Zone, are shorter than the long periods of sun-light; the sun spending fewer days in the southern portion of the zodiac. (Prob. XI., Examples 5 and 6). How far the obliquity of the ecliptic to the equinoctial interferes to produce a disagreement between the sun-dial and the clock, may be understood in solving, by the globe, such questions as those which are contained under the next problem.

PROBLEM XIII.

CELESTIAL GLOBE.

To find that portion of the equation of time which results from the obliquity of the ecliptic.

Repeat sidereal day, (def. 83); Solar day, (def. 84); Apparent noon, (def. 85); True or mean noon, (def. 86); Equation of time, (def. 87), reading its note.

RULE. Find the sun's place, in the ecliptic, bring it to the brass meridian, and count the number of degrees from the first point of Aries to the brass meridian on the equinoctial and on the ecliptic: the difference, reckoning four minutes of time to a degree, is this portion of the equation of time. If the degrees on the ecliptic exceed, the sun is faster than the clock: if the degrees of the ecliptic are deficient, the sun, (as far as this circumstance is concerned,) is slower than the clock.

1. When the sun has no declination, (i. e. at the equinoxes,) it is evident that, as far as the obliquity of the ecliptic is concerned, sun-dials and clocks agree: but supposing that from the 21st March until the 19th April the sun had proceeded 30° in the equinoctial instead of in the ecliptic, how much later (in absolute time) would he have come to any meridian on that day?

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2. How much sooner (regarding the absolute duration of time) is the sun on our meridian on the 5th June, than he would have been had he fulfilled his 75° of apparent motion (from the 21st March to that date) in the equinoctial line?

3. Does the sun, on the 10th July, come to the meridian before or after the time at which he would have come to it, had he, from the 21st March, performed his apparent course of 108° in the equinoctial: i. e. had the earth's axis been perpendicular to the plane of its orbit?

4. What is this portion of the equation of time on the 6th and 28th September, 1st November, 21st December, and 16th February?

5. Refer to the note to definition 87, and find, by the globe, what portion of the equation of time is due to the obliquity of the ecliptic, and what portion, consequently, is due to the unequal rate of the earth's orbitual revolution, on the 1st September, the 1st November, (a) and the 12th February.

PROBLEM XIV.

CELESTIAL GLOBE.

The latitude, day, and hour being given, to find the azimuth or bearing of the sun or of a star, and its altitude.

Conversely. To find the hour of a certain day, and the altitude of the sun, or of a star, the azimuth and latitude being given.

RULE.-Rectify the globe for the latitude: bring the sun's place for the last noon to the meridian, and set the index of the hour circle to 12. Turn the globe until the index have passed over the number of hours elapsed since the last noon; and the quadrant, affixed to the zenith and

(a) Since, from both causes, the sun dial is minutes faster than the clock (as given in that definition) and since the sun is only minutes faster in consequence of the obliquity of the ecliptic; it is evident that the remainder is owing to the other cause.

made to pass over the sun's place, or the star, will show its altitude on the graduated edge, and its azimuth where the graduated edge cuts the horizon.

Conversely. The pole being elevated to the latitude, and the sun's place being brought to the meridian for setting the index to noon,-let the quadrant be made to cut the horizon in the given azimuth: then, the sun's place, or the star, being brought to coincide with its graduated edge, it will point out the altitude, whilst the index is showing the hour.

*** At noon and midnight the azimuth of the sun is nothing. At any time after culminating the altitude and azimuth of the sun, or of a star, are such as they were at a corresponding interval before culminating, so that the pupil may always find the azimuth and altitude of the sun for a morning hour by taking those of the corresponding afternoon hour. It is true the sun's motion in the ecliptic, and, consequently, his change of declination are going on; but they are insignificant for so small a portion of time.

1. Find the azimuths and altitudes of Algol (8 Persei) and Vega (a Lyræ) at 24m. past 5 P. M. of the 25th November at Edinburgh.

