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 / by Capt. Samuel Sturmy.

CHAP. III. A Formal and Exact Way of Setting down and Perfecting a Sea-Reckoning.* 1.1

THis being the most necessary Rule in this Art of Navigation, How to keep an Exact Reckoning; Although the Course and Distance cannot be so truly and certainly known, as the Latitude may be; yet we must endeavour in these also to come as neer the truth as may be; the rather, for that some Reckonings must necessarily depend wholly upon them. Therefore we come now to shew an Orderly and Exact way of Framing and Keeping a Reckoning at Sea; for which purpose I have inserted this Table following, which sheweth how much a Ship is more Nor∣therly or Southerly, and how much Easterly or VVesterly, by sailing upon any Point

or Quarter-point of the Compass, any distance or number of Miles or Leagues propo∣sed.

Mr. Norwood many Years since laid the ground of making this Table, after this Proportion, [As Radius is in Proportion to Distance run: So is the Sine-Complement of the Rhomb, to the Distance of North or South: And so is the Sine of the Rhomb to the Distance of East or West] as you may see by the first and second Case of Plain Triangles.

Therefore for every Point and Quarter-point from the Meridian, there are four Columns: In the first thereof is set down the number of Leagues or Miles run or sailed upon that Point or Quarter-point of the Compass; The second sheweth how much you have altered the Latitude, that is, how much you are more Southerly or Northerly, by running so far upon that Point or Quarter-point; The third sheweth how much you are more Easterly or Westerly, by running or sailing that Course and Distance, as you have been before directed.

Note this, The Numbers set in the first Column from 1 to 10, are also to be un∣derstood from 10 to 100, or from 100 to 1000: and the Figure of the fourth place answers to the Figure in the first.

Course	Distance.	Southing.	Westing.
South	100	995	98
½ Po. W.	70	697	68
	3	29	3
Leagues.	173	1721	168

As, Suppose a Ship sails away South ½ a Point Westerly 173 Leagues or Miles; we set down this Number thus. Look into thefirst Column for the ½ Point, or ½ the first Rhomb from the Meridian against 10 is sometimes made use of, and understood to be 100. I find in the second Column against it 995 (or you may have the same Number at 100 towards the Foot of the Table, omitting the last Figure) and then in the third Column you may see 98; also against 70, or 7, there is 697, and in the second 68; and in the third against three in the first Column is 29, in the second is 2 and 9/100, which is almost 3/10; therefore I put down 3.

These summed up as in the Table, shews that the Ship sailing upon the first half Point from the Meridian, as namely, S. ½ W. is to the Southwards of the Place she de∣parted 172 1/10 Leagues or Miles, and to the Westward 16 Leagues and 8/10. If you desire more Exactness, you may use all the Places for the greatest Number, which is 100, (viz.)

A Traverse-Table for every Point, Half-Point, and Quarter-Point of the Compass, to the 100 part of a League or Mile; which gives the Difference of Lat. and Departure from the Meridian.

