A N O 
A N O 
74 * 
modern agronomy, in which a planet P is conficfered as 
.H deforibihg an cLlipfe APB 
I "'■■■ about the fun S, placed in 
one focus, it is the time in 
w hicii the planet moves from 
its aphelion A, to the mean 
place or point of its orbit P. 
iB Hence, as the elliptic area 
ASP is proportional to the 
time in which the planet de- 
fcribes the arc AP, that area 
may t eprefent the mean ano¬ 
maly. Or, if PD be drawn 
perpendicular to the tranfverfe axis AB, and meet the cir¬ 
cle in D defcribed on the Janie axis; then the mean ano¬ 
maly may all’o he reprefented by the circular trilineal ASD, 
which is always proportional to the elliptic one ASP. Or, 
drawing SG perpendicular to the radius DC produced ; 
then the mean anomaly is alfo proportional to SG -p the 
circular arc AD, as is demonftrated by Keil, in his Left. 
Aflron. Hence, taking DH —SG, the arc AH, or angle 
ACM, will be the mean anomaly in practice, as expreded 
in degrees of a circle, the number of thofe degrees being 
to 36o°, as the elliptic trilineal area ASP, is to the whole 
area of the ellipfe ; tire degrees of mean anomaly, being 
thofe in the arc AH, or angle ACH. 
Eccentric Anomaly , or of the centre, in the modern aftro- 
nomy, is the arc AD of the circle ADB intercepted be¬ 
tween the aplis A and the point D determined by the per¬ 
pendicular DPE to the line of the apfes, drawn through 
the place P of rite planet. Or it is the angle ACD at the 
centre of the circle. Hence the eccentric anomaly is to the 
mean anomaly, as AD to AD-f-SG, or as AD to AH, or 
-as the angle ACD to the angle ACH. 
True or Equated Anomaly, is the angle ASP at the fun, 
which the planet’s difiance AP from the aphelion appears 
under; or the angle formed by the radius vector or line 
SP drawn from the fun to the planet, with the line of the 
apfes. The true anomaly being given, it is eafy from 
thence to find the mean anomaly. For the angle ASP, 
■which is the true anomaly, being given, the point P in the 
ellipfe is given, and thence the proportion of the area ASP 
to the whole ellipfe, or of the mean anomaly to 360 de¬ 
grees. And for this purpofe, the following eafy rules for 
‘practice are deduced from the properties of the ellipfe, by 
M. de.la Caille, in his Elements of Aftronomy, and M. de 
la Lande, art. 1240, &c. of Ins aftronomy. ift, As the 
fquare root of SB tire perihelion diftance, is to the fquare 
root of SA the aphelion diftance, fo is the tangent of half 
the true anomaly ASP, to the tangent of half the eccen¬ 
tric anomaly ACD. 2d, The difference DH or SG be¬ 
tween the eccentric or mean anomaly, is equal to the pro¬ 
duct of the eccentricity CS, by the fine of SCG the ec¬ 
centric anomaly juft; found. And in this cafe, it is proper 
to exprefs the eccentricity in feconds of a degree, which 
.will be found by this proportion, as the mean diftance 1 : 
the eccentricity :: 206264-8 feconds, or 57 0 17' 44" - 8, in 
the arc whofe length is equal to the radius, to the feconds 
in the arc which is equal to the eccentricity CS ; which 
being multiplied by the fine of the eccentric anomaly, to 
radius 1, as above, gives the feconds in SG, or in the arc 
DH, being the difference between the mean and eccentric 
anomalies. 3d, To find the radius vector SP, or diftance 
of the planet from the fun, fay either, As the fine of the 
the true anomaly is to the fine of the eccentric anomaly, fo 
is half the lefs axis of the orbit, to the radius veftor SP; 
or, as the fine of half the true anomaly is to the fine of 
half the eccentric anomaly, fo is the fquare root of the 
perihelion diftance SB, to tire fquare root of the radius 
vector or planet's diftance SP. 
