only fhew the hour during the fpring and summer season. And again, as the fun only illumines the lower furface of an equinoctial plane, while he is in the fouthern hemisphere, or on the other fide of the equator, a lower equinoctial dial will only fhew the hour in autumn and winter. To have an equinoctial dial therefore that fhall ferve all the year round, the upper and lower must be joined together; that is, it must be drawn on each fide of the plane.

This diagram, it is to be obferved, reprefents only the diatonic genus, where the notes or founds are by no means diftinct, the paranete fynemmenon coinciding with the trite diezeugmenon, and the nete fynemmenon with the paranete diezeugmenon. It is also obferv able, that fome of the notes ftand nearer together than the reft; the interval between the latter being a tone, and between the former only a femitone. See the article INTERVAL. DIAGRYDIUM, in pharmacy, a preparation of feammony, invented by Galen: it confifts in baking the fcammony in a quince, but is at prefent feldom ufed, the fcammony being found not to need any correction. See the article SCAMMONY.

DIAHEXAPLA, or DÍAHEXAPTE, ámong farriers, a compound medicine, fo called from its containing fix ingredients, viz. birthwort and gentian roots, juniper-berries, bay-berries, myrrh, and ivory fhavings. It is commended for colds, confumptions, pursiness, and many other disorders in horses.

DIAL, or SUN-DIAL, an inftrument ferving to measure time by means of the fhadow of the fun.

Sun-dials are differently denominated according to their different fituation, and the figure of the furfaces upon which they are described, as horizontal, vertical, equinoctial, polar, direct, erect, declining, inclining, reclining, cylindrical, &c. We fhall here proceed to defcribe these particular kinds of dials; and explain the philofophical principles on which dialing is founded under the article DIALING.

Dials are distinguished into primary and fecondary.

Primary DIAL, that either drawn on the plane of the horizon, called an horizontal dial; or perpendicular thereto, on the planes either of the meridian, or prime vertical, called a vertical dial; to which are added those drawn on the polar and equinoctial planes, though neither horizontal nor vertical.

Equinoctial DIAL, is that described on an equinoctial plane, or a plane reprefenting that of the equinoctial. They are ufually diftinguished into upper, which look towards the zenith, and lower, which respect the nadir. Now as the fun only illumines the upper furface of an equinoctial plane, while he is in our hemifphere, or on the northern fide of the equator, an upper equinoctial dial will

To defcribe an upper equinoctial DIAL. From a center C (plate LXX, fig. 3. no 1.) describe a circle A B D E, and by two diameters A D and BE, interfecting each other at right angles, divide it into quadrants A B, BD, DE and E A. Subdivide each quadrant into fix equal parts by the right lines, C1, C1, Cш, &c. which lines will be hour lines, and thro' the center C drive a ftyle or pin perpen dicular to the plane ABDE. The dial thus defcribed being raised fo as to be in the plane of the equator, the line CxII, in the plane of the meridian, and the point A looking towards the fouth; the fhadow of the ftyle will thew the hours both of the forenoon and afternoon.

A lower equinoctial DIAL is defcribed in the fame manner, with this exception, that no hour lines are to be drawn beyond that of fix o'clock.

To defcribe an univerfal equinoctial DIAL: join two metal planes ABCD and CDEF, (ibid. n° 2.) fo as to be moveable at the joint. On the upper furface of the plane ABCD defcribe an upper equi. noctial dial; and upon the lower, a low. er, as already directed, and through the center I, drive a ftyle. In the plane DEFC cut a box, and put a magnetical needle G therein; fit on the fame plane a brass quadrant LH, nicely graduated, and paffing through a hole H cut in the plane ABCD. Now fince this may be fo placed by means of the needle, as that the line I r2 fhall be in the plane of the meridian, and by means of the quadrant fo raifed, as that the angle BCF fhall be equal to the elevation of the equator, it will ferve as a dial in any part of the world. On this dial may be drawn feveral concentric circles, which will fhew the fun's place and declination. Thus divide the style into 100 parts, which being the radius of a circle, take the complement of the declination 5°, 10°, 15°, &c, and with the tangent

of thefe degrees defcribe concentric circles, and when the end of the fhadow of the ftyle comes into one of them, it fhews the declination and the fun's place, which may be marked on the circles. Horizontal DIAL, that described on a plane parallel to the horizon.

