PERIODS OF CONTINUOUS SUNLIGHT, ETC. 137 15. On what day does the sun cease to give twilight to the North Pole, and on what day does twilight begin again? (1) PROBLEM XI. TERRESTRIAL GLOBE. A number of days being given during which the sun is above the horizon or below it in the Frigid Zones, to find the latitude and the places. Learn "climate" (def. 80.) We have seen (particularly from Examples 1 and 9 of the last problem) that if a heavenly body have declination equal to the co-latitude of a place, it cannot rise, or cannot set there, according as the declination has, or has not, the same name with the latitude. The 21st June and the 21st December are the days of greatest declination of the sun; on these two days, therefore, either he is at his greatest elevation or at his lowest depression in the Frigid Zones; they are the middle days of the long period of light or of darkness. Hence For the long period of sun-light. RULE.-Take half the number of days, and reckon them from the 21st of June: that declination of the sun which answers to the last day will give the co-latitude. For the long period of the sun's absence. Reckon half the number of days from the 21st of December, and the declination of the sun answering to the last day will give the co-latitude. The latitude may be found by subtracting the co-latitude from 90°; or the places may be seen as they pass (!) It must be remembered, that the equinoctial coincides with the horizon of the north pole, and that, consequently, the sun's depression at any date of the winter period, is equal to his declination. below the pole, the under semi-circle of the brass meridian being graduated for co-latitude. * **If these periods be required for the South Frigid Zone, for 21st June read 21st December. 1. In what part of the North Frigid Zone have the inhabitants, if there be any, constant sun-light for 158 days? Here, (half the number of days being 79,) the 9 days remaining in June, the 31 of July, the 31 of August and the first 8 of September will make up the half period, and point out the declination of the sun, when he sets, to be 51° north; hence the latitude must be 8410. 2. In what part of the North Frigid Zone are the inhabitants, if there be any, deprived of sun-light for 149 days? * 3. In what part of the South Frigid Zone would the sun be absent during exactly 103 days, if the refraction of the atmosphere did not cause his disk to appear for some days above the horizon when he is really below it? 4. In what latitude of the South Frigid Zone would the sun be present exactly 97 days, if the same circumstance did not lengthen the period of his constant appearance? 5. In what latitude, north, is the sun above the horizon during 133 rotations of the earth about its axis? (m) 6. In what latitude, north, is the sun totally absent whilst the earth is turning on its axis 126 times? 7. Find the latitudes (and any places situated in them) which are the boundary latitudes of the month climates; i.e. those latitudes which have their long periods of sun-light one, two, three, four, and five months, reckoning 30 days to the month? Conversely-8. By how many days does the period of the sun's constant presence at the north pole exceed that of his absence, whilst above the horizon of the south pole? * If the number of days given be uneven, the 21st December or the 21st June need not be included. (m) The pupil is requested to note any remarkable coincidence that may present itself in answering these questions. CLIMATES. 139 PROBLEM XII. TERRESTRIAL GLOBE. To find what places are situated in a given climate. Conversely. To find the climate in which a given place is situated. Repeat Zones, (def. 71); with the smaller print following that definition. Since the climates of the Torrid and Temperate Zones are divisions in latitude depending on the half-hours of their longest day, and the sun sets so much after 12 as it rises before 12; the sun-set of the longest day in any one of these climates must differ exactly a quarter of an hour from that of the climate to the north or to the south of it. We have learned that the length of any given day depends entirely upon latitude: hence any meridian may serve to mark the boundaries of these climates, in the following manner; For the Northern Hour Climates. Elevate the north pole 234°, (the declination of the sun on the longest day); bring that portion of the first meridian* which cuts the equator, to the east of the terminator, and set the index to 6, (the invariable time of sun-set there.) Turn the globe such a portion of its rotation as is measured by the number of quarter-hours agreeing with the number of the climate; and that portion of the meridian which is then setting out of sun-light will be of the latitude which is the northern boundary of the climate required. Find its latitude by bringing it to the brass meridian, and the places may be seen as they pass underneath that latitude. Conversely. To find the climate in which a given place We take the first meridian as the most convenient; especially as, on some globes, the degrees of latitude are marked upon it. is situated. Having the pole elevated, as before, for the sun's greatest declination, bring the given place to the brazen meridian, and set the index to 12: give the globe its eastward rotation, and the number of quarter-hours past 6 at which the given place sets out of sun-light, will show the climate in which it is situated. The hour climates of the southern hemisphere may be found in a similar manner, the south pole being elevated for the 21st December; or, they may be inferred from the corresponding latitudes of the north. *** If the several portions of a meridian thus differing by quarters of an hour in sun-setting, be marked by a dot of ink from a soft pen*, it will be seen that whilst the first of these geographical divisions contains nearly 850, they are so crowded in the high latitudes as to render it impossible to distinguish these with great accuracy on the globe; there are 8 climates between latitude 64° and latitude 66. 1. What places bound the 1st climate north of the Equator, and what bound the 2d ? 2. What places are situated in the boundary of the 3rd climate? 3. What places are situated in the boundary of the 7th climate? 4. What places are situated in the boundary of the 9th climate? 5. What places are situated in the boundary of the 14th climate? 6. What places are situated in the boundaries of the 19th 20th and 24th climates? Conversely. 7. In what climates are the following places situated? Malacca, Delhi, Havannah, Gibraltar, Jerusalem, Pekin, London, Edinburgh, Archangel, Mount Hecla, (Iceland.) * A small blot of ink may easily be wiped off from the varnished surface of the globe; a pencil will probably scratch it. EQUATION OF TIME. 141 EQUATION OF TIME. If our earth's axis were perpendicular to the plane of the annual orbit, (i. e. if our tee-totum button were spinning in an upright position,) it is shown in pages 106 and 107, that the lines, on the wall or in the sky, which represent the positions of the ecliptic and equinoctial planes, might be considered as one line; their separation being so little as to be insignificant, when considered with the distance of the wall, &c. Now the earth's diurnal rotation, rudely represented by the spinning of our tee-totum, is the most equable of all known motions; astronomical science having records which prove that it has not deviated by any appreciable fraction of a moment during 2000 years. The time of the sidereal day which brings a star back to the exquisitely delicate cross wires of the transit instrument, is fulfilled each revolution to the hundreth portion of a second. It is then, evident, that if, whilst so rotating in an upright position, the earth's orbitual motion also were uniform, the sun (or ball) would appear to traverse the ecliptic (in this case the same with the equinoctial) in uniform daily portions; and each noon, or completion of the solar day, would bring his centre also into the exact centre of a telescope (so fixed as to be directed to his altitude) at the precise moment of time indicated by an exact clock, constructed (as our clocks are) to beat uniformly to such an interval. Now, there are two circumstances which prevent this :First. The alternate acceleration and retardation of the earth's orbitual motion, as it gets nearer to the sun or goes farther from it in an elliptical course; and the consequent faster or slower apparent movement of the sun in the ecliptic. And, secondly, the inclination of the earth's axis (our button peg) as shown on page 108; and the consequent obliquity of the equinoctial to the ecliptic. The effect of the former of these two circumstances is not exhibited by the globe; except as we have found it in the fact, that the long winter periods of the North Frigid |