The Traverse-Table. The 1 Points Quarter.
Dist. in Leagues or Miles sail'd.	2 deg.	49 m.	5 deg.	38 m.	8 deg.	26 m.	11 deg.	15 m.	Dist. in Leagues or Miles sail'd.
0 Point ¼	0 Point ½	0 Point ¾	1 Point.
N S	E W	N S	E W	N S	E W	N S	E W
1	01 00	00 05	01 00	00 10	00 98	00 14	00 98	00 20	1
2	02 00	00 10	01 99	00 20	01 97	00 29	01 96	00 39	2
3	03 00	00 15	02 98	00 29	02 96	00 44	02 94	00 58	3
4	04 00	00 20	03 98	00 39	03 95	00 58	03 92	00 78	4
5	04 09	00 25	04 97	00 49	04 94	00 73	04 90	00 93	5
6	05 09	00 29	05 97	00 59	05 93	00 88	05 88	01 17	6
7	06 09	00 34	06 97	00 69	06 92	01 02	06 86	01 37	7
8	07 09	00 39	07 96	00 78	07 91	01 17	07 85	01 56	8
9	08 09	00 44	08 96	00 88	08 90	01 32	08 83	01 76	9
10	09 09	00 49	09 95	00 98	09 89	01 46	09 81	01 95	10
11	10 98	00 54	10 95	01 08	10 88	01 61	10 79	02 15	11
12	11 98	00 59	11 94	01 18	11 87	01 76	11 77	02 34	12
13	12 98	00 63	12 94	01 27	12 86	01 91	12 75	02 54	13
14	13 98	00 68	13 93	01 37	13 85	02 05	13 73	02 73	14
15	14 98	00 73	14 93	01 47	14 84	02 20	14 71	02 19	15
16	15 98	00 78	15 92	01 57	15 83	02 34	15 69	03 12	16
17	16 98	00 83	16 92	01 67	16 82	02 49	16 67	03 32	17
18	17 97	00 88	17 91	01 76	17 80	02 64	17 65	03 51	18
19	18 97	00 93	18 91	01 86	18 79	02 79	18 64	03 71	19
20	19 97	00 98	19 90	01 96	19 78	02 93	19 62	03 90	20
21	20 97	01 03	20 90	02 06	20 77	03 08	20 60	04 10	21
22	21 97	01 08	21 98	02 16	21 76	03 22	21 58	04 29	22
23	22 97	01 13	22 89	02 25	22 75	03 37	22 56	04 49	23
24	23 97	01 17	23 88	02 35	23 74	03 52	23 54	04 68	24
25	24 97	01 22	24 88	02 45	24 73	03 66	24 52	04 88	25
26	25 96	01 27	25 87	02 55	25 71	03 81	25 50	05 07	26
27	26 96	01 32	26 87	02 65	26 70	03 96	26 48	05 27	27
28	27 96	01 32	27 86	02 75	27 69	04 10	27 46	05 46	28
29	28 96	01 42	28 86	02 84	28 68	04 25	28 44	05 66	29
30	29 96	01 47	29 86	02 94	29 67	04 40	29 42	05 85	30
31	30 96	01 52	30 85	03 04	30 66	04 55	30 40	06 05	31
32	31 96	01 57	31 85	03 14	31 65	04 69	31 38	06 24	32
33	32 96	01 61	32 84	03 23	32 64	04 84	32 37	06 44	33
34	33 95	01 66	33 84	03 33	33 63	04 98	33 35	06 63	34
35	34 95	01 71	34 83	03 43	34 62	05 13	34 33	06 83	35
36	35 95	01 75	35 83	03 53	35 61	05 28	30 31	07 02	36
37	36 95	01 81	36 82	03 63	36 60	05 42	36 29	07 22	37
38	37 95	01 86	37 82	03 73	37 59	05 57	37 27	07 41	38
39	38 95	01 91	38 81	03 82	38 58	05 72	38 25	07 6••	39
40	39 95	01 96	39 81	03 92	39 57	05 87	39 23	07 80	40
41	40 95	02 01	40 80	04 02	40 55	06 02	40 21	08 00	41
42	41 95	02 06	41 80	04 12	41 54	06 16	41 19	08 19	42
43	42 95	02 11	42 79	04 21	42 15	06 31	42 17	08 39	43
44	43 94	02 15	43 79	04 31	43 52	06 45	43 15	08 58	44
45	44 94	02 20	44 78	04 41	44 51	06 60	44 14	08 78	45
46	45 94	02 25	45 78	04 51	45 60	06 75	45 12	08 77	46
47	46 94	02 30	46 77	04 61	46 49	06 89	46 10	09 17	47
48	47 94	02 35	47 77	04 70	47 48	07 04	47 08	09 36	48
49	48 94	02 40	48 76	04 80	48 47	07 20	48 06	09 56	49
50	49 94	02 45	49 76	04 90	49 46	07 33	49 04	09 75	50
51	50 93	02 50	50 75	05 00	50 44	07 48	50 02	09 95	51
52	51 93	02 55	51 75	05 10	51 43	07 63	51 00	10 14	52
53	52 93	02 60	52 74	05 20	52 42	07 77	51 98	10 34	53
54	53 93	02 65	53 74	05 29	53 41	07 92	52 96	10 53	54
55	54 93	02 70	54 73	05 39	54 40	08 07	53 94	10 73	55
56	55 93	02 75	55 73	05 49	55 30	08 21	54 92	10 92	56
57	56 93	02 79	56 72	05 59	56 38	08 36	55 90	11 12	57
58	57 93	02 84	57 72	05 68	57 37	08 51	56 89	11 31	58
59	58 92	02 89	58 71	05 78	58 36	08 65	57 87	11 51	59
60	59 92	02 94	59 71	05 88	59 35	08 80	58 85	11 70	60
70	69 91	03 43	69 66	06 86	69 24	10 27	68 65	13 65	70
80	79 90	03 92	79 61	07 84	79 13	11 73	78 46	15 60	80
90	89 89	04 41	89 56	08 82	89 02	13 20	88 27	17 55	90
100	99 87	04 90	99 51	09 80	98 91	14 67	98 08	19 50	100
200	199 76	09 80	199 02	19 60	197 82	29 34	196 16	39 00	200
	E W	N S	E W	N S	E W	N S	E W	N S
	7 Point ¾	7 Point ½	7 Point ¼	7 Point.
	87 deg.	11 m.	84 deg.	22 m	81 deg.	34 m.	78 deg.	45 m.
The 7 Points Quarters.

A Traverse-Table for every Point, Half-Point, and Quarter-Point of the Compass, to the 100 part of a League or Mile; which gives the Difference of Lat. and Departure from the Meridian.

