The mariners magazine, or, Sturmy's mathematical and practical arts containing the description and use of the scale of scales, it being a mathematical ruler, that resolves most mathematical conclusions, and likewise the making and use of the crostaff, quadrant, and the quadrat, nocturnals, and other most useful instruments for all artists and navigators : the art of navigation, resolved geometrically, instrumentally, and by calculation, and by that late excellent invention of logarithms, in the three principal kinds of sailing : with new tables of the longitude and latitude of the most eminent places ... : together with a discourse of the practick part of navigation ..., a new way of surveying land ..., the art of gauging all sorts of vessels ..., the art of dialling by a gnomical scale ... : whereunto is annexed, an abridgment of the penalties and forfeitures, by acts of parliaments appointed, relating to the customs and navigation : also a compendium of fortification, both geometrically and instrumentally

Sturmy, Samuel, 1633-1669.

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STƲRMY'S MATHEMATICAL and PRACTICAL ARTS The Sixth Book. Wherein is contained a Definition of the Circles of the Sphere, with the manner how to Resolve all the most necessary Propositions thereunto belonging, by a Line of Chords and Signs, or by Chords and Tangents; as also by Calculation by Tables.

CHAP. III. How to Calculate the Sun's true place.

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Page 106

PROBL. I.

Example.

ON the 12 of May I would find the Suns true place by the former Rules; The Sun enters Gemini May 11; which Substract from 12, the Remainer is 1, which shews the Sun to be in 1 deg. of Gemini the third Sign; that is, 61 degr. from the next Equinoctial-Point.

2. Example.

Let it be required to know the Suns Place the 4th of November; on the 11 day of that Month the Sun enters Sagitarius, and the 13th day of September he enters Libra: betwixt the 13 of September, and the 4 of November is 52 days, and consequently 52 degr. from the Equinoctial-Point Libra; then 30 taken from 52, there remains 22 degr. the Suns place in Scorpio, which is the thing required.

But here is a nearer Rule yet than this, to find the Suns place exactly, and that is by Mr. Vincent Wing's Hypothesis, and Tables in Astronomia Britanica, how to Calculate his true place from Earth, the Rule is,

First, enter the Table of the Middle-Motion of the Sun, and write out the Epocha next going before the time given, under which set the Motion distinctly belonging to the Years, Months, and Days, and Hours, and Minutes, if any be; (only in the Bissextile or Leap-Years,) after February a Day is to be added to the number of Days given; then adding them all together, the sum will be the Middle-Motion of the Sun for the time given.

As for Example.

Suppose the time given be the 12 of May at Noon 1667, at which time the Suns place is required.

Time given.	Longitude ☉	Apog. ☉
	S	D	M	S	S	D	M	S
The Epocha 1661 years In∣cluding 6 May. Days 12.	9	20	24	49	3	6	45	5
11	29	33	07	0	0	6	10
3	28	16	39				20
0	11	49	40				2
The Suns Mean-motion, or Longitude.	2	00	04	15	3	6	51	37

2. Substract the Apog. of the Sun from his Mean-Longitude, and the Remain will be his Mean Anomaly.

Example.	S	D	M	S
The Suns Mean-Longitude is	2	00	04	15
The Apogeum Substracted	3	06	51	37
The Suns Anomaly.	10	23	12	38

With the Suns Anomaly enter the Table of his Equation with the Sign on the Head and the deg. descending on the left hand, if the Number thereof be under 6 Signs; but if it be more than 6 Signs, enter with the Sign in the bottom, and the degr. ascending on the right hand, and in the common-Angle you have the Equation answering thereunto; only you must, if need require, remember to take the Proportional part.

Example.

	S	D	M	S
In the Table of Equation answering to 23 degr. is	0	01	11	51
The Suns Mean-Longitude, add	2	00	04	15
The Suns true Longitude.	2	01	16	06

Therefore the true place of the Sun is in 1 degr. 16 min. 6 seconds of Gemini.

Another Example.

In the Year 1583 March 14 at Noon, in the Meridian of Ʋraneburg in Denmark, thrice Noble Ticho-Brahe, most excellently observed the Suns true place in 3 deg. 17 min. 40 seconds of ♈. The time at London was 1583 March 13 day 23 h. 8 m.

Page [unnumbered]

[illustration] [geometrical diagram]

The Convex-Sphere, which resolves all the most useful Problems in Astronomy, by the Direction of 13 Problems following.

[illustration] [geometrical diagram]

The Concave-Sphere, which resolves 13 Problems, viz. and by them may be resolved, most of the useful Problems in Astronomy.

Page [unnumbered]

A Table of the Suns Mean Motion.The Apoche, or Radius.

Year.	Longit. ☉	Apog. ☉
S	D	M	S	S	D	M	S
Ch. 1	9	07	59	51	2	08	20	03
1581	9	19	48	55	3	05	22	55
1601	9	19	57	54	3	50	43	28
1621	9	20	06	52	3	06	04	00
1641	9	20	15	51	3	06	24	33
1661	9	20	24	49	3	06	45	05
1681	9	20	33	48	3	07	05	38

☉ Mean Motion in Years above 20.

