di and suppose a low voice uttered at A, the rects the man in the right angle to turn vibrations extending themselves every very slowly, and every one to wheel from way, some of them will impinge upon the the left to the right, regarding him as points, E, É, &c.; and thence be reflect. their centre; and vice versa when they ed to the points, F, F, &c.; thence to G, are to wheel to the left. When a divi. G, &c.; till at last they meet in C; where, sion of men are on the march, if the word by their union, they cause a much strongbe to wheel to the right or to the left, er sound than in any part of the segment then the right or left hand man keeps whatever, even at A, the point from his ground, only turning on his heel, and whence they came. Accordingly, all the the rest of the rank move about quick contrivance in whispering places is, that till they make an even line with the said near the person who whispers there may right or left hand man.

be a smooth wall, arched either cylindri. WHEELS, water. See MILL.

cally or elliptically. A circular arch will WHIRLWIND, a wind that rises sud- do, but not so well. denly, is exceedingly rapid and impetu The most considerable whisperingous, in a whirling direction, and often places in England are, the whisperingprogressively also ; but it is commonly gallery in the dome of St. Paul's, Lon. soon spent. Dr. Franklin, in his Physi. don, where the ticking of a watch may cal and Meteorological Observations, be heard from side to side, and a very read to the Royal Society in 1756, sup easy whisper be sent all round the dome. poses a whirlwind and a water-spout to The famous whispering-place in Glouces. proceed from the same cause: their only ter cathedral is no other than a gallery difference being, that the latter passes above the east end of the choir, leading over the water, and the former over the from one side thereof to the other. It land. This opinion is corroborated by the consists of five angles and six sides, the observations of many others, who have middlemost of which is a naked window, remarked the appearances and effects of yet two whisperers hear each other at both to be the same. They have both a the distance of twenty-five yards. progressive as well as a circular motion ; WHISTON, (William,) an English ihey usually rise after calms and great divine, philosopher, and mathematician, heats, and mostly happen in the warmer of uncommon parts, learning, and extralatitudes : the wind blows every way ordinary character, was born the 9th of from a large surrounding space, both to December, 1667, at Norton, in the coun. the water-spout, and whirlwind ; and a ty of Leicester, where his father was recwater-spout has, by its progressive mo. tor. He was educated under his father tion, passed from the sea to the land, and till he was seventeen years of age, when produced all the phenomena and effects he was sent to Tamworth school, and two of a whirlwind ; so that there is no reason years after admitted of Clare-hall, Camto doubt that they are meteors arising bridge, where he pursued his studies, from the same general cause, and expli- and particularly the mathematics, with cable upon the same principles, furnish- great diligence.


In 1693, he was made Master of Arts, subscription was made for the sapport and Fellow of the College, and soon after of his family, whicb amounted to 4701. commenced one of the iutors; but his For though he drew some profits from ill state of health soon after obliged bim reading astronomical and philosophical to relinquish this profession. Having en. lectures, and also from his publications, tered into orders, in 1694, he became which were very numerous, yet these of chaplain to Dr. More, Bishop of Norwich; themselves were very insufficient: nor, and while in this station he published bis when joined with the benevolence and first work, entitled A New Theory of charity of those who loved and esteemed the Earth, &c.” in which he undertook to him for bis learning, integrity, and piety, prove that the Mosaic doctrine of the did they prevent his being frequently in earth was perfectly agreeable to reason great distress. and philosophy; which work, having In 1739, Mr. Whiston put in his claim much ingenuity, brought considerable to the mathematical professorship at Cam. reputation to the author

bridge, then vacant by the death of Dr. In the year 1698, Bishop More gave Saunderson, in a letter to Dr. Ashton, him the living of Lowestoff in Suffolk, the Master of Jesus College ; but no rewhere he immediately went to reside, gard was paid to it. Among a variety of and (levoted himself with great diligence works, he published Memoirs of his own to the discharge of that trust. In the be. Life and Writings, which are very curiginning of the last century he was made Sir Isaac Newton's deputy, and after Whiston continued many years a memwards his successor in the Lilcasian pro. ber of the established church; but at fessorship of mathematics, when he re. length forsook it on account of the read. signed his living at Lowestoff, and went ing of the Athanasian Creed, and went to reside at Cambridge. From this time over to the Baptists; which happened his publications became very frequent, while he was at the house of Samuel Barboth in theology and mathematics. By ker, Esq. at Lindon, in Rutlandshire, who his researches into the writings of the had married his daughter; where he died Fathers, he was led to embrace the Arian after a week's illness, the 22d of August, hypothesis respecting the person of 1752, at upwards of eighty-four years of Christ; on account of which he was, in age. October, 1710, deprived of his professor. The character of this conscientious and ship, and expelled the University of worthy man has been attempted by two Cambridge, after he had been formally very able personages, who were well acconvened and interrogated for some days quainted with him, namely, Bishop Hare, together. At the conclusion of this year and Mr. Collins, wbo unite in giving him he wrote his “ Historical Preface,” after the highest applauses for his integrity, wards prefixed to his “ Primitive Chris- piety, &c. Mr. Whiston left some chil. tianity Revived," containing the reasons dren bebind them; among them, Mr. for his dissent from the commonly re- John Whiston, who was for many years ceived notions of the Trinity, which a very considerable bookseller in London. work he published the next year in four WHITE, one of the colours of bodies. vols. 8vo. for which the Convocation fell Though white cannot properly be said to upon him most vehemently.