But, the mean anomaly being given, it is not fo eafy to 
find the true anomaly, at leaft by a direft procefs. Kepler, 
who firft propofed this problem, could not find a direft 
way of refolving it, and therefore made ufe of an indirect 
Vol. J. No. 47. 
one., by the rule of falfe polition, as may be feen page 695 
of Kepler’s Epitom. Aftron. Copernic. See alfo §. 628 of 
Wolfius Elem. Aftron. Now the eafieft method of per¬ 
forming - this operation, would be to work firft for the ec¬ 
centric anomaly, viz. a flu me it nearly, and from it lo af- 
fumed compute w hat would be its mean anomaly by the 
rule above given, and find the difference ‘between this re- 
full and the mean anomaly given; then aftlime another 
eccentric anomaly, and proceed in the fame way with ir, 
finding another computed mean anomaly, and its difference 
from tiie given one ; and treating thefe differences as in 
the rule of polition for a nearer value of the eccentric ano¬ 
maly : repeating tire operation till the refult comes out 
exaCt. Then, front the eccentric anomaly, tints found, 
compute the true anomaly by the firft rule above laid down. 
Of tiiis problem, Dr. Wallis firft gave the geometrical 
folution by means of the protracted cycloid; and Sir Naac 
Newton did the fame at prop. 31. lib. 1. Princip. But, 
thefe methods being unfit for the purpofe of the practical 
aftronomer, various feries for approximation have been 
given, viz. feveral by Sir Ifaac Newton, in his “ Frag- 
menta Epiftolarum,” page 26, as alfo in the Schol. to the 
prop, above-mentioned, which is his belt, being not oniy 
fit for the planets, but alfo for the comets, whofe orbits 
are very eccentric. Dr. Gregory, in his Aftron. lib. 3. has 
alfo given the folution by a feries, as well as M. Reyneau, 
in his “ Analyfe Demontree,” page 713, rcc. And a better 
(till for converging is given by Keil, in iiis “ PrafteCt. 
Aftron.” page 375 ; lie fays, if the arc AH be the mean 
anomaly, calling its line c, coiin <cf the eccentricity g, alio 
putting 2 —ge, and a —1 -\- fg ; then the eccentric anomaly 
TZ 2. “ 
AD will be 2=—x(i -y &c.) fuppofing r^257-29578 
. CL Cl 
T Z 
degrees ; of which the firft term — is fufficient for all the 
a 
planets, even for Mars itfelf, where the error will not 
exceed the 200th part of a degree ; and in the orbit of 
the earth, the error is lefs than the 1 ooooth part of a 
degree. 
Dr. Seth Ward, in his “ Aftronomia,Geometries,” takes 
the angle AFP at the other focus, where the Jim is not, 
for the mean anomaly, and thence gives an elegant folu¬ 
tion. But this method is not fufficiently accurate when 
the orbit is very eccentric, as in that of tiie planet Mars, 
as is fhewn by Bullialdus, in his defence of the Philolaic. 
Aftron. againil Dr. Ward. Plowever, when Newton’s cor¬ 
rection is made, as in tiie SChol. above-mentioned, and the 
problem refolved according to Ward’s hypothefis, Sir Ifaac 
affirms that, even in the orbit of Mars, there -will fcarcely 
ever be an error of more than one fecund. 
ANO'MIA, f in zoology, a genus of infects belonging 
to tiie order of vermes teftacea. The fliell is bivalve, and 
the valves are unequal. One valve is perforated near the 
hinge; affixed by that perforation to fome other body. 
There are twenty-five fpecies of tiie anemia; of which 
only two are natives of the Britifli feas, viz. 1. Theephip, 
•pium, with tiie habit of an oyfter ; tit? one fide convex, 
the other flat ; perforated; adherent to both bodies, often 
to cyfter-fhells, by a ftrong tendinous ligature ; colour of 
tiie inlide perlaceous. Size, near two inches diameter. 
2. Tiie fquaremula, with fiiells refembling; the fca'es of 
fifti; very delicate and filvery; much flatted ; perforated ; 
very fmall. Adheres to oyfters, crabs, lobfters, and fiiells. 
The fpecies of this genus are commonly called beaked cockles . 
No name lias been given to tiie fifu that inhabit it; for the 
recent fiiells of this kind are fo very rare, that there is 
fcarcely one to be found perfect. They are perhaps, as 
well as that which lias given its form to file cornu ammonis, 
inhabitants of tiie deepeft part of the ocean ; confequcntly 
it muft be fome extraordinary agitation of that great body 
of water that can bring, them at all to our knowledge ip 
their recent ftate. The foflile fpecies of the anoniia genus 
are uncommonly numerous in this ifland, in our chalk- 
.9 C pits. 