Find the altitudes and azimuths of the sun as required below:

2. Madrid, 28th July or 15th May, at half past 3 P. M. and half past 8 a. m.

3. London, 19th November or 22d January, at three quarters past 1 P. M. and a quarter past 10 A. M.

4. Cape of Good Hope, 19th November or 22d January, at three quarters past 1 P. M. and a quarter past 10 a. м.

"I well remember going on deck with a certain flutter of spirits to see, for the first time in my life, the sun to the northward, and moving from right to left, instead of left to right. No one doubts that the earth is round; yet these conspicuous and actual proofs of its rotun dity always amuse the fancy and frequently interest the judgment.** "At one time the sun, even at noon, was seen creeping stealthily along, low (a) down in the horizon, at another his jolly countenance was

(a) That is when the ship was yet in the high latitudes.

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blazing away right over head. On the 5th May when our latitude was 17° north, the sun's declination was 161°. * * * Shadows

we had none." Capt. Hall's Fragments, Vol. 1, 2d Series, p. 149.

"The gradual rise, night after night, of new stars and constellations, belongs to a still higher order of curiosity; for it not merely places well known objects in strange positions; but brings totally new objects of contemplation before our eyes." Ibid.

5. What are the azimuths and altitudes of a of Crux, Canopus, Sirius, and Rigel, at Swan River (Western Australia) lat. 32° S., at three quarters past 9 P. M. 16th February?

6. Latitude 744° south on 13th December. Find the azimuths and altitudes of the sun at noon, (b) at 10 P. M., at midnight, and at 2 A. M. of the next day.

Any heavenly body having more degrees of declination in the same hemisphere with a given place than correspond to the latitude of that place, will have the same azimuth or bearing twice before and twice after it culminates. Hence the sun, during several days of the year, when to the north of places lying between the northern tropic and the equator, will appear at those places on the same point of the compass twice in the forenoon and twice in the afternoon; and the shadow of any church-spire or other perpendicular object must consequently "go back;" retracing, for instance, a part of the progress which it made from the south towards the west, whilst the sun was making his way from the north towards the east; as his bearing from the north becomes less again before he culminates.

Had the "sun-dial of Ahaz," (Isaiah xxxviii.) been situated in the torrid zone, instead of at Jerusalem, (latitude 32° N.) the circumstance of the shadow of some of its "degrees" being brought back, would not, at a certain time of year, have been miraculous. The astronomical Babylonian princes sent ambassadors to Hezekiah quire of the wonder that was done in the land" on occasion of that king's recovery from sickness.

Conversely.

7. Greenwich, 1st January.

"to en

What is the hour at which Dubhe (a Ursa Majoris) has azimuth 35° north towards

(7) Here the sun was north at noon and south at midnight.

east; and at what time and with what altitude will it again have the same azimuth before it culminates ?

8. My garden wall, at Blackheath, stretches 20° north of west at what hour on the 21st of June does the sun begin (a) to shine on the grape vine trained over its southern face; and during how many hours does it shine upon it on that day, there being no impediments?

9. In latitude 35° north, on the 23rd September, at what hour will Capella bear exactly north-east; and at what hour, and with what altitude, will it again have the same bearing before it culminates ?

10. At what hour on the 1st July will the sun first appear east-north-east at Port Royal, Jamaica, and at what hour of that day will he again have this bearing, after having cast shadows to the north of west-south-west?

11. At Lima, on the 20th January, at what hour of the morning will the sun cast shadows 70° from the north towards the west, and at what time will shadows again have this bearing, after having been directed farther towards the south?

12. At 3 o'clock P. M. of the 16th January, in a certain longitude on the parallel of 40° south, I observed the sun's " magnetic azimuth" to be 90°, or due west: how far was the sun, really, at that time, from this prime vertical (b); and how much, and in what direction, did my azimuth compass vary from the true meridian in that situation?

PROBLEM XVI.

TERRESTRIAL GLOBE.

which

Having the latitude, to find the two days of the year are of a given length, and in what time that length of day is altered by a certain quantity.

Repeat again definitions 8, 13, 19, 11, 14, 33, 34.

(a) It is evident that the sun will begin to shine on this wall when his azimuth is opposite the other end, viz. 20° S. of E. or more properly 70° E. of S.

(b) The azimuth arc passing through the east or west is called the Prime Vertical.