taken, count the number of degrees from the sun's place on the brass meridian towards the south point of the horizon, and mark where the reckoning ends; bring this mark to coincide with the south point of the horizon, and the elevation of the north pole will shew the latitude. If the sun was north of the observer when the altitude was taken, the degrees must be counted in a similar manner, from the sun's place towards the north point of the horizon, and the elevation of the south pole will shew the latitude.

OR, WITHOUT A GLOBE.

Subtract the sun's altitude from ninety degrees, the remainder is the zenith distance. If the sun be south when his altitude is taken, call the zenith distance north; but, if north, call it south; find the sun's declination in an ephemeris * or a table of the sun's declination, and mark whether it be north or south then, if the zenith distance and declination have the same name, their sum is the latitude; but, if they have contrary names, their difference is the latitude, and it is always the same name with the greater of the two quantities.

Examples. 1. On the 10th of May 1808, I observed the sun's meridian altitude to be 50°, and it was south of me at that time; required the latitude of the place.

40 0 N., the zenith distance.

17 39 N., the sun's declination 10th of May, 1808.

57 39 N., the latitude sought.

2. On the 10th of May 1808, the sun's meridian altitude was observed to be 50°, and it was north of

The most convenient is Whites Ephemeris; see the note page 36, or the Nautical Almarrac.

the observer at that time; required the latitude of the

3. On the 5th of August 1808, the sun's meridian altitude was observed to be 74° 30′ north of the observer; what was the latitude?

4. On the 19th of November 1808, the sun's meridian altitude was observed to be 40° south of the observer; what was the latitude ?

5. At a certain place where the clocks are two hours faster than at London, the sun's meridian altitude was observed to be 30 degrees to the south of the observer on the 21st of March; required the place.

6. At a place where the clocks are five hours slower than at London, the sun's meridian altitude was observed to be 60° to the south of the observer on the 16th of April 1808; required the place.

PROBLEM XLVIII.

The length of the longest day at any place, not within the polar circles being given, to find the latitude of that place.

Rule. Bring the first point of Cancer or Capricorn to the brass meridian (according as the place is on the north or south side of the equator,) and set the index of the hour circle to twelve; turn the globe westward on its axis till the index of the hour circle has passed over as many hours as are equal to half the length of the day; elevate or depress the pole till the sun's place (viz. Cancer or Capricorn) comes to the horizon; then the elevation of the pole will shew the latitude.

NOTE. This problem will answer for any day in the year, as well as the longest day, by bringing the sun's place to the brass meridian, and proceeding as above.

Or, Bring the middle of the analemma to the brass meridian, and set the index of the hour circle to 12; turn the globe westward on its axis till the index has passed over as many hours as are equal to half the length of the day; elevate or depress the pole till the day of the month coincides with the horizon, then the elevation of the pole will show the latitude

Examples. 1. In what degree of north latitude, and at what places is the length of the longest day 10 hours?

Answer In latitude 52°, and all places situated on, or near that parallel of latitude, have the same length of the day

2. In what degree of south latitude, and at what places is the longest day 14 hours?

3. In what degree of north latitude is the length of the longest day three times the length of the shortest night?

4. There is a town in Norway where the longest day is five times the length of the shortest night; pray what is the name of the town?

5. In what latitude north does the sun set at seven o'clock on the 5th of April?

6. In what latitude south does the sun rise at five o'clock on the 25th of November?

7. In what latitude north is the 20th of May 16 hours long?

8. In what latitude north is the night of the 15th of August 10 hours long?

PROBLEM XLIX.

The latitude of a piace, and the day of the month being given, to find how much the sun's declination must increase or decrease towards the elevated pole, to make the day an hour longer or shorter than the given day.

Rule. Find the sun's declination for the given day, and elevate the pole to that declination; bring the given place to the brass meridian, and set the index of the hour circle to twelve; turn the globe eastward on its axis till the given place comes to the horizon, and observe the hours passed over by the index: then, if the days be increasing, continue the motion of the globe eastward till the index has passed over another half hour, and raise the pole till the place comes again into the horizon, the elevation of the pole will show the sun's declination when the day is an hour longer than the и h

given day but, if the days be decreasing, turn the globe westward till the index has passed over half an hour, and depress the pole till the place comes a second time into the horizon, the last elevation of the pole will show the sun's declination when the day is an hour shorter than the given day.

OR,

Elevate the pole to the latitude of the place, find the sun's place in the ecliptic, bring it to the brass meridian, and set the index of the hour circle to twelve; turn the globe westward on its axis till the sun's place comes to the horizon, and observe the hours passed over by the index; then, if the days be increasing, continue the motion of the globe westward till the index has passed over another half hour, and observe what point of the ecliptic is cut by the horizon; that point will show the sun's place when the day is an hour longer than the given day, whence the declination is readily found: but, if the days be decreasing, turn the globe eastward till the index has passed over half an hour, and observe what point of the ecliptic is cut by the horizon; that point will shew the sun's place when the day is an hour shorter than the given day.

OR, BY THE ANALEMMA.

Proceed exactly the same as above, only, instead of bringing the sun's place to the brass meridian, bring the analemma there, and, instead of the sun's place, use the day of the month on the analemma.

Examples. 1. How much must the sun's declination vary that the day at London may be increased one hour from the 24th of February?

Answer. On the 24th of February the sun's declination is 9° 38′ south, and the sun sets at a quarter past five: when the sun sets at three quarters past five, his declination will be found to be about 41° south, answering to the 10th of March: hence the declination has decreased 5° 23′, and the days have increased 1 hour in 14 days.

2. How much must the sun's declination vary, that the day at London may decrease one hour in length from the 26th of July?

Answer The sun's declination on the 26th of July is 19° 38' north, and the sun sets at 49 min. past seven; when the sun sets at 19 min. past seven, his declination will be found to be 14° 43'

north, answering to the 13th of August: hence the declination has decreased 5° 55', and the days have decreased one hour in 18 days.

3. How much must the sun's declination vary, from the 5th of April, that the day at Petersburg may increase one hour?

4. How much must the sun's declination vary, from the th of October, that the day at Stockholm may decrease one hour?

PROBLEM L.

To find the sun's right ascension, oblique ascension, oblique descension, ascensional difference, and time of rising and setting at any place.

Rule. Find the sun's place in the ecliptic, and bring it to that part of the brass meridian which is numbered from the equator towards the poles ;* the degree on the equator cut by the graduated edge of the brass meridian, reckoning from the point Aries eastward, will be the sun's right ascension.

Elevate the pole so many degrees above the horizon as are equal to the latitude of the place, bring the sun's place in the ecliptic to the eastern part of the horizon,† and the degree on the equator cut by the horizon, reckoning from the point Aries eastward, will be the sun's oblique ascension. Bring the sun's place in the ecliptic to the western part of the horizon,‡ and the degree on the equator cut by the horizon, reckoning from the point Aries eastward, will be the sun's oblique descension.

Find the difference between the sun's right and oblique ascension; or, which is the same thing, the differ ence between the right ascension and oblique descension, and turn this difference into time by multiplying by 4t; then, if the sun's declination and the latitude of the place be both of the same name, viz both north

* The degree on the meridian above the sun's place is the sun's declination. See Prob. XX.

†The rising amplitude may be seen at the same time. See Prob. lem XLIII.

The setting amplitude may here be seen. Vide Prob. XLII. † See Problem XVIII.