and to be complete across the whole area of 12 cm. by 5, across which the heat was conducted in that part of the composite slab; and to give rise to palpably imperfect fitting together of the solid above and below it. We therefore repeated the experiment with the composite slab turned upside down, so as to bring the crack in one half of it now to be above the middle, instead of below the middle, as at first. We still found for the composite slab less conductivity in the hot part below the middle than in the cool part above the middle. We inferred that, in respect to thermal conduction through slate across the natural cleavage planes, the thermal conductivity diminishes with increase of temperature.

§ 5. We next tried a composite square slab of sandstone of the same dimensions as the slate, and we found for it also decisive proof of diminution of thermal conductivity with increase of temperature. We were not troubled by any cracking of the sandstone, with its upper side kept cool by an ice-cold metal plate resting on it, and its lower side heated to probably as much as 300° or 400° C.

§ 6. After that we made a composite piece, of two small slate columns, each 3.5 cm. square and 6-2 cm. high, with natural cleavage planes vertical, pressed together with thermoelectric junctions as before; but with appliances (§ 10 below) for preventing loss or gain of heat across the vertical sides, which the smaller horizontal dimensions (7 cm., 3.5 cm.) might require, but which were manifestly unnecessary with the larger horizontal dimensions (25 cm., 25 cm.) of the slabs of slate and sandstone used in our former experiments. The thermal flux lines in the former experiments on slate were perpendicular to the natural cleavage plaues, but now, with the thermal flux lines parallel to the cleavage planes, we still find the same result, smaller thermal conductivity at the higher temperatures. Numerical results will be stated in § 12 below.

§ 7. Our last experiments were made on a composite piece of Aberdeen granite, made up of two columns, each 6 cm. high and 76 cm. square, pressed together, with appliances similar to those described in § 6; and, as in all our previous experiments on slate. and sandstone, we found less thermal conductivity at higher temperatures. The numerical results will be given in § 12 below.

§8. The accompanying diagram represents the thermal appliances and thermoelectric arrangement of §§ 6, 7. The columns of slate or granite were placed on supports in a bath of melted tin with about 0-2 cm. of their lower ends immersed. The top of each column was kept cool by mercury, and water changed once a minute, as described in § 3 above, contained in a tank having the top of the stone column for its bottom and completed by four vertical metal walls fitted into grooves in the stone and made tight against wet mercury by marine glue.

F. Junctions of platinoid and copper wires. The wires are insulated from one another, and wrapt all together in cotton wool at this part, to secure equality of temperature between these four junctions, in order that the current through the galvanometer shall depend solely on differences of temperature between whatever two of the four junctions, X, T, M, B, is put in circuit with the galvanometer.

G. Galvanometer.

pair of thermoelectric junctions.

x, b, m, t, are connected, through copper and platinoid, with X, B, M, T, respectively.

$9. The temperatures, v(B), v(M), v(T) of B, M. T, the hot, intermediate, and cool points in the stone, were determined by equalising to them successively the temperature of the mercury thermometer placed in the oil-tank, by aid of thermoelectric circuits and a galvanometer used to test equality of temperature by nullity of current through its coil when placed in the proper circuit, all as shown in the diagram. The steadiness of temperature in the stone was tested by keeping the temperature of the thermometer constant, and observing the galvanometer reading for current when the junction in the oiltank and one or other of the three junctions in the stone were placed in circuit. We also helped ourselves to attaining constancy of

temperature in the stone by observing the current through the galvanometer, due to differences of temperature between any two of the three junctions B, M, T placed in circuit with it.

§ 10. We made many experiments to test what appliances might be necessary to secure against gain or loss of heat by the stone across its vertical faces, and found that kieselguhr, loosely packed round the columns and contained by a metal case surrounding them at a distance of 2 cm. or 3 cm., prevented any appreciable disturbance due to this cause. This allowed us to feel sure that the thermal flux lines through the stone were very approximately parallel straight lines on all sides of the central line BMT.

§ 11. The thermometer which we used was one of Cassella's (No. 64,168) with Kew certificate (No. 48,471) for temperature from 0° to 100°, and for equality in volume of the divisions above 100°. We standardised it by comparison with the constant volume air thermometer of Dr. Bottomley with the following result. This is satisfactory as showing that when the zero error is corrected the greatest error of the mercury thermometer, which is at 211°C., is only 0.3°.

