LAT . XI. A.M. X. A.M. IX. A.M. VIII. A.M. VII. A.M. VI.

A. M. 1111. P.M. I. P.M. II. P.M. III. P.M. V. P.M.

VI. P.M 50° 0' 11° 36' ~3° 51' 37° 27 53° 0' 70° 43, 90° 0' 50 30 II 41 24 I 37 39 53 12 70 51 90 0 51 0 II 46 24 10 37 51 53 23 70 59 90 0 51 30 II 51 24 19 38 3 53 35 71 6 90 0 52 0 II 55 24 28 38 14 53 46 71 13 90 0 52 30 12 0 24 37 38 25 53 57 71 20 90 0 53 0 12 5 24 45 38 37 54 8 71 27 90 0 53 30 12 9 24 54 38 48 54 19 71 34 90 0 54 0 12 14 25 2 38 58 54 29 7i 40 90 0 54 30 12 18 25 10 39 9 54 39 71 47 90 0 55 0 12 23 25 19 39 19 54 49 71 53 90 0 55 30 12 27 25 27 39 30 54 59 71 59 90 0 56 0 12 31 25 35 39 40 55 9 72 5 90 0 56 30 12 36 25 43 39 50 55 18 72 II 90 0 57 0 12 40 25 50 39 59 55 27 72 17 90 0 57 30 12 44 25 58 40 9 55 36 72 22 90 0 58 0 12 48 26 5 40 18 55 45 72 28 90 0 58 30 12 52 26 13 40 27 55 54 72 33 90 0 59 0 12 56 26 20 40 36 56 2 72 39 90 0 59 30 13 0 26 27 45 45 56 II 72 44 90 0 See also:

• VERTICAL (from Lat. vertex, highest point)

There is no See also:

• NECESSITY (Lat. necessitas)

Equatorial Dial.—The name equatorial dial is given to one whose plane is at right angles to the style, and therefore parallel to the See also:

• EQUATOR (Late Lat. aequator, from aequare, to make equal)

TRIAL). With all these elements of uncertainty, it is obvious that the compass can only give a rough approximation to the position of the meridian, but it will serve to See also:

• FIX, THEODORE (180o-1846)

FDB, approaching the point H as the sun advances towards noon, and reced - See also:

• ING

The most favourable times are at the end of See also:

• JUNE

The Pole See also:

• STAR

In all these cases it will be convenient, instead of fixing the plane by means of the eye and one fixed plummet, to have a second plummet at a See also:

• SHORT, FRANCIS JOB (1857– )

At some time in the morning, when the sun is high enough to be free from the mists and uncertain refractions of the horizon—but to ensure accuracy, while the See also:

• RATE

Instead of hour-lines they had hour-points; and the style, instead of being parallel to the axis of the earth, might make any chosen angle with the horizon. There was no practical See also:

• ADVANTAGE

The observations must not be made within a couple of hours of noon, on account of the slow rate of change at that time, nor too near the horizon, on account of the uncertain refractions there ; and the same restrictions must be observed in using a portal !e dial. To compare roughly the accuracy of the fixed and the portable dials, let us take a mean position in Great See also:

• BRITAIN (Gr. Hperavuml vi7vot, Bperravia; Lat. Britannia, rarely Britannia)

Suppose that the observations are continued all day, the cylinder being very gradually turned so thzt the style may always face the sun, and suppose that marks are made on the vertical line to show the extremity of the shadow at each exact hour from sunrise to sunset—these times being taken from a good fixed sun-dial,—then it is obvious that the next year, on the same date, the sun's declination being about the same, and the observer in about the same latitude, the marks made the previous year will serve to tell the time all that day. What we have said above was merely to make the principle of the instrument clear, for it is evident that this mode of marking, which would require a whole year's See also:

• SUNSHINE

It is not even requisite that the divisions should go completely and exactly round the cylinder, although they were always so drawn, and both these conditions were insisted upon in the directions for the construction. card (fig. 8) and another DCE at right angles to it ; with C as centre, and any convenient See also:

• RADIUS

Now, taking a second year after leap year (because the declinations of that year are about the mean of each set of-foul years), find the days of the month when the sun has these different declinations, and place these dates, or so many of them as can be shown without confusion, opposite the corresponding marks on FDG. Draw the sun-line at the top of the card parallel to the line ACB ; and, near the extremity, to the right, draw any small figure intended to See also:

• FORM (Lat. forma)

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 W FIG. 9. 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 See also:

• CAST (from the verb meaning " to throw "; the word is Scand. in origin, cf. Dan. kaste, and Swed. kasta; " cast " in Middle Eng. took the place of the A.S. weor pan, cf. Ger. werf en)

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 DAHis 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: AD = a cos decd. DH =a sin decl. PQ =a sin alt. CX = AC = AD cos lat. = a cos See also:

• DECK

PN = CV = CX cos ACX = a cos decd. cos lat. cos ACX. N =MH=DH sin MDH=a sin decl. sin lat. '. the angle MDH = DAC = latitude.) And since PQ=NQ+PN, we have, by simple substitution, a sin alt. = a sin decl. sin lat. +a cos decd. cos lat. cos ACX ; or, dividing by a throughout, sin altr=sin decd. sin lat.+cos decl. cos lat. cos ACX . . (I) 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. io represent the celestial sphere, HR the horizon, P the pole, Z the zenith and S the sun. From the spherical triangle PZS, we have cos ZS=cos PS cos ZP+sin PS sin ZP cos ZPS but ZS = zenith distance 90°—altitude ZP =9o°— PR = 90°—latitude PS= polar distance =9o°— declination, therefore, by substitution sin alt. sin decd. sin lat.+cos decl. cos lat. cos ZPS . (a) and ZPS is the hour-angle of the sun. A comparison of the two formulae (I) 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.