Year.	Longit. ☉	Apog. ☉
S	D	M	S	S	D	M	S
20	0	00	08	59	0	00	20	33
40	0	00	17	57	0	00	41	05
60	0	00	26	56	0	11	01	38
80	0	00	35	54	0	11	22	10
100	0	00	44	53	0	11	42	43
200	0	02	29	45	0	03	25	26
300	0	02	14	38	0	05	08	08
400	0	02	59	31	0	06	50	51
500	0	03	44	23	0	08	33	34
600	0	04	29	16	0	10	16	17
700	0	05	14	09	0	11	59	00
800	0	05	59	01	0	13	41	42
900	0	06	43	54	0	15	24	25
1000	0	07	28	47	0	17	07	08
2000	0	14	57	34	1	04	14	15
3000	0	22	26	21	1	21	21	22
4000	0	29	55	08	2	08	28	30
5000	1	07	33	55	2	25	35	37
6000	1	14	52	42	3	12	42	44

☉ Mean Motion in years under 20

Years.	Longit. ☉	Apog. ☉
S	D	M	S	M	S
1	11	29	45	40	1	02
2	11	29	31	20	2	04
3	11	29	16	59	3	05
L 4	00	00	01	48	4	07
5	11	29	47	28	5	08
6	11	29	33	07	6	10
7	11	29	10	47	7	12
L 8	00	00	03	35	8	13
9	11	29	49	15	9	14
10	11	29	34	55	10	16
11	11	29	20	35	11	18
L 12	00	00	05	23	12	20
13	11	29	51	03	13	21
14	11	29	36	43	14	23
15	11	29	22	23	15	25
L 16	00	00	07	11	16	26
17	11	29	52	51	17	28
18	11	29	38	31	18	29
19	11	29	24	10	19	31
L 20	00	00	08	59	20	33

☉ Mean Motion in Months.

	Longit. ☉	Apog. ☉
S	D	M	S	M	S
Janu.	00	00	00	00	00	00
Febr.	01	00	33	18	00	05
Marc.	01	28	09	11	00	10
April	02	28	42	30	00	15
May	03	28	16	39	00	20
June	04	28	49	58	00	25
July	05	28	24	07	00	31
Aug.	06	28	57	25	00	36
Sept.	07	29	30	44	00	42
Octo.	08	29	04	54	00	47
Nov.	09	29	38	12	00	53
Dec.	10	29	12	22	00	59

The Calculation. Apog. ☉

	Long. ☉
S	D	M	S	S	D	M	S
The ☉ Apocha.
☞ 1581.	9	19	48	55	3	5	22	55
Years added 2	11	29	31	20			2	4
March.	1	28	9	11				10
Days 13		12	48	48				2
Hours 23			56	40				0
Minutes 8				20				0
The Suns Mean Motion.	0	1	15	14	3	5	25	11
Apogeum Substract.	3	5	25	11
The Anomaly of ☉	8	25	50	03
The Equator added to 115′ 14′		2	2	51
The Suns true place, with Observation.	♈	3	18	5	Agreeing.

(3) Example the time given the 10 of April 1665 at Noon; and admit by the former Rules we have found the Suns Mean Motion 29 degr. 0 min. 30′ his Apogeum 3 s. 6 d. 49 m. 29 s. his Anomally 9 s. 22 d. 11′ 1″; first find a Proportional part, the Equat. answering to 22 s. 1 d. 52′ 22″

The Equator answering to 23 d.	1 51 29
their difference	59

Then I say, if 1 deg. or 60 min. give 53 seconds, what shall 11 of the Anomaly give? by the Rule of proportion, 〈 math 〉

A Table of the Suns Mean Motion.

	Longit. ☉	Apog.	H	Long. ☉	M	Lon. ☉.
S	D	M	S		S	D	M	S	M	S
1	0	0	59	08	0	0	1	0	2	24	31	1	17
2	0	01	58	17	0	0	2	0	4	56	32	1	19
3	0	02	57	25	0	0	3	0	7	24	33	1	21
4	0	03	56	33	0	1	4	0	9	51	34	1	24
5	0	04	55	42	0	1	5	0	12	19	35	1	26
6	0	05	54	50	0	1	6	0	14	47	36	1	29
7	0	06	53	58	0	1	7	0	17	15	37	1	31
8	0	07	53	07	0	1	8	0	19	43	38	1	34
9	0	08	52	15	0	1	9	0	22	11	39	1	36
10	0	09	51	23	0	2	10	0	24	38	40	1	39
11	0	10	50	31	0	2	11	0	27	6	41	1	41
12	0	11	49	40	0	2	12	0	29	34	42	1	43
13	0	12	48	49	0	2	13	0	32	2	43	1	46
14	0	13	47	57	0	2	14	0	34	30	44	1	48
15	0	14	47	05	0	2	15	0	36	58	45	1	51
16	0	15	46	13	0	3	16	0	39	25	46	1	53
17	0	16	45	22	0	3	17	0	41	53	47	1	56
18	0	17	44	30	0	3	18	0	44	21	48	1	58
19	0	18	43	38	0	3	19	0	46	40	49	2	01
20	0	19	42	47	0	3	20	0	49	17	50	2	03
21	0	20	41	55	0	3	21	0	51	45	51	2	06
22	0	21	41	03	0	4	22	0	54	13	52	2	08
23	0	22	41	12	0	4	23	0	56	40	53	2	11
24	0	23	40	20	0	4	24	0	59	8	54	2	13
25	0	24	39	28	0	4	25	1	01	34	55	2	18
26	0	25	38	37	0	4	26	1	04	04	56	2	18
27	0	26	37	45	0	4	27	1	06	32	57	2	20
28	0	27	36	53	0	5	28	1	09	00	58	2	23
29	0	28	35	02	0	5	29	1	11	27	59	2	25
30	0	29	35	10	0	5	30	1	13	55	60	2	28
31	0	00	34	18	0	5	M	m	se.	th.	sec	sec	th.

