nearly the same; that is, almost double of the expansion of iron, It is likewise observable, that the flames placed together cause a greater rarefaction than when they have a sensible interval between them; iron, in the former case, being expanded 117 degrees, and only 109 in the latter; the reason of which difference is obvious. By comparing the expansions of the same metal, produced by one, two, three, or more flames, it appears, that two flames do not cause double the expansion of one; nor three flames three times that expansion, but always less; and these expansions differ so much the more from the ratio of the number of flames, as there are more flames acting at the same time. It is also observable, that metals are not expanded equally, at the time of their melting, but some more, some less. Thus tin began to run, when rarefied 219 degrees; whereas brass was expanded 377 degrees, and yet was far from melting.

By the help of this instrument Mr. Ellicott found upon a medium, that the expansions of bars of different metals, as nearly of the same dimensions as possible, by the same degree of heat, were as follow:

Gold,

78

Silver, Brass, Copper, Iron, Steel, Lead,

The great difference between the expansions of iron and brass has been applied with good success to remedy the irregularities in pendulums arising from heat. (Phil. Trans. vol. xlvii. p. 485.) See PENDULUM.

Mr. Graham used to measure the minute alterations, in length, of metal bars, by advancing the point of a micrometerscrew, till it sensibly stopped against the end of the bar to be measured. This screw, being small and very lightly hung, was capable of agreement within the three or four-thousandth part of an inch. On this general principle Mr. Smeaton contrived his pyrometer, in which the measures are determined by the contact of a piece of metal with the point of a micrometer

screw.

The following table shows how much a foot in length of each metal grows longer by an increase of heat, corresponding to 180° of Fahrenheit's thermometer, or to the difference between freezing and boiling water, expressed in such parts of which the unit is equal to the 10,000 part of an inch.

1. White glass barometer tube, 2. Martial regulus of antimony,

3. Blistered steel,

4. Hard steel,

5. Iron,

100

130

138

147

151

12. Speculum metal,

13. Spelter solder, viz. brass two parts, zinc one,

14. Fine pewter,

15. Grain tin,

16. Soft solder, viz. lead two, tin one,

17. Zinc eight parts, with tin one, a little hammered,

18. Lead,

M. de Luc, in consequence of a hint suggested to him by the late Mr. Ramsden, invented a pyrometer, the basis of which is a rectangular piece of deal board two feet and a half long, 15 inches broad, and one inch and a half thick; and to this all the other parts are fixed. This is mounted in the manner of a table, with four deal legs, each a footlong and an inch and a half square, well fitted near its four angles, and kept together at the other ends by four firm cross pieces. This small table is suspended by a hook to a stand; the board being in a vertical situation in the direction of its grain, and bearing its legs forward in such a manner as that the cross-pieces which join them may form a frame, placed vertically facing the observer. This frame sustains a microscope, which is firmly fixed in another frame, that moves in the former by means of grooves, but with a very considerable degree of tightness; the friction of which may be increased by the pressure of four screws. The inner sliding frame, which is likewise of deal, keeps the tube of the microscope in a horizontal position, and in great part without the frame, insomuch that the end which carries the lens is but little within the space. between the frame and the board. This microscope is constructed in such a manner as that the object observed may be an inch distant from the lens; and it has a wire which is situated in the focus of the glasses, in which the objects appeared reversed. At the top of the apparatus there is a piece of deal, an inch and a half thick and two inches broad, laid in a horizontal direction from the board to the top of the frame. To this piece the rods of the different substances, whose expansion by heat is to be measured, are suspended: one end of it slides into a socket, which is cut in the thickness of the board; and the other end, which rests upon the frame, meets there with

a screw which makes the piece move backward and forward, to bring the objects to the focus of the microscope. There is a cork very strongly driven through a hole bored vertically through this piece; and in another vertical hole made through the cork, the rods are fixed at the top; so that they hang only, and their dilatation is not counteracted by any pressure. In order to heat the rods, a cylindrical bottle of thin glass, about 21 inches high, and four inches in diameter, is placed in the inside of the machine, upon a stand independent of the rest of the apparatus. In this bottle the rods are suspended at a little less than an inch distance from one of the insides, in order to have them near the microscope. Into it is poured water of different degrees of heat, which must be stirred about, by moving upwards and downwards, at one of the sides of the bottle, a little piece of wood, fastened horizontally at the end of a stick: in this water is hung a thermometer, the ball of which reaches to the middle of the height of the rods. During these operations the water rises to the cork, which thus determines the length of the heated part; the bottle is covered, to prevent the water from cooling too rapidly at the surface; and a thin case of brass prevents the vapour from fixing upon the piece of deal to which the rods are fixed.

The late Mr. Ferguson also invented two pyrometers, de scriptions and figures of which are given in his Lectures.

