Astronomia Britannica exhibiting the doctrine of the sphere, and theory of the planets decimally by trigonometry, and by tables : fitted for the meridian of London ... / by John Newton ...

CHAP. 17. Of the Motion of Mercury.

THe forme of calculating the place of this Planet is the same with Venus, the Dimensions of whose orbs we shall give you, as the learned Bullialdus hath computed them, but first we will set down the middle motions thereof to the former time.

The middle motions of Mercury.

An. Christ.	Longit. ☿	Aphel. ☿	Node ☿
1500	352. 53750	248. 73556	039. 85639
80	59. 53472	2. 31611	2. 12417
6	326. 41889	. 17361	. 15917
Iuly	147. 58583	. 01694	. 01528
D 1••	65. 47806	. 00126	. 00117
H 18	3. 06917
P 4564	. 07781
Meane Mot.	234. 70198	251. 24348	42. 15618
Aphel. Snbt.	251. 24348	Rest Anom.	343. 45850

The proportion between the Earths orb, and the orbe of Mercury is as 100. 000 to 38585 Semicentricity in the same parts is, 8105. The parts or greatest inclination 4635. And the angle it selfe 6. 90. In the trian∣gle therefore M E H, of the first Diagram of the former Chapter we have known. 1. The halfe sum of the opposite angles M E H and M H E, 8. 27075 the halfe of 16. 54150 which is the complement of the meane A∣nomaly, 343. 4585 to a circle.

2. The side M E	77170
3. The side M H	16210
Summe	93380 co. ar.	5. 0297462
Differ.	60960	4. 7850449
So tang. halfe sum.	8. 27075	9. 1628126
To tang. halfe differ.	5. 42532	8. 9776037
Difference	2. 84543 Angle M E H
Difference doubled	5. 69086 Angle M B H or the E∣quation to be added to the meane longitude, because the Anomaly is more then a semicircle.

Example.

The meane Longitude of Mercury

234. 70198

Equation adde

5. 69086

Eccentrick place

240. 39284

Node subtract

42. 15618

Argument of Latitude K L

198. 23666

To finde the distance of Mercury from the Sun.

As the sine of MBH	5. 69086 co. ar.	1. 0036592
To the side MH	16210	4. 20978••0
So sine of EMH	16. 54150	9. 4544022
To the side BH	46541	4. 6678444

To finde the Reduction.

As Radius, to cosine of XKL	6. 90	9. 9968431
So tangent of KL	18. 23666	9. 5178453
To tangent of XK	11. 11322	9. 5146884
Reduction	12344

And because the argument of Latitude is more then 180, it must be sub∣tracted from the eccentrick place 240. 39284

And then the eccentrick reduced will be. 240. 26940

To finde the present inclination.

As Radius
To the greatest inclination EB	4635	3. 6660497
So sine of KL.	18. 23666	9. 4954646
To the inclinat. XL	1450	3. 1615143

Which are the parts of inclination agreeing to the common Radius 38585. But the distance of Mercury from the Sun being put for Radius, the inclination will be. 1749

For as Radius DL	38585 co. ar.	5. 41358••5
To Mercury dist. BH or AL	46541	4. 6678444
So is XL	1450	3. 1615143
To XL	1749	3. 2429402

To finde the distance corrected by Curtation.

As AL	46541 co. ar.	5. 3321556
To Radius		10. 0000000
So is XL	1749	3. 2429402
To the sine of LAX	2. 15437	8. 5750958
As Radius		10. 0000000
To AL	46541	4. 6678444
So cosine of LAX	2. 15437	9. 9996929
To AX	46509	4. 6675373

To finde the second inequality of Mercury.

We must have given, 1. The Angle NAS which is to be found by sub∣ductiug the Suns place, from the eccentrick place of Mercury reduced, or this from it, so that less then 6 signes may remain, this remainer is the

Anomaly of the orbe, and the complement thereof is the Angle NAS, or the halfe, is the halfe sum of the opposite angles.

Example.

The eccentrick of Mercury reduced

220. 26940

The Suns true place

154. 07347

Anomaly of the orbe

96. 19593

Complement is NAS

83. 80407

Halfe Anomaly

48. 09796

These given with the sides NA and SA. the Analogies are

As the greater side SA	100895 co. ar.	4. 9961293
Is to Radius		10. 0000000
So is the lesser side NA	46509	4. 6675373
To the tangent of	24. 74799	9. 6636666
Adde	45.
As Radius
To the cotang. of	69. 74799	9. 5669785
So tang. halfe summe	48. 09796	10. 0470559
To tang. halfe difference	22. 35160	9. 6140344
Summe	70. 44956 Angle ANS
Difference	25. 74636 Angle ASN

Because the Suns place was subtracted from the eccentrick of Mercury reduced, therefore the angle of Elongation ASN must be added to the

Suns place.

154. 07347

Elongation ASN adde

25. 74636

True place of Mercury

179. 81983

To finde the distance of Mercury from the Earth.

As the sine of ANS	70. 44956 co. ar.	0. 0257891
To the side AS	100895	5. 0038707
So the sine of NAS	83. 80407	9. 9974556
To the side SN	106442	5. 0271154

To finde the Latitude of Mercury from the Earth.

As the side SX	106442 co. ar.	4. 9728846
Is to Radius		10. 0000000
So is XL	1749	3. 2429402
To the tang. of XSL	0. 94169	8. 2158248
Which is the south Latitude of Mercury.