A Table of the Suns Equation.

	Sig. 0 AE Sub.	Sig. 1 AE Sub.	Sig. 2 AE Sub.	Sig. 3 AE Sub.	Sig. 4 AE Sub.	Sig. 5 AE Sub.
	D	M	S	D	M	S	D	M	S	D	M	S	D	M	S	D	M	S
0	0	0	0	0	59	32	1	44	28	2	2	54	1	48	23	1	3	26	30
1	0	2	5	1	1	21	1	45	34	2	2	56	1	47	20	1	1	32	29
2	0	4	9	1	3	10	1	46	38	2	2	56	1	46	15	0	59	37	28
3	0	6	12	1	4	57	1	47	41	2	2	55	1	45	9	0	57	40	27
4	0	8	16	1	6	42	1	48	40	2	2	52	1	44	1	0	55	42	26
5	0	10	19	1	8	26	1	49	38	2	2	47	1	42	50	0	53	43	25
6	0	12	22	1	10	9	1	50	34	2	2	39	1	41	37	0	51	43	24
7	0	14	25	1	11	51	1	51	29	2	2	29	1	40	22	0	49	42	23
8	0	16	28	1	13	32	1	52	22	2	2	17	1	39	4	0	45	39	22
9	0	18	30	1	15	11	1	53	13	2	2	2	1	37	45	0	45	35	21
10	0	20	32	1	16	49	1	54	1	2	1	46	1	36	24	0	43	31	20
11	0	22	34	1	18	26	1	54	43	2	1	29	1	35	3	0	41	26	19
12	0	24	37	1	20	02	1	55	31	2	1	7	1	32	30	0	39	20	18
13	0	26	39	1	21	36	1	56	14	2	0	44	1	32	2	0	37	14	17
14	0	28	41	1	23	9	1	56	55	2	0	18	1	30	44	0	•5	•	16
15	0	30	42	1	24	41	1	57	34	1	59	49	1	29	13	0	3•	•8	15
16	0	32	43	1	26	11	1	58	10	1	59	19	1	27	41	0	3	50	14
17	0	34	44	1	27	40	1	58	44	1	58	47	1	26	7	0	2•	•1	13
18	0	36	43	1	29	8	1	59	16	1	58	12	1	24	32	0	26	•1	12
19	0	38	41	1	30	34	1	59	46	1	57	35	1	22	56	0	24	•	11
20	0	40	38	1	31	58	2	0	14	1	56	56	1	21	18	0	22	1•	10
21	0	32	35	1	33	20	2	0	40	1	56	14	1	19	38	0	19	5•
22	0	34	81	1	34	41	2	1	04	1	55	30	1	17	56	0	17	4•
23	0	46	27	1	36	0	2	1	26	1	54	44	1	16	12	0	15	36
24	0	48	22	1	37	17	2	1	46	1	53	56	1	14	26	0	13	33
25	0	50	16	1	38	33	2	2	3	1	53	5	1	12	40	0	11	10
26	0	52	09	1	39	48	2	2	18	1	52	12	1	10	52	0	8	57
27	0	54	1	1	41	1	2	2	30	1	51	18	1	9	2	0	6	43
28	0	55	52	1	42	12	2	2	40	1	50	21	1	7	11	0	4	29
29	0	57	42	1	43	21	2	2	48	1	49	23	1	5	18	0	2	15
30	0	59	42	1	44	28	2	2	54	1	48	23	1	3	36	0	0	0
	Add Sig. 11	Add Sig. 10	Add Sig. 9	Add Sig. 8	Add Sig. 7	Add Sig. 6

Place this Table between Pag. 106 and 107.

Page 107

Multiply 53 by 11, the Product is 583, which Divide by 60, the Quotient will be 9″ 45/60; and because the Equation decreases I Substract it from the Equa. answering 22 degr. which is 1 d. 52″ - 12″ for the true Equation desired, which according to the Title, being added to the Suns Mean-Longitude, giveth the true place of the Sun re∣quired.

Example.

	S	D	′	″
The Suns Mean-Longitude.	0	29	00	30
The Equation added.		1	52	12
The Suns true Longitude.	1	00	52	42

D. ″ ″

Therefore the Suns true place is in 0 52:42 of Taurus; these Examples are suffi∣cient for Direction, to find the Suns true place at any time.

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