RULE.-Place the poles in the horizon, so that, in causing the globe to revolve westward, all the stars mapped upon it may pass under review. Place the thumb nail (of the right or left hand according to position) on the given declination, and bring the given right ascension to the brass meridian ; then, under the given declination will be the star required. Conversely. If a given star be brought to the brass meridian, the declination will be that found exactly over the star; and the R. A. will be cut by the brass meridian on the equinoctial. 1. Find the stars answering to the following R. A. and Declination? 2. Find the R. A. and Declination of the following stars? 1st. The R. A. in hours or sidereal time. (8 of Orion) "Rigel." y of Leo Major. 2nd. The R. A. in degrees. a of Crux. B of Corvus. of Ursa Major, “Mizar." a of Ursa Minor, Pole Star. y of Grus. 3. The telescope of my Transit instrument is elevated to 23° 26' N. declination, and my sidereal clock is showing 3 hours 31 minutes: what star shall I see at the intersection of the wires which point out the centre of the tube, if I look through it just six minutes and three quarters after this? DIFFERENCE OF LONGITUDE. 99 PROBLEM XVII. TERRESTRIAL GLOBE. To find the difference of Longitude of any two places; and the hour of the day at the one place being given, to find the hour at the other place. Learn S. T. V. W. on page 12, and X. on page 13. RULE. Find the longitudes of both places, beginning with that place which is eastern of the two. If the longitudes be both of the eastern hemisphere, or both of the western, subtract the less longitude from the greater; but, if the one longitude be of the eastern, and the other of the western hemisphere, their sum will be the difference of longitude, unless it exceed 180 degrees. If the sum of the two longitudes exceed 180°, take that sum from 360°, and the remainder will show the difference of longitude. N. B. The difference of longitude may be turned into minutes of time by multiplying the degrees by 4; or into hours by dividing them by 15. What is the difference of longitude between the following places: Pekin and Lisbon; Botany Bay and Cairo; Port Royal and Owhyhee; Naples and Lassa, (Thibet); Geneva and Lima; Philadelphia and Venice; Paris and Rome; Lisbon and Canton; Astracan and Barbadoes; Mexico and Otaheite; the North Foreland and the Isle of Wight; Dublin and Edinburgh; what is the difference of time between these places, and which one, of every two of them, has the time in advance? ANGULAR MOTION, (PROPERLY, ANGULAR VELOCITY,) Of any body moving about a centre, (as distinguished from its real velocity,) is measured by the number of degrees through which it passes in a given time, as an hour, a second, &c. S N Thus the knots E. M. P. we have supposed to be made in the skipping-rope, have, all of them, the same angular velocity, although varying in their real velocity as their respective distances from their centres of motion, viz. the chest, arm, and wrist. If my watch, which performs correctly, after having had its minute hand, three quarters of an inch long, set by St. Paul's clock, could be hung up in the exact centre of the face of that clock, it is plain that the direction of the pointers, of the watch and of the clock, could agree constantly only because of their corresponding angular ve locity. But the pointer, or extremity, of the clock-hand which measures 8 feet, or 96 inches, must have a real velocity according with that length; and move over rather more space in one half minute, than the pointer of my watch-hand does in an hour's complete revolution. Apply this, in the Problem next succeeding, to the velocities of different latitudes; and in a Problem of the third Section, we shall consider how the Divine Contriver has adapted this means, amongst others, to the production of fertility and convenience on our planetary habitation. DIFFERENCE OF LONGITUDE. 99 PROBLEM XVII. TERRESTRIAL GLOBE. Learn S. T. V. W. on page 12, and X. on page 13. RULE. Find the longitudes of both places, beginning with that place which is eastern of the two. If the longitudes be both of the eastern hemisphere, or both of the western, subtract the less longitude from the greater; but, if the one longitude be of the eastern, and the other of the western hemisphere, their sum will be the difference of longitude, unless it exceed 180 degrees. If the sum of the two longitudes exceed 180°, take that sum from 360°, and the remainder will show the difference of longitude. N. B. The difference of longitude may be turned into minutes of time by multiplying the degrees by 4; or into hours by dividing them by 15. What is the difference of longitude between the following places: Pekin and Lisbon; Botany Bay and Cairo ; Port Royal and Owhyhee; Naples and Lassa, (Thibet); Geneva and Lima; Philadelphia and Venice; Paris and Rome; Lisbon and Canton; Astracan and Barbadoes; Mexico and Otaheite; the North Foreland and the Isle of Wight; Dublin and Edinburgh; what is the difference of time between these places, and which one, of every two of them, has the time in advance ? graphical miles in a degree of longitude, since each degree answers to 4 minutes of time, the rate per minute, multiplied by 4, will give those Geographical miles. If the meridians be drawn, (as they are on some Globes,) through every 10 degrees, the rate in Geographical miles is similarly found for every two-thirds of a minute only: in this case the rate per minute will be half as much again as that shown by the measure ment. 1. At what rate per minute are the inhabitants of Petersburgh carried by the rotation of the earth? Here I find, that the 15° of Petersburgh answer to 73° only of the Equatorial degrees, and that, consequently, its inhabitants are carried only 7 Geographical miles per minute. 2. At what rate per minute, (in Geographical miles,) are the inhabitants of the following places carried by the revolution of the earth upon its axis:-1. Madrid, or Pekin, or Philadelphia. 2. North point of St. Domingo, or north of Owhyhee. 3. Port Jackson, or Cape Town. 4. Edinburgh, or Cape Horn. 5. London. ton. 8. St. Helena. 9. Cape Verd. 3. What also is the rate per hour at each of these places, and what the length of a degree in English miles? 6. Bermuda. 7. Can10. S. of Spitzbergen. Note. The learner, in performing the foregoing Problem, will have noticed that the quadrant, (the measure of a great circle,) does not conform sufficiently to any arc of a parallel of latitude, (a small circle,) to enable us to obtain more than an approximation to the truth. If it be required to know the rate in English miles, they may be found, in this case with sufficient exactness, by multiplying the Geographical miles by 70, and dividing by 60; or by adding . |