§ 12. Each experiment on the slate and granite columns lasted about two hours from the first application of heat and cold; and we generally found that after the first hour we could keep the temperatures of the three junctions very nearly constant. Choosing a time. of best constancy in our experiments on each of the two substances, slate and granite, we found the following results: :

Slate flux lines parallel to cleavage.

:

v(T) = 50°2 C.

v(M) = 123°3.

v(B) =202°.3.

* 'Phil. Mag.,' August, 1888, and 'Edinb. Roy. Soc. Proc.,' January 6, 1888.

The distances between the junctions were BM = 2:57 cm. and MT = 26 cm. Hence by the formula of § 2,

The distances between the junctions were BM = 1.9 cm. and MT = 2.0 cm.

§13. Thus we see, that for slate, with lines of flux parallel to cleavage planes, the mean conductivity in the range from 123° C. to 202° C. is 91 per cent. of the mean conductivity in the range from 50° C. to 123° C., and for granite, the mean conductivity in the range from 145° C. to 214° C. is 88 per cent. of the mean conductivity in the range from 81° C. to 145° C. The general plan of apparatus, described above, which we have used only for comparing the conductivities at different temperatures, will, we believe, be found readily applicable to the determination of conductivities in absolute

measure.

II. "The Kinematics of Machines." By T. A. HEARSON, M.Inst.C.E., Professor of Mechanism and Hydraulic Engineering, Royal Indian Engineering College, Coopers Hill. Communicated by Professor COTTERILL, F.R.S. Received March 19, 1895.

(Abstract.)

In this paper the author regards a machine as an embodiment of a movement. The method of construction and the proportions of the parts are not taken into consideration, except so far as may be necessary to explain the conditions requisite for the kinds of motions with which they are supposed to be endowed. All other considerations relating to form and proportion are omitted, as belonging to the subject of machine design. Neither does the author take account of the forces which actuate and oppose the movement of the machine, such matters belonging to the subject Dynamics of Machines.

The object of the paper is to analyse the movements only, and to

show the likeness and the differences between machines in similarities in the movements or the contrary.

It is claimed by the author that in those movements the principal feature of a machine resides, distinguishing it from other engineering constructions.

It is shown that all movements, however complex, are derived from the association together of some of a comparatively limited number of kinds of more or less simple motions, which take place between consecutive directly connected pieces.

Certain geometrical laws are enunciated, from which are derived the conditions necessary for the association of those motions together in one machine. It is shown that those laws preclude the existence of certain combinations of motions, and it is suggested that one may be enabled by this analysis to enumerate an exhaustive list of the possible combinations which must include all existing machines, and suggest the design of others not in existence. Moreover, by attaching to each kind of motion a suggestive symbol, a method of expressing the constitution of a machine movement by a simple formula is proposed, whereby similarities and differences between machines may be exhibited at a glance.

The author commences by considering a very simple mechanism, consisting of four bars united in one continuous linkage by four pins which have parallel axes. By imagining the length of the links to undergo variation from zero to infinity, it is shown that this simple mechanism is representive of all the simple plane mechanisms, and, by imagining other variations to occur, this same mechanism is shown to be representive of still further classes of mechanisms, in which the parts do not move in or parallel to one plane. In this simple mechanism the relative motions of consecutive pieces are either turning, when one piece revolves completely around relatively to the other, the representative symbol being the letter O, or swing. ing when one piece turns through a limited angle relatively to the adjoining one, represented by the letter U.

The first law enunciated, which governs the association of the O and U motions, is founded on the geometrical fact that the sum of the three angles of a plane triangle is constant, and the sum of the four angles of the quadrilateral therefore also constant. After a complete revolution the angle between the bars is considered to have been increased or diminished by 27. With this extension of the proposition the constancy of the sum of the angles is unimpaired.

From this it is seen to be impossible for only one motion to be turning and the other three swinging, otherwise the sum of the four angles would increase or decrease by 2# each revolution.

The second law, which governs the association of the motions, has to do with the proportions between the length of the links necessary