DIAL and DIALLING. Dialling, sometimes called gnomonics, is a See also:

• BRANCH (from the Fr. branche, late Lat. branca, an animal's paw)

The Arabians, as appears from the See also:

• WORK

This is a regular octagon, on the faces of which the eight See also:

• PRINCIPAL

Where or when the great and important step already conceived by Abu'l Hassan, and perhaps by others, of reckoning by equal hours was generally adopted cannot now be determined. The history of gnomonics from the 13th to the beginning of the 16th century is almost a See also:

• BLANK (from the Fr. blanc, white)

The See also:

• ART

Four times a year the clock and the sun-dial agree exactly; but the sun-dial, now going a little slower, now a little faster, will be sometimes behind, sometimes before the clock—the greatest accumulated difference being about sixteen minutes for a few days in See also:

• NOVEMBER (Lat. novem, nine)

The style itself will beusually a stout See also:

• METAL
• METAL (through Fr. from Lat. metallum, mine, quarry, adapted from Gr. µATaXAov, in the same sense, probably connected with ,ueraAAdv, to search after, explore, µeTa, after, aAAos, other)

The ancients, with the means at their disposal, could obtain these results only very roughly. Dials received different names according to their position:—Horizontal dials, when traced on a horizontal plane; Vertical dials, when on a vertical plane facing one of the cardinal points; Vertical declining dials, on a vertical plane not facing a cardinal point ; Inclining dials, when traced on planes neither vertical nor horizontal (these were further distinguished as reclining when leaning backwards from an observer, proclining when leaning forwards); Equinoctial dials, when the plane is at right angles to the earth's axis, &c. &c. Dial Construction.—A very correct view of the problem of dial construction may be obtained as follows: Conceive a transparent See also:

• CYLINDER (Gr. KvAwSpos, from KvXivaety, to roll)

. . I at one hour after noon, on II . II at two hours after noon, and so on. If now the cylinder be cut by any plane MN representing the plane on which the dial is to be traced, the shadow of AB will be intercepted by this plane and fall on the lines AXII AI, AII, &c. The construction of the dial consists in determining the angles made by Al, All, &c. with AXII ; the line AXII itself, being in the vertical plane through AB, may be supposed known. For the purposes of actual calculation, perhaps a transparent See also:

• SPHERE (Gr. vclsa?pa, a ball or globe)

. . . These will exactly correspond to the equidistant generating lines on the cylinder in the previous construction, and the shadow of the style will fall on these circles after successive intervals of 1, 2, 3, &c., hours from noon. If they meet the horizontal circle in the points B, C, D, &c., then EB, EC, ED, &c.... will be the I, I I, III, &c., hour-lines required ; and the problem of the horizontal dial consists in calculating the angles which these lines make with the XII o'clock line EA, whose position is known. The spherical triangles FAB, PAC, &c., enable us to do this readily. They are all right-angled at A, the side PA is the latitude of the place, and the angles APB, APC, &c., are respectively 15° 30°, &c., then tan AB =tan 15° See also:

• SIN
• SIN (O. Eng. syn: a common Teutonic word, cf. Dutch zonde, Ger. Siinde)

Therefore the hour-lines between VI in the evening and VI the next morning are the prolongations of the remaining twelve. Let us now remove the imaginary sphere with all its circles, and retain only the style EP and the plane HMA with the lines traced on it, and we shall have the horizontal dial. On the longest day in London the sun rises a little before 4 o'clock, and sets a little after 8 o'clock; there is therefore no See also:

• NECESSITY (Lat. necessitas)

3). The line of demarcation between the shadow and the See also:

• LIGHT

If a series of such dials were constructed, differing by 30 m. in latitude, then an intending purchaser could select one adapted to a place whose latitude was within 15 m. of his own, and the error of time would never exceed a small fraction of a minute. The following table will enable us to check the accuracy of the hour-lines and of the angle of the style,—all angles on the dial being readily measured with an ordinary protractor.