radii FA and GA, draw the two arcs AY and AZ which will limit the hour-lines; for in an observation the bead will always be found between them. The forenoon and afternoon hours may then be marked as indicated in the figure. The dial does not of itself discriminate between forenoon and afternoon; but extraneous circumstances, as, for instance, whether the sun is rising or falling, will settle that point, except when close to noon, where it will always be uncertain.
To rectify the dial (using the old expression, which means to prepare the dial for an observation),—open the small door, by turning it about its hinge, till it stands well out in front. Next, set the thread in the line FG opposite the day of the month, and stretching it over the point A, slide the bead P along till it exactly coincides with A.
Fig. 9.
To find the hour of the day,—hold the dial in a vertical position in such a way that its plane may pass through the sun. The verticality is ensured by seeing that the bead rests against the card without pressing. Now gradually tilt the dial (without altering its vertical plane), until the central line of sunshine, passing through the open slit of the door, just falls along the sun-line. The hour-line against which the bead P then rests indicates the time.
The sun-line drawn above has always, so far as we know, been used as a shadow-line. The upper edge of the rectangular door was the prolongation of the line, and, the door being opened, the dial was gradually tilted until the shadow cast by the upper edge exactly coincided with it. But this shadow tilts the card one-quarter of a degree more than the sun-line, because it is given by that portion of the sun which just appears above the edge, that is, by the upper limb of the sun, which is one-quarter of a degree higher than the centre. Now, even at some distance from noon, the sun will sometimes take a considerable time to rise one-quarter of a degree, and by so much time will the indication of the dial be in error.
The central line of light which comes through the open slit will be free from this error, because it is given by light from the centre of the sun.
The card-dial deserves to be looked upon as something more than a mere toy. Its ingenuity and scientific accuracy give it an educational value which is not to be measured by the roughness of the results obtained.
The theory of this instrument is as follows:—Let H (fig. 9) be the point of suspension of the plummet at the time of observation, so that the angle DAH is the north declination of the sun,—P, the bead, resting against the hour-line VX. Join CX, then the angle ACX is the hour-angle from noon given by the bead, and we have to prove that this hour-angle is the correct one corresponding to a north latitude DAC, a north declination DAH and an altitude equal to the angle which the sun-line, or its parallel AC, makes with the horizontal. The angle PHQ will be equal to the altitude, if HQ be drawn parallel to DC, for the pair of lines HQ, HP will be respectively at right angles to the sun-line and the horizontal.
Draw PQ and HM parallel to AC, and let them meet DCE in M and N respectively.
Let HP and its equal HA be represented by a. Then the following values will be readily deduced from the figure:—
PN＝CV＝CX cos ACX＝a cos decl. cos lat. cos ACX.
NQ＝MH＝DH sin MDH＝sin decl. sin lat.
we have, by simple substitution,
a sin alt.＝a sin decl. sin lat. + a cos del. cos lat. cos ACX; or, dividing by a throughout,
| sin alt.＝sin decl. sin lat. + cos decl. cos lat. cos ACX . . . | (1) |
which equation determines the hour-angle ACX shown by the bead.
To determine the hour-angle of the sun at the same moment, let fig. 10 represent the celestial sphere, HR the horizon, P the pole, Z the zenith and S the sun.
From the spherical triangle PZS, we have
ZP＝90°− PR＝90°− latitude
PS＝polar distance ＝90°− declination,
therefore, by substitution
| sin alt.＝sin decl. sin lat. + cos decl. cos lat. cos ZPS . . . | (2) |
and ZPS is the hour-angle of the sun.
Fig. 10.
A comparison of the two formulae (1) and (2) shows that the hour-angle given by the bead will be the same as that given by the sun, and proves the theoretical accuracy of the card-dial. Just at sun-rise or at sun-set the amount of refraction slightly exceeds half a degree. If, then, a little cross m (see fig. 8) be made just below the sun-line, at a distance from it which would subtend half a degree at c, the time of sun-set would be found corrected for refraction, if the central line of light were made to fall on cm.
Literature.—The following list includes the principal writers on dialling whose works have come down, to us, and to these we must refer for descriptions of the various constructions, some simple and direct, others fanciful and intricate, which have been at different times employed: Ptolemy, Analemma, restored by Commandine; Vitruvius, Architecture; Sebastian Münster, Horologiographia; Orontius Fineus, De horologiis solaribus; Mutio Oddi da Urbino, Horologi solari; Dryander, De horologiorum compositione; Conrad Gesner, Pandectae; Andreas Schöner, Gnomonicae; F. Commandine, Horologiorum descriptio; Joan. Bapt. Benedictus, De gnomonum usu; Georgius Schomberg, Exegesis fundamentorum gnomonicorum; Joan. Solomon de Caus, Horologes solaires; Joan. Bapt. Trolta, Praxis horologiorum; Desargues, Manière universelle pour poser l'essieu, &c.; Ath. Kircher, Ars magna lucis et Umbrae; Hallum, Explicatio horologii in horto regio Londini; Joan. Mark, Tractatus horologiorum; Clavius, Gnomonices de horologiis. Also among more modern writers, Deschales, Ozanam, Schottus, Wolfius, Picard, Lahire, Walper; in German, Paterson, Michael, Müller; in English, Foster, Wells, Collins, Leadbetter, Jones, Leybourn, Emerson and Ferguson. See also Hans Löschner, Über Sonnenuhren (2nd ed., Graz, 1906). (H. G.)
DIALECT (from Gr. διάλεκτος, conversation, manner of speaking, διαλέγεσθαι, to converse), a particular or characteristic manner of speech, and hence any variety of a language. In its widest sense languages which are branches of a common or parent language may be said to be “dialects” of that language; thus Attic, Ionic, Aeolic and Doric are dialects of Greek, though there may never have at any time been a separate language of which they were variations; so the various Romance languages, Italian, French, Spanish, &c., were dialects of Latin. Again, where there have existed side by side, as in England, various branches of a language, such as the languages of the Angles, the Jutes or the Saxons, and the descendant of one particular language, from many causes, has obtained the predominance, the traces of the other languages remain in the “dialects” of the districts where once the original language prevailed. Thus it may be incorrect, from the historical point of view, to say that “dialect” varieties of a language represent degradations of the standard language. A “literary” accepted language, such as modern English, represents the original language spoken in the Midlands, with accretions
