(11) On what two days of the year will the sun be vertical to Candy in the isle of Ceylon? (12) What places are those in the north frigid zone, on which the sun begins to shine constantly, without setting, on the 20th of May ? (13) On what day does the sun begin to shine constantly, without setting, at the Cherry island, whose lat. is 74° north; and how long? (14) What places are those to which the sun is rising, setting, or in the meridian; also those places which are enlightened, and those which are not; on the 20th of May, at 8 in the morning? (15) By the almanack for this present year, on the will happen an eclipse of the sun. at I demand to know to what part of the globe the same will be visible. (16) On the 3d of June, 1769, in the afternoon, happened a transit of Venus over the sun; the beginning of this transit was at 7 h. 13 m., middle 10 h. 35 m., end 1 h. 55 m. I demand to know where the beginning, middle, and end thereof were visible. 17) In what latitude is the longest day 20 hours long? 18) What inhabitants of the earth are those called Antoci, Perioci, and Antipodes, with respect to London? (19) What is the sun's declination on the 20th of June by the analemma? (20) It is required to find, by the analemma, the sun's place in the ecliptic, and his right ascension, on the 12th of May. (21) Required to find, by the analemma, the time of the sun's rising and setting, with his amplitude, on the 30th of March. (22) What is the sun's altitude and azimuth for the 26th of April, at 10 in the morning, by the añalemma? (23) On the 24th of April in the morning, in lat. 51° 30′ N. the sun's altitude was 20°; required the hour and azimuth, by the analemma. (24) Suppose a ship sails from a port A, in lat. 38°, to another port B, in lat. 5° N. and then finds her difference of longitude 43°: required her course, and distance sailed. (25) A ship sails from a port A, in lat. 26° N. to another port B, in lat. 20° S. upon a course of 46°. Required the difference of longitude, and distance sailed. (26) Suppose a ship sails from a port A, in lat. 51° 30', to another port B, in lat. 18°, distance 2226 miles: required the difference of longitude, and angle of the course. (27) Suppose a ship sails from a place A, in lat. 51°, on a course making an angle with the meridiau of 40%, till the difference of longitude be found to be 20°: required the difference of latitude, and distance sailed. (28) A ship from the latitude 47° 30′ N. has sailed S. W. by S. 1980 miles. Required the difference of latitude and longitude. EXAMPLES on the CELESTIAL GLOBE. (1) Required the time of the sun's rising and setting, also the beginning and end of the crepusculum, or twilight, on the 21st of June. (2) What is the moon's diurnal motion in the ecliptic, also at what time does she rise, set, and come to the meridian, on the 20th of May? (3) Required the latitude of the Moon, and her declination, on the 20th of May ? (4) At what time does the planet Jupiter rise, culminate, and set, on the 20th of May? Also, what is its right ascension, declination, amplitude, and the azimuth, on the above day? (5) What is the right ascension, declination, latitude, and longitude, of Peilux? (6) What star is that whose right ascension is 65° 30′, and its declination 12° 15′ 30′′ north? Also what time does it rise, come to the meridian, set, and what is its amplitude, on the 20th of July, in the lat. of London? (7) On what day of the year will the star Arcturus rise and set cosmically at London? (8) Required the time when Procyon and Canis Minor will. rise and set acronically at London. (9) On what day of the year will Altayr culminate, or come to the meridian, with the sun? (10) At what time of the year will the Pleiades, or Seven Stars, be upon the meridian at midnight? (11) What is the oblique ascension of Sirius, and what is the time of its continuance above the horizon of London ? (12) What is the altitude and azimuth of Capella, on the 20th of May, at 10 o'clock at night, in the latitude of London? (13) The altitude of Cor Leonis, on the 22d of May, at London, was 20°; required the hour of the night. (14) A person being in a certain place, on the 20th of May, at after 3 in the morning, observed the Pleiades were then rising. Required the latitude of the place of ob servation. (15) On the 11th of May, in the latitude 51° 30', the two stars, Luci a Lyræ, and Altayr, will be both on the same azimuth. Required the hour of the night. (16) On the 11th of May (lat. as before) the bright star marked in Pegasus's wing, and that in the head of Andromeda, will both have an equal altitude. Required the hour. (17) A person being at sea, found, by observation, that Sirius was then upon the meridian, and Arcturus rising: required the lat. of the place of observation. (18) Another person being at a certain place, found, by observation, Cor Hydra and Procyon both on the azi muth of 78° 45′ S. E. one with 5o of altitude, and the other with 35°. Required the latitude of the place of observation. (19) To what latitude south must I travel, to lose sight of the star Capella? (20) Represent the face of the heavens on the globe on the 20th of May, at 10 at night. (21) By an observation made at Jamaica, of a comet, on the 31st of March, 1759, at 5 o'clock in the morning, its altitude was found to be 22° 50′, and azimuth 71° South East. Another observation was made at London on the 6th of May, 1759, at 10 at night, of the same comet, and then its altitude was found to be 16°, and its azimuth 37° S. W. It is required to know the place of the comet at each observation. (22) Required the time of the above comet's rising, southing, and setting, at London, on the 31st of March, 1759; also its latitude, longitude, declination, and ascension. (23) Required the apparent path, among the fixed stars in the heavens, of the above comet, also its velocity. Note. These problems are answered by Mr. Hill's twelveinch globes. PART VI. LXXX. ALGEBRA. ALGEBRA is a kind of specious arithmetic, or an arithmetic in letters; and is that science which teaches, in a general manner, the comparison of abstract quantities; by means whereof such questions are resolved whose solutions would be sought in vain from common arithmetic. Here every quantity, whether given or required, is commonly represented by some letter of the alphabet; the known or given quantities, for distinction's sake, being noted by the first letters, a, b, c, d, &c. and the unknown ones by the last letters, x, y, z, &c. There are, moreover, in algebra, certain signs or notes, made use of to show the relation and dependence of quantities one upon another, whose signification the learner ought first of all to be made acquainted with. (See the characters for abbreviation, next before page 1.) LXXXI. ADDITION. ADDITION in Algebra is performed by connecting the quantities by their proper signs, and joining in any sum such as can be united. For performing which, observe the following RULE. 1. If the quantities to be added are alike, and have the same sign, add the coefficients together, and to their sum prefix the common sign, and subjoin the common letter or letters. 2. If the quantities to be added are alike, but have unlike signs, add together the coefficients of the affirmative terms (if there be more than one), and do the same by the negative ones; and to their difference prefix the sign of the greater, adding the common letter or letters. 3. If the quantities to be added are unlike, write them down one after the other, with their proper signs and coefficients prefixed. Change the signs of the quantity to be subtracted into their contrary signs, and then add it, so changed, to the |