T ji, r m. This method is very eafy in practice, and fuf- 
ficiently accurate to obtain a diftance Sj from which you 
may begin to compute, in order to find the orbit more 
corrcdlly, when the comet is not too near to the Sun. 
Having determined the parobola nearly, we firft alfume 
foine one quantity as knoSvn at the fit ft and fecond obfer¬ 
vations, and thence compute the place of the comet at 
thofe times, and alfo the time between ; and, if that time 
agree with the obferved interval, you have got a parabola 
which agrees with the two firft obfervations ; if the times 
do not agree, alter one of the alfumed quantities, and fee 
how it agrees; and then, by the rule of falfe, you may 
correct the fuppofition which was altered, and get a pa¬ 
rabola which will agree with the two firft obfervations. In 
like manner, by altering the other alfumed quantity, you 
get another parabola agreeing with the two firft obferva¬ 
tions. Then fee how they agree with the third obfer- 
vation ; and, if they do not, a corrreilion muft be 
made by proportion, and the three obfervations will be 
anfwered. 
When great accuracy is required, we muft take into 
confideration the etfedt of aberration and parallax ; the for¬ 
mer may be computed by the rules already given, and the 
latter, by faying, As the horizontal parallax is to that of 
the Sun —8 •75” fo is the diftance of the Sun to the diftance 
of the comet; and then finding the parallax in latitude and 
longitude, as for the planets. 
Ex. On Auguft 21, 1769, the diurnal motion of a co¬ 
met was fixty-three minutes in longitude, and twenty-five 
minutes in latitude, and its diftance from the Earth 0-667. 
Hence the aberration in longitude equal fourteen feconds, 
and in latitude equal fix feconds, both to be added. Now 
the apparent longitude was 47 0 1' 31", and latitude 5° 53' 
48" ; hence the apparent longitude corredled for aberra¬ 
tion was 47 0 1' 45", and latitude 5 0 53' 54". Alfo, As 
0-667 is to x fo is 8-75" to 13" the horizontal parallax. 
Hence, the parallax in longitude is found to be four fe¬ 
conds, to be added to the true, to give the apparent lon¬ 
gitude ; and, as the true longitude (by computation) was 
47° 2 ' 3"> the apparent ought to have been 47 0 2' 7" ; 
hence the error in longitude was twenty-two feconds. Alfo 
the parallax in latitude was ten feconds, to be added to 
the true, to give the apparent latitude; and, as the true la¬ 
titude (by computation) was 5 0 34' 16", the apparent ought 
to have been 5 0 54' 26" ; hence the error in latitude was 
thirty-two feconds. 
Longomontanus Ihews an eafy method of finding and 
tracing out the places of a comet mechanically ; which is, 
to find two liars in the fame line with the comet, by ftretch- 
ing a thread before the eye over all the three ; then do the 
feme by two other liars and the comet ; this done, take 
a celeftial globe, or a planifphere, and draw a line upon 
it firft through the-former two liars, and then through the 
latter two ; lo Ihall the interfedliomof the two lines be the 
place of the comet at that time. If this be repeated from 
time to time, and all the points of interleclion connected, 
it will ftiew the path of the comet in the heavens. 
To find the Altitude and Height of Fire-balls, 
and other Meteors, in the Atmosphere, by the 
Quadrant. 
Though the extreme velocity and tranfient nature of 
fiery meteors in the atmolphere, in a great mealure pre¬ 
vents the making of fuch obfervations as might tend to 
afeertain their diftance, yet they form a fubject of inquiry 
fo curious and intereliing, as to render fuch as can be 
made of great value. An obferver, who perceives an ap¬ 
pearance of this kind, ought carefully to note the build¬ 
ings, trees, liars, &c. near which it palfes ; and, as foon af¬ 
terwards as convenient, take their altitude and bearings, 
If two fuch obfervations be taken by perlons at different 
places, fufticiently diftant from each other, the diftance on 
the Earth may be conlidered as the bale, and from this 
and the two obferved angles the height of the meteor may 
be found. By obfervations of this kind it has been found 
Vol. II. No, 82. 
