14. " To find the length of the day or night, or the sun's rising or setting, in any latitude ; having the day of the month given." Rectify the globe for the lati tude of the place ; then bring the sun's place on the globe to the meridian, and set the index to twelve at noon, or the upper twelve, and then the globe is in the pro per position for noon-day. Next turn the globe about towards the east till the sun's place come just to the wooden horizon, and the index will then point to the hour of sun-rise ; also turn the globe as far to the west side, or till the sun's place come just to the horizon on the west side, and then the index will point to the hour of sun-set. These being now known, dou ble the hour of setting will he the length of the day, and double the rising will be the length of the -night. And thus also may the length of the longest day, or the shortest day, be found for any latitude.
15. " 'I'o find the beginning and end of twilight on any day of the year, for any latitude." It is twilight all the time from sun-set till the sun is eighteen degrees below the horizon, and the same in the morning from the time the sun is eighteen degrees below the horizon till the moment of his rise. Therefore, rectify the globe for the latitude of the place, and for noon, by setting the index to twelve, and screw on the quadrant of altitude. When take the point of the ecliptic opposite the sun's place, and turn the globe on its axis west ward, as also the quadrant of altitude, till that point cut this quadrant in the eigh teenth degree below the horizon ; then the index will shew the time of dawning in the morning ; next turn the globe and quadrant of altitude towards the east, till the said point opposite the sun's place meet this quadrant in the same eighteenth degree, and then the index will shew the time when twilight ends in the evening.
16. " At any given day, and hour of the day, to find all those places on the globe where the sun then rises, or sets, as also where it is noon-day, where it is day-light, and where it is in darkness." Find what place the sun is vertical to, at that time ; and elevate the globe according to the latitude of that place, and bringthe place also to the meridian ; in which state it will also be in the zenith of the globe. Then is all the upper hemisphere, above the wooden horizon, enlightened, or in day light ; while all the lower one, below the horizon, is in darkness, or night : those places by the edge of the meridian, in the upper hemisphere, have noon-day, or twelve o'clock ; and those by the me ridian below, have it midnight : lastly, all those places by the eastern side of the ho rizon have the sun just setting, and those by the western horizon have him just ris ing.
Hence, as in the middle of a lunar eclipse, the moon is in that degree of the ecliptic opposite to the sun's place ' • by the present problem it may be shown what placesof the earth; then see the of the eclipse, and what the beginning orending, by using the moon's place in stead of the sun's place in the problem.
17. " To find the bearing of one place from another, and their angle of position." Bong the one place to the zenith, by rec tifying the globe for its latitude, and turn ing the globe till that place come to the meridian ; then screw the quadrant of al titude upon the meridian at the zenith, and make it revolve till it come to the other place on the globe ; then look on the wooden horizon for the point of the compass, or number of degrees from the south, where the quadrant of altitude cuts it, and that will be the bearing of the lat ter place from the former, or the angle of position sought.
18. " The day and hour of a solar or lunar eclipse being given, to find all those places in which the same will be visible." Find the place to which the sun is vertical at the given instant ; and elevate the globe to the latitude of the place ; then, in most of those places above the horizon will the sun be visible during his eclipse ; and all those places below the horizon will see the moon pass through the shadow of the earth in her eclipse.
19. " The length of a degree being gi. gen, to find the number of milds in a great circle of the earth, and thence the diameter of the earth." Admit that one degree contains 691 English statute miles; then multiply 360(the number of degrees in a great circle) by 691 and the pro duct will be 25,020, the miles which mea sure the circumference of the earth. If this number be divided by 3.1416, the quotient will be miles, for the diameter of the earth.
20. " The diameter of the earth being known, to find the surface in square miles,' and its solidity in cubic miles." Admit the diameter be 7,964 miles ; then multi- i ply the square of the diameter by 3.1416, and the product will be 199,250,205 very near, which are the square miles in the surface of the earth. Again, multiply the cube of the diameter by 0,5236, and the product 264,466,789,170 will be the num ber of the cubic miles in the whole globe of the earth.
21. " To express the velocity of the diurnal motion of the earth." Since a place in the equator describes a circle of 25,020 miles in twenty-four hours it is evident that the velocity with which it moves is at the rate of 1,0421 in an both', or miles per minute. The velocity in any parallel of latitude decreases in the proportion of the co-sine of the lati tude to the radius. Thus for the latitude of London, 51° 30', say, As radius 10.000000 To the co-sine of lat. 51° 30' 9.794149 So is the velocity in the equa- 2 2.238046 tor, - - - To the velocity of the city of 2D32195 London, - That is, the city of London moves about the axis of the earth at the rate of 10i6 miles every minute of time : but this is far short of the velocity of the annual motion about the sun ; for that is at the rate of more than 65,000 miles per hour.