ASTRONOMY. 
left. But the theory of refractions, found out by Snel- 
lius, was not fully underltood in his time. 
The horizontal refraftion, being the greateft, is the 
caufe that the Sun and Moon appear of an oval form at 
their riling and felting; for the lower edge of each being 
more refracted titan the upper edge, the perpendicular dia¬ 
meter is Ihortened, and the under edge appears more flat¬ 
ted. Hence alfo, if we take with an inftrument the dif- 
tance of two (tars when they are in the fame vertical and 
near the horizon, we (hall find it conliderably lefs than if 
•we meafure it when they are both at fuch a height as to 
1'uflier little or no refraction ; becaufe the lower (tar is more 
elevated than the higher. There is alfo another altera¬ 
tion made by refraCtion in the apparent didance of flars : 
when two flars are in the fame almicanter, or parallel of 
declination, their apparent diftance is lefs than the true; 
for, fince refraCtion makes each of them higher in the azi¬ 
muth or vertical in which they appear, it mult bring them 
into parts of the vertical where they come nearer to each 
other; becaufe all vertical circles converge and meet in 
the zenith. This contraction of diftance, according to 
Dr. Halley, (Phil. Tranf. No. ccclxviii.) is at the rate of 
at lead one fecond in a degree ; fo that, if the diftance be¬ 
tween two (tars in a polition parallel to the horizon mea¬ 
fure 30 0 , it is at molt to be reckoned only 29 0 59' 30''. 
The quantity of the refraCtion at every altitude, from 
the horizon, where it is greateft, to the zenith, w'here it is 
nothing, has been determined by obfervation, by many 
aftronomers; thofe of Dr. Bradley and Mr. Mayer are 
efteemed the mod: correCt of any, being nearly alike, and 
are now ufed by mod aftronomers. Dr. Bradley, from 
his obfervations, on the different dates of the atmofphere 
at different times, deduced this very Ample and general 
rule for the refraction r at any altitude a whatever, viz. 
As radius 1 : cotang. <z-j-3r :: 57" : r", the refraCtion in 
feconds. This rule is adapted to thefe dates of the baro¬ 
meter and thermometer, viz. 
Either 29-6 inc. barometer, and 50° thermometer, 
Or 30 — barometer, and 33 thermometer, 
for both which dates it anfwers equally the fame. But, 
for any other dates of the barometer and thermometer, 
the refraCtion above-found is to be corrected in this man¬ 
ner, viz. If b denote any other height of the*barometer in 
inches, and t the degrees of the thermometer, r being the 
refraCtion uncorrected, as found in the manner above ; then 
As 29-6 : b :: r : R, the refraCtion corrected on account 
of the barometer, 
And 400 : 430 1 :: R : the refraCtion corrected both on 
account of the barometer and thermometer; which final 
4CO-1 
corrected refraftion is therefore =-—-— br. Or. to cor- 
11840 
reft the fame refraCtion r by means of the latter date, viz. 
barometer 30, and thermometer 55, it will be 
br 
As 30 : b :: r : R =:—, 
3 ° 
And 400 : 433— t :: R : — ^ — R — —- br , the cor- 
400 12000 
reft refraCtion. 
Mr. Mayer fays his rule was deduced from theory, and, 
when reduced from French meafure and Reaumur’s ther¬ 
mometer, to Englilh meafure and Fahrenheit’s thermo¬ 
meter, it is this, 
74*4^ X cof. a! 
(iX'00248<) 2 
74 ' 4 ^ X cof. 
» + 
i7‘i4fin. a i7‘i4 fin. 
i 4 --oo 248 i 
a X tang. A 
$ 
(1 -f- -oo248t) 5 
the refraCtion in fe- 
(i+ , 00248t) 2 
conds, corrected for both barometer and thermometer: 
where the letters denote the fame things as before, except A, 
which denotes the angle whofe tangent is 
\f 1 + •00248/ 
17-14 fin. a 
Mr. Simpfon, too, (Diflert. p. 46, See.) has ingenioufly 
determined by theory the adronomical refraCtions, from 
which he brings out this rule, viz. As 1 to '9986, or as ra¬ 
dius to fine of 86° 38' 30", fo is the fine of any given ze¬ 
nith didance, to the fine of an arc ; then of the diffe¬ 
rence between this arc and the zenith diftance, is the re¬ 
fraction fought for that zenith didance. And, by this 
rule, Mr. Simpfon computed a Table of the mean refrac¬ 
tions, which are not much different from thofe of Dr. 