To draw the bour lines upon an horizontal DIAL, geometrically, draw a right line NS (ibid. n° 3.) for the meridian and hour line of 12, and crofs it with another E W, for the hour line of 6 at right angles in Z and upon Z as a center defcribe a circle ENWS, representing the horizon, of London, for example, whofe latitude is 51° 32', and likewife this dial plane. Within this circle projet the fphere according to your latitude: then fhall the feveral hour circles touching the plane of the horizon give you points to draw the hour lines upon your dial plane. If a ruler therefore is laid to Z, and every one of the points 1, 2, 3, &c. 11, 10, 9, &c. and straight lines drawn, thefe lines fhall be the true hour lines for your horizontal dial. There is nothing required to compleat this dial but to make the height of the Ryle equal to the latitude of the place. Wherefore for the latitude of London take 51° 32′ from your fcale of chords, and fet them upon the horizon from S to A, and draw a line Z A for the style. This fubftyle, upon which the ftyle stands in all horizontal dials, is the meridian, or hour line of 12.

In large dials, where great accuracy is required, it is beft to determine the lines of the dial by trigonometrical calculation, in which the elevation of the pole of the place being given, the angles which the hour lines make with the meridian in the center of the dial are found by the following canon. As the fine of 90°, is to the line of the elevation of the pole or latitude of the place; fo is the tangent of each hour's equinoctial diftance from the meridian, to the tangent of the angle required.

Vertical DIAL, that drawn on the plane of

a vertical circle. The verticals chiefly ufed are the prime vertical and the meridian, whence arife fouth, north, east, weft dials. If the dial refpects the cardinal points of the horizon, it is called direct, but if any other vertical be chofen, it is faid to decline. Again, if the circle whofe plane is ufed be perpendicular to the horizon, the dial is denominated erect;

but if the plane be oblique to the horizon, it is faid to incline or recline. Erelt, direct, fouth or north DIAL, is that defcribed on the furface of the prime vertical circle, looking fouthward or northward.

To defcribe the hour lines upon a vertical erect, direct, fouth or north DIAL. Having drawn a right line N S, (ibid. n° 4. and 5.) for the meridian, or line of 12, and another at right angles EW, for the horizontal line of the plane, croffing in the point Z; upon Z as a center, defcribe a circle NESW reprefenting the horizon, and thereon project the sphere. Then draw a line upon your projection to reprefent your plane. Now an erect direct plane, which beholds the south, must needs be in the azimuth circle of east and weft, and therefore a right line drawn from east to west fhall reprefent your plane. Having drawn the plane upon the projection, you must find its pole. Now, this plane EW lying in the azimuth of eaft and weft, its poles muft lie in the azimuth of north and fouth, fo that N is the pole of the north face of this plane, and S of the south face, either of which poles are removed 90 degrees from the plane, and a line drawn from the one pole to the other, will cut the plane at right angles in Z. The next thing to be found is the ele vation of the pole of the world above the plane. Now P the pole of the world is elevated above this plane EW the quantity of the arch of the meridian Z P. To find the quantity of which, take the distance ZP in your compaffes, and measure it upon the fcale of half tangents, and you will find it to be equal to the complement of the latitude. Then as for the hour distances upon the plane, they are found thus. Lay a ruler to N, the pole of the plane, and to the feve ral points 1, 2, 3, &c. 11, 10, 9, &c. where the hour circles of the projection cut the plane, and where the ruler cuts the primitive circle make fmall *** and lines drawn from the center Z, through thefe ftars, fhall be the true hour lines upon the dial plane. The height of the pole above the plane being equal to the complement of the latitude, take that in degrees from a fcale of chords and fet them from S to B, and draw a line Z B for the ftyle, which muft ftand upon the meridian, and on the south face must point downwards to the fouth

pule,