be one colour, but rather a composition In 1713, he and Mr. Ditton composed of all the colours together; for Newton their scheme for finding the longitude, has demonstrated that bodies only appear which they published the year following, white by reflecting all the kinds of coloura method which consisted in measuring ed rays alike ; and that even the light of distances by means of the velocity of the sun is only white, because it consists sound.

of all colours mixed together. On Mr. Whiston's expulsion from Cam This may be shown mechanically in the bridge, he went to London, where be following manner : Take seven parcels conferred with Doctor's Clarke, Hoadly, of coloured fine powders, the same as the and other learned men, who endeavour- primary colours of the rainbow, taking ed to moderate his zeal, but he was not such quantities of these as shall be proto be intimidated; he continued to write, portional to the respective breadths of and to propagate his opinions with as these colours in the rainbow, which are of much ardour as if he had been in the red 45 parts, orange 27, yellow 48, green most flourishing circumstances; which, 60, blue 60, indigo 40, and of violet 80; however, were so bad, that in 1721, a then mix intimately together these seven



parcels of powders, and the mixture will was accommodated with a room directly be a whitish colour : and this is only simi over that in which the favourite piece lar to the uniting the prismatic colours was kept carefully locked up; and he together again, to form a white ray or had not long to wait for his gratification : pencil of light of the whole of them. The for the artist, while one day employed in same thing is done conveniently thus: Let examining his machine, was suddenly callthe flat upper surface of a top be divided ed down stairs; which the young inqui. into 360 equal parts, all around its edge ; rer happening to overhear, softly slipped then divide the same surface into seven into the room, inspected the machine, and sectors, in the proportion of the numbers presently satisfying himself as to the seabove, by seven radii or lines drawn from cret, escaped undiscovered to his own the centre; next let the respective colours apartment. His end thus compassed, he be painted in a lively manner on these shortly after bid the artist farwell, and spaces, but so as the edge of each colour returned to his father in England. may be made nearly like the colour next About two or three years after his readjoining, that the separation may not be turn from Ireland, he left Congleton, and well distinguished by the eye; then, if the entered into business for himself at Derby, top be made to spin, the colours will thus where be soon got into great employment seem to be mixed all together, and the and distinguished himself very much by whole surface will appear of a uniform several ingenious pieces of mechanism, whiteness: and if a large round black both in his own regular line of business, spot be painted in the middle, so as there and in various other respects, as in the may be only a broad flat ring of colours construction of curious thermometers, around it, the experiment will succeed barometers, and other philosophical inthe better.

struments, as well as ingenious contrivWhite bodies are found to take heat ances for water-works, and the erection slower than black ones; because the lat of various larger machines, being conter absorb or imbibe rays of all kinds and sulted in almost all the undertakings in colours, and the former reflect them. Derbyshire, and in the neighbouring Hence it is that black paper is sooner in- counties, where the aid of superior skill flamed by a burning glass, than white; in mechanics, pneumatics, and hydrauand hence also, black clothes, hung up in lics was requisite. the sun by the dyers, dry sooner than In this manner his time was fully and white ones.

usefully employed in the country, till, in WAITEHURST, (John) in biogra. 1775, when the act being passed for the phy, an ingenious English philosopher, better regulation of the gold coin, he was was born at Congleton, in the county of appointed stamper of the money.weights; Cheshire, the 10th of April, 1713, being an office conferred upon him, altogether the son of a clock and watch-maker there. unexpectedly, and without solicitation. On his quitting school, where it seems Upon this occasion, he removed to Lonthe education he received was very de- don, where he spent the remainder of his fective, he was bred by his father to his days, in the constant habits of cultivating own profession, in which he soon gave some useful parts of philosophy and mehopes of his future eminence.

chanism. At about the age of twenty-one, his In 1778, Mr. Whitehurst published his eagerness after new ideas carried him to Inquiry into the Original State and For. Dublin, having heard of an ingenious mation of the Earth; of which a second piece of mechanism in that city, being a edition appeared in 1786, considerably clock with certain curious appendages, enlarged and improved ; and a third in which he was very desirous of seeing, 1792. This was the labour of many and no less so of conversing with the ma years; and the numerous investigations ker. On his arrival, however, he could necessary to its completion were in them. neither procure a sight of the former, nor selves also of so untoward a nature, as, at draw the least hint from the latter con times, though he was naturally of a cerning it. Thus disappointed, he fell strong constitution, not a little to prejulipon an expedient for accomplishing his dice lis health. When he first entered design; and accordingly took up his resi. upon this species of research, it was not dence in the house of the mechanic, pay- altogether with a view to investigate the ing the more liberally for his board, as he formation of the earth, but in part to ob. had hopes from thence of more readily tain such a competent knowledge of subobtaining the indulgence-wished for. He terraneous geography, as might becoms

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