the places of the latter being determined from the ephe- 
* meris, 
Pron. XIV.—To illustrate, generally, the phenomena 
of the harvest and hunter’s moons. 
The moon's orbit forms with the ecliptic an angle of 
5}°, and advances about 13° daily from west to east. 
But to simplify the problem, let it be ae in the 
first instance, that her orbit coincides with the ecliptic, 
and that her place and hour of rising being given for 
one day, it is required to find her hour of rising for the 
next. 
Rectify the globe for the latitude, pes the moon’s 
place to the east side of the horizon, and the hour to 
the brazen meridian, then turn the globe westward till 
the point of the ecliptic, 13° from the given point, come 
to the horizon, and the hour required will be under the 
By solving this problem for various points of the 
ecliptic, assumed as the moon’s places, it will appear, 
that the difference in the time of her rising on any two 
consecutive days, to a place not under the equator, is 
always considerably less when the moon is in Pisces 
and Aries, and greater in the opposite signs, than in 
any other point of the ecliptic, and that this difference 
increases with the latitude of the place of observation. 
Thus if the globe be rectified for the latitude of 56° 
north, and the above problem solved, supposing the 
moon's place to be the beginning of Libra, it will be 
found, that the time of her rising one day, will be up- 
' wards of 1} hour later than on the preceding ; but if her 
lace be the beginning of Aries, her time of rising will 
little more one quarter of an hour later, so that 
she rises for several days nearly at the same time. This 
phenomenon, though it must obviously happen every 
month, was long considered as peculiar to the autumnal 
months, when the sun is in Virgo and Libra, because it 
is only then that the moon is in Pisces and Aries, at the 
time of her being full. 
Such isa brief illustration of the harvest and hunter’s 
moon, on the supposition that the moon revolves in 
the ecliptic. As her orbit, however, is inclined to that 
circle at an angle of 52°, and as her nodes, or points 
where her orbit intersects the ecliptic, are constantly 
shifting, it may easily be shewn by describing several 
sa circles, itielined to the ecliptic at an angle of 51°, 
but cutting it at different points, and solving the above 
problem, That the difference of time in the moon’s ri- 
| om sing during these months, is sometimes greater, and 
___- Sometimes less than it would be if she revolved in the 
ecliptic. See Astronomy, Vol. ii. Page 668. 
nog. XV.—To trace the apparent path of a comet 
on the celestial globe. ~ 
_ Ifthe right ascension and declination of the comet 
be known, at two different periods, find its position at 
each by Prob. VII. lay the quadrant of altitude through 
both, and join them with a pencil line, which will re- 
mee the intermediate path. If the longitude and 
titude of the comet be observed, its places may be de- 
termined by Prob. IX. and if its azimuth and altitude 
be known at any hour, the latitude of the place of ob- 
servation “ps also given, its place may be found thus: 
____ Dispose the globe as in Prob. IV. fix the quadrant of 
altitude on the zenith, and make its | -cigeate edge in- 
| tersect the horizon in the azimuth of the comet ; then 
the degree of the quadrant denoting its altitude will be 
over the comet’s place. If the positions of the comet, 
as determined in any of',these, ways, be at a greater 
ce from each other, than the length of the qua- 
drant of altitude, they may be both brought to coin- 
cide with the horizon, and the path traced accordingly. 
GEOGRAPHY. 
157 
The preceding examples, though only a few of the Mathematis 
sae pe that may be solved by the celestial globe, wil] ©! Geogra- 
sufficient to shew the general principle of such solu- — P®Y- 
tions, and if that principle be well understood, the rea- 
der will find no difficulty in applying it to any particu- 
lar case. The problems relating to the sun, and which 
are frequently solved by the celestial globe, we consi- 
der as bearing more directly on the subject of this arti- 
cle. Wehave therefore reserved them for the second 
class of problems, viz, those solved by the terrestrial 
globe, to which we now proceed. 
II. By the Terrestrial Globe. 
Pros. XVI.—To find the latitude and longitude of a To find the 
given place on the earth’s surface. poem age 
Set the twelfth hour of the horary circle to the first me- pot ns 
ridian, bring both to the brazen meridian, and turn the the earth. 
globe till the given place be under the brazen meridian ; 
then the degree of the meridian over the place will be 
its latitude, the point of the equator intersected by the 
meridian its longitude in degrees, and the hours of the 
horary that pass under the meridian the longitude in 
time. 
If the equator be divided into hours as well as de- 
grees, the problem may be solved without any previous 
adjustment of the hour circle, by simply bringing the 
place to the brazen meridian. 
Pros. XVII.—The latitude and longitude of a place To find a 
being given, to find the place on the globe. place from 
Find the longitude on the equator, and bring it to Spee 
the brazen meridian, then the degree of the meridian el 
denoting the latitude will be over the place. f 
: Pros. XVIII.—To find the difference of latitude and To find the 
the difference of longitude between two given places. difference 
Find the latitudes of both places by Prob. XVI. and a 
take the difference or sum of these according as they vee eagad 
lie on the same side, or on different sides of the equa- 
tor. The difference of longitude is found in the same 
way, by taking the difference or sum of the longitudes 
according as they lie on the same side, or on opposite 
sides of the first meridian. 
Pros. XIX.—The hour being given at one place, to To find the 
find the hour at any other place at the same time. cae Rex! 
Bring the given place and hour to the meridian, then ?'““* 
turn the globe till the other place comes to the meri- 
dian, and the hours that pass under the meridian added 
to, or subtracted from the first given hour, according as 
the second place, is to the east or west of the first, will 
give the hour required. 
Pros. XX.—The hour being given at any place, to To find 
find the places where it is any other given hour at the when it is 
same time. any eeren 
Bring the given place, with the hour at that place, to ®°°" 
the meridian, then turn the globe towards the east. or 
west, according as the second given hour is earlier or 
later than the frst, till the difference between them pass 
under the meridian, and the places required will be un- 
der the meridian. 
Pros. XXI.—To find the distance between.two gi- To find the 
ven places on the earth. distance be- 
Find the number of degrees, of a great circle, inter- ands ¢ 
cepted between them ; these degrees multiplied by 60, “°° 
or by 69.045, will give the distance in geographical and 
English miles respectively. The. number of degrees 
may, be found fromthe brazen-meridian, if the places 
are under the same meridian ; from the equator, if they 
are both under the equator; and from the quadrant of 
altitude applied to them, if they are neither under the 
equator, nor on the same meridian. 