Mr. Wedgwood, the ingenious manufacturer of the finest earthenware from basaltic masses, or terra cotta, has contrived a curious pyrometer: he employs small cubes of dry clay; because that species of earth has the remarkable property of contracting in its bulk, when submitted to the fire, and not again expanding on suddenly exposing it to the cold air. In order to ascertain the precise degree of heat in an oven, he puts one of his claycubes into it; and, after having acquired the temperature of the place, he immediately plunges it into cold water. Now, the size of the cube (that was exactly adjusted to half an inch square) is measured between two brass rules, the sides of which are somewhat obliquely disposed, so as to form an inclining groove, into which the cube may be slidden. In proportion as the bulk of the latter has been contracted by heat, it passes down deeper between the scales, on which the various degrees of temperature have been previously marked. Thus, when the division of the scale commences from the point of red heat visible in day-light, and the whole range is divided into 240 equal parts, it will be found that Swedish copper melts at 28; gold at 32; iron at from 130 to 150 degrees: above this point, the cubes could not be heated. But if one of these clay squares be put into an oven where other materials, such as bread, earthen

ware, &c. are to be baked, they may be usefully employed, for regulating the necessary degree of heat.

M. Fourmy has lately given, in the Journal des Mines, a paper "On the Thermometers of baked Earths, termed Pyrometers;" in which he shews that the effect of shrinking, upon which Wedgwood's pyrometer is founded, does not result solely and invariably from the cause to which it is ascribed; that it is not necessarily proportionate to it; that, whatever may be the graduation and the continuity of temperature applied to an aluminous mixt, its shrinking is not only not necessarily graduated, or necessarily continuous, but it also does not always necessarily take place; and therefore that a pyrometer founded upon such shrinking does not afford so constant and accurate a measure for the highest degrees of heat, as the dilatation of mereury or of alcohol does for the lower. A translation of M. Fourmy's observations is inserted in the Repertory of Arts, &c. No. 38. N. S.

RAMSDEN'S MACHINE for dividing MATHEMATICAL INSTRUMENTS is a useful invention, by which these divisions can be performed with exceedingly great accuracy, such as would formerly have been deemed incredible. On discovering the method of constructing this machine, its inventor, Mr. Jesse Ramsden, received 6157. from the commissioners of longitude; engaging himself to instruct a certain number of persons, not exceeding ten, in the method of making and using this machine from the 28th October 1775, to 28th October 1777: also binding himself to divide all octants and sextants by the same engine, at the rate of three shillings for each octant, and six shillings for each brass sextant, with Nonius's divisions to halfminutes, for as long time as the commissioners should think proper to let the engine remain in his possession. Of this sum of 6157. paid to Mr. Ramsden, 300l. were given him as a reward for the improvement made by him in discovering the engine, and the remaining 3157. for his giving up the property of it to the commissioners. The following description of the engine is that given upon oath by Mr. Ramsden himself.

This engine consists of a large wheel of bell-metal, supported on a mahogany stand, having three legs, which are strongly connected together by braces, so as to make it perfectly steady. On each leg of the stand is placed a conical friction pulley, whereon the dividing wheel rests: to prevent the wheel from sliding off the friction-pulleys, the bell-metal centre under it turns in a socket on the top of the stand.

"The circumference of the wheel is ratched or cut (by a method which will be described hereafter) into 2160 teeth, in

which an endless screw acts. Six revolutions of the screw will move the wheel a space equal to one degree.

"Now a circle of brass being fixed on the screw arbor, having its circumference divided into 60 parts, each division will consequently answer to a motion of the wheel of 10 seconds, six of them will be equal to a minute, &c.

"Several different arbors of tempered steel are truly ground into the socket in the centre of the wheel. The upper parts of the arbors that stand upon the plane are turned of various sizes, to suit the centres of different pieces of work to be divided.

"When any instrument is to be divided, the centre of it is very exactly fitted on one of these arbors; and the instrument is fixed down to the plane of the dividing wheel, by means of screws, which fit into holes made in the radii of the wheel for that purpose.

"The instrument being thus fitted on the plane of the wheel, the frame which carries the dividing point is connected at one end by finger screws with the frame which carries the endless screw; while the other end embraces that part of the steel arbor which stands above the instrument to be divided, by an angular notch in a piece of hardened steel: by this means both ends of the frame are kept perfectly steady, and free from any shake. "The frame carrying the dividing-point or tracer is made to slide on the frame which carries the endless screw to any distance from the centre of the wheel as the radius of the instrument to be divided may require, and may be there fastened by tightening two clumps; and the dividing-point or tracer being connected with the clumps by the double-jointed frame, admits a free and easy motion towards or from the centre for cutting the divisions, without any lateral shake.

"From what has been said, it appears that an instrument thus fitted on the dividing-wheel may be moved to any angle by the screw and divided circle on its arbor, and that this angle may be marked on the limb of the instrument with the greatest exactness by the dividing-point or tracer, which can only move in a direct line tending to the centre, and is altogether freed from those inconveniences that attend cutting by means of a straight edge. This method of drawing lines will also prevent any error that might arise from an expansion or contraction of the metal during the time of dividing.

"The screw frame is fixed on the top of a conical pillar, which turns freely round its axis, and also moves freely towards or from the centre of the wheel, so that the screw-frame may be entirely guided by the frame which connects it with the centre: by this means any eccentricity of the wheel and the