NODES. 
other fide, in the half of her orbit that is fartheft from the 
fun. Whence we fhall have this general rule for judging of 
the effeét of the fun onthe nodes: that while the moon is in 
the half of her orbit that is neareft the fun, the node towards 
i ing i towards the con- 
contrary direGtion, and for the fame reafon makes the en- 
i When the line of 
to either fide; and therefore, in that cafe, the nodes have no 
motion at all. 
(See Moon 
ecliptic is alfo fubje& to many variations. When the nodes 
in th i m one quarter 
creafes again as fhe moves from the conjunction to the next 
quarter, and is there reftored nearly to its firft quantity. 
When the line of the nodes paffes through the fun, the in- 
clination of the moon's orbit is not affected by the aétion of 
the fun; becaufe, in that cafe, the plane of her orbit pro- 
duced, paffes through the fun, and, therefore, the a¢tion of 
the fun can have no effe& to bring the moen out of this 
plane to either fide. In this laft cafe the inclination of the 
moon’s orbit is greateft; it increafes as the nodes move to- 
wards the quarters; and it is leaft of all when the nodes are 
in the quarters, and the moon either in the conjunction or op- 
pofition. Newton has calculated thefe irregularities from 
their caufes, and finds his conclufions agree very well with 
e moon is in the 
bfervations of aftronomers. ent 
the points E, F, th 
fouth latitude, according as fhe is then on the north or fouth 
fide of the ecliptic. 
The moon muft be is or near one of the nodes when there 
is an eclipfe, either of the fun or moon. 
The place of the moon’s nodes may be determined, either 
in the fame wzy as that of the nodes of the other planetary 
orbits, or by the following method. 
the moon, the moon’s place at the middle of the eclipfe is di- 
reGtly oppofite to the fun, and the moon muft alfo then be 
in the node; calculate therefore the true place of the fun, or, 
which is more exa@, find its place by obfervation, and the 
In a central eclipfe of 
you have the longitude of the earth at E, or theangle ~ SE; 
compute alfo the longitude of the planet, or the an gle p Sv; 
and the difference of thefe two angles is the angle ES v of 
commutation.”? Obferve the place of the planet in the 
angle vES 
known, the place feen from the fun will be known. Alfo, 
tang. o: rad.::v P: Ew by trig. and rad. : tan. 
PSv:vS:oP:.«tang. PEo: tan PSo:: Ev 
:: fin. 
longitude : 
earth and planet :: 
the heliocentric latitude. When the latitude is {mall, 
very nearly as PS: 
S » of the planet from the fun may be found by this propor- 
tion, rad.: cof. PSv::PS:S. See HeLiocentRic 
Latirupe. 
ow to determine the place of the node, find the planet’s 
heliocentric latitudes juft before and after it has paffed the 
node, and let a and b be the places in the orbit, m and 2 the 
places reduced to the ecliptic; then the triangles am N, 
ban ig. 2.), which we may confider as rectilinear, being 
fimilar, we have am: b2:: Nm: Na; therefore, am + ba 
sam: Na +N 
e the two 
degree, this rule will not be fufficiently accurate. 
cafe our computations muft be made for {pherical triangles in 
the following manner. Put mn = a,am = 
fin. a — @ 
—— = cotan, N = 
tan. } 
N m= «x; then by trigon. 
fin.xy : . —— 
aa radius being unity ; but fin. a — # = fin. a x cof. © 
an. B 
fin. a x cof.x — fin. x x cof.a 
— fin x X cof. a; hence _— 
tang. 6 
_ fe 7 Fae. fin.a x tang. B _ fin. «x 
~ tang. B’ pee tang. 5 + cof.a x tang. 8 ~ cof. x 
= tang. x. 
The longitudes of the nodes of the planets for the begin- 
ning of 1750 are, Mercury, 1° 15° 20' 43" Venus, 2° 14° 
26' 18"; Mars, 18 17° 38 38"; Jupiter, 3° 7°55! 325 Sa- 
turn, 3° 21° 32' 22" Georgian, 2° 12° 47’. 
To determine the inclination of the orbit, we have a m the 
latitude of the planet, and m V its diftance upon the ecliptic 
the node; hence, fin. m N : tang. @ m :: rad. ; tang. 
of theangle N. But the obferva 
muft 