Bradley and Mr. Mayer, and are as in the following Table : 
Appa¬ 
rent 
Altitude 
Refraftion 
Appa¬ 
rent 
Altitude 
Refraftion 
Appa¬ 
rent 
Altitude 
Refraftion 
o° 
jd 
O" 
1 7° 
/ 
5°" 
3S° 
l' 
7 " 
I 
2 3 
3° 
18 
2 
40 
40 
I 
2 
2 
17 
43 
!9 
2 
3 1 
42 
O 
58 
3 
13 
44 
20 
2 
23 
44 
O 
54 
4 
I I 
5 
21 
2 
l 6 
46 
O 
5° 
5 
9 
IO 
22 
2 
9 
48 
O 
47 
6 
7 
49 
23 
2 
3 
5° 
O 
44 
7 
6 
48 
24 
I 
57 
52 
O 
41 
8 
5 
39 
23 
I 
52 
54 
O 
38 
9 
5 
21 
26 
I 
47 
56 
0 
35 
IO 
4 
3° 
27 
I 
42 
53 
0 
32 
I I 
4 
24 
28 
I 
3S 
60 
0 
3° 
I 2 
4 
2 
29 
I 
34 
65 
0 
24 
*3 
3 
43 
3° 
I 
3° 
7° 
0 
19 
14 
3 
27 
32 
I 
23 
75 
0 
14 
15 
3 
13 
34 
I 
17 
80 
0 
9 
16 
3 
, * 1 
36 
I 
I 2 
85 
© 
4 * 1 
It is evident, that all obferved altitudes of the heaven¬ 
ly bodies ought to be dimini died by the numbers taken 
out of the foregoing Table. It is alfo evident that the 
refraCtion diminiflies the right and oblique afeenfions of a 
ftar, and increafes the defcenlions: it increafes the nor¬ 
thern declination and latitude, but decreafes the fouthern : 
in the eaftern part of the heavens it diminiflies the longi¬ 
tude of a ftar, but in the weftern part of the heavens it 
increafes the fame. 
Terrejlrial refraCtion is that by which terreftrial objefts 
appear to be raifed higher than they really are, in obfer- 
ving their altitudes. The quantity of this refraCtion is ef- 
timated by Dr. Mafkelyne at one-tenth of the diftance of 
the objeft obferved, exprelfed in degrees of a great circle. 
So, if the diftance be 10,000 fathoms, its tenth part, 1000 
fathoms, is the fixtieth part of a degree of a great circle 
on the Earth, or 1', which therefore is the refraftion it} 
the altitude of the objeft at that diftance. See his Tables, 
1766, p. 134. But M. le Gendr© is induced, he fays, by 
feveral experiments, to allow only a fourteenth part of the 
diftance for the refraftion in altitude. So that, upon the 
diftance of 10,000 fathoms, the fourteenth part of which 
is 714 fathoms, he allows only 44'' of the terreftrial refrac¬ 
tion, fo many being contained in the 7.14 fathoms. Again, 
M. de Lambre, an ingenious French aftronomer, makes 
the quantity of the terreftrial refraftion to be the eleventh 
part of the arch of diftance. But the Englifti nteafurers, 
colonel Edw. Williams, captain Mudge, and Mr. Dalby, 
from a multitude of exaft obfervations made by them, de¬ 
termine the quantity of the medium refraftion to be the 
twelfth part of the faid diftance. The quantity of this 
refraftion, however, is found to vary conliderably, with 
the different dates of the w eather and atmofphere, from 
the fifteenth part of the diftance, tuthe ninth part of the 
fame; the medium of which is the twelfth part, as above 
determined. 
Some lingular effefts of this refraftion are alio related, 
arifing from peculiar lituations and circumftances. Thus, 
it is faid, any perfon (landing by the fide of the river 
Thames at Greenwich, when it is high-water thepe, he 
can fee the cattle grazing on the Ifle of Dogs, which is 
the marfliy meadow on the other fide of the river at that 
place j but, when it is low-water there, he cannot fee any 