ASTRONOMY. 433 
that the larger fire-balls are elevated about fixty miles 
above the Earth’s furface, and that fome of them are 
near five miles in diameter. 
To find the Height of a Cloud, by Obfervation of a Flajli of 
Lightning. If the altitude of that part of a cloud, from 
which a flafh of lightning has ilfued, be immediately ta¬ 
ken with i*he quadrant, and the number of feconds ot time 
elapfed between the inftant of the flafh and the firft ar¬ 
rival of the thunder be reckoned, thefe data will be fuffi- 
cient to determine the height of the thunder-cloud. For 
found is admitted to pafs through 1142 feet in a fecond ; 
but light has fuch an extreme velocity, that it paffes thro’ 
35,000 miles in a fecond, and may therefore be reckoned 
inllantaneous in all obfervations upon the Earth. Hence 
it follows, that the number of feconds obferved, multi¬ 
plied by 1142, will give the diftance of the cloud; and. 
As radius is to the fine of the obferved angle, fo is the 
diftance of the cloud to its height. 
Ex. Suppofe the angle of elevation, from which a flafh 
of lightning ilfued, w>as 53 0 8', and that between the fialli 
and the report of the thunder 5" were counted ; then, 1142 
feet multiplied by 5 gives 5710 feet for the diftance of the 
cloud. 
And as the radius or fine of 90 0 
Is to the fine of the obferved angle 53 c 
So is the diftance of the cloud 5710 
To its height 4568 
10 - 000000(9 
9-9031084 
3*756636 1 
3-6597445 
Or, by conftrudlion. From a point in any right line, 
draw another right line, forming the obierved angle. Set 
off on this left line, from the angular point, the diftance 
of the cloud, taken from a fcale of equal parts. From 
the-extreme of the laft-mentioned line let fall a perpendi¬ 
cular on the other line ; and this perpendicular will be the 
height required. If the flafh of lightning ftrikes direftly 
down, the height of the cloud will alfo be the length of 
the flafh. But this is not often the cafe. 
The latitude of the Place, and the Zenith Difiance of a Star, 
being given-, to find the Declination of the Star. When the 
latitude of the place and zenith diftance are of different 
kinds, that is, one north and the other fouth, their difference 
is the declination ; and it is of the fame name with the la¬ 
titude, when that is the greater of the two ; othervvife it 
is of the contrary kind. When the latitude and zenit li 
diftance are of the fame kind, that is, both north, or both 
fouth, their fum is the declination, and it is of the fame 
kind with the latitude. 
To find the Obliquity of the Ecliptic. 
The obliquity of the ecliptic is a very important element 
of aftronomy, becaufe it enters into the calculation of all 
fpheric triangles where the ecliptic and equator are con¬ 
cerned. The obliquity of the ecliptic being equal to the 
Sun’s greateft declination, i. e. when in the tropics, the 
obliquity may be afeertained by obferving the meridian 
height of tlfe Sun’s centre on one of the folfticial days; 
and this quantity taken from the height of the equator, at 
the place of oblervation, gives the declination of the tro¬ 
pic. Or, more accurately, obferve the Sun’s meridian al¬ 
titude in each tropic : this will give their diftance, half of 
which is the diftance of each tropic from the equator, that 
is, the obliquity of the ecliptic. 
Of Corresponding or Eqjjal Altitudes. 
At equal diftances from the meridian, a ftar has equal 
altitudes. If, therefore, equal altitudes of an heavenly 
body be taken on different fides of the meridian, the mid¬ 
dle point of time between the obfervations will give the 
time when the body is upon the meridian, if it lias not 
changed its declination. By this means the time when any 
body comes to the meridian may be afeertained ; and, when 
applied to the Sun, or a fixed Har, the rate at which a clock 
(adjufted to the mean folar or lidcrial time) gains or loles, 
may be determined with accuracy. 
5 2 . The 