The Traverse-Table, The 2 Points Quarter.
Dist. in Leagues or Miles sail'd.	14 deg.	04 m.	16 deg.	52 m.	19 deg.	41 m.	22 deg.	30 m.	Dist. in Leagues or Miles sail'd.
1 Point ¼	1 Point ½	1 Point ¾	2 Points.
N S	E W	N S	E W	N S	E W	N S	E W
1	00 97	00 24	00 96	00 29	00 94	00 33	00 92	00 38	1
2	01 94	00 48	01 91	00 58	01 88	00 67	01 85	00 76	2
3	02 91	00 72	02 87	00 87	02 82	01 01	02 77	01 75	3
4	03 88	00 97	03 83	01 16	03 77	01 34	03 70	01 53	4
5	04 85	01 21	04 78	01 45	04 71	01 68	04 62	01 91	5
6	05 82	01 45	05 74	01 74	05 65	02 02	05 54	02 30	6
7	06 79	01 70	06 70	02 03	06 59	02 35	06 47	02 68	7
8	07 76	01 94	07 66	02 32	07 53	02 70	07 39	03 16	8
9	08 73	02 18	08 61	02 61	08 47	03 03	08 31	03 44	9
10	09 70	02 43	09 57	02 90	09 41	03 37	09 24	03 83	10
11	10 67	02 67	10 53	03 19	10 36	03 71	10 16	04 21	11
12	11 64	02 91	11 48	03 48	11 30	04 04	11 09	04 59	12
13	12 61	03 15	12 44	03 77	12 24	04 36	12 01	04 97	13
14	13 58	03 40	13 40	04 06	13 18	04 72	12 93	05 36	14
15	14 55	03 64	14 35	04 35	14 12	05 05	13 86	05 74	15
16	15 52	03 88	15 31	04 64	15 06	05 39	14 78	06 12	16
17	16 49	04 13	16 27	04 93	16 00	05 73	15 71	06 51	17
18	17 46	04 37	17 22	05 22	16 95	06 06	16 63	06 89	18
19	18 43	04 61	18 18	05 51	17 89	06 40	17 55	07 27	19
20	19 40	04 86	19 14	05 81	18 83	06 74	18 48	07 65	20
21	20 37	05 10	20 10	06 10	19 77	07 08	19 40	08 04	21
22	21 34	05 34	21 05	06 39	20 71	07 41	20 32	08 42	22
23	22 34	05 48	22 01	06 68	21 66	07 75	21 25	08 80	23
24	23 28	05 83	22 97	06 97	22 60	08 08	22 17	09 18	24
25	24 25	06 07	23 91	07 26	23 54	08 42	23 10	09 57	25
26	25 22	06 31	24 88	07 55	24 48	08 76	24 02	09 95	26
27	26 19	06 56	25 84	07 84	25 42	09 10	24 94	10 33	27
28	27 16	06 80	26 79	08 13	26 36	09 43	25 87	10 71	28
29	28 13	07 04	27 75	08 42	27 30	09 77	26 79	11 10	29
30	29 10	07 28	28 71	08 71	28 25	10 11	27 72	11 48	30
31	30 07	07 53	29 66	09 00	29 19	10 44	28 64	11 86	31
32	31 04	07 77	30 62	09 29	30 13	10 74	29 56	12 25	32
33	32 01	08 01	31 58	09 58	31 07	11 12	30 49	12 63	33
34	32 98	08 26	32 54	09 87	32 01	11 45	31 44	13 01	34
35	33 95	08 50	33 49	10 16	32 95	11 79	32 34	13 39	35
36	34 92	08 74	34 45	10 45	33 89	12 13	33 26	13 78	36
37	35 80	08 99	35 41	10 74	34 84	12 47	34 18	14 16	37
38	36 26	09 23	36 36	11 03	35 78	12 80	35 11	14 54	38
39	37 83	09 47	37 32	11 32	36 72	13 14	36 03	14 92	39
40	38 80	09 71	38 28	11 61	37 66	13 48	36 96	15 31	40
41	39 77	09 96	39 23	11 90	38 60	13 81	37 88	15 69	41
42	40 74	10 20	40 19	12 19	39 34	14 15	38 80	16 07	42
43	41 71	10 44	41 15	12 48	40 49	14 49	39 73	16 45	43
44	42 68	10 69	42 12	12 77	41 43	14 72	40 65	16 84	44
45	43 65	10 63	43 06	13 06	42 37	15 16	41 57	17 22	45
46	44 62	11 17	44 62	13 35	43 41	15 50	42 50	17 60	46
47	45 59	11 42	44 98	13 64	44 25	15 83	43 42	17 99	47
48	46 56	11 66	45 95	13 93	45 19	16 17	44 35	18 37	48
49	47 33	11 90	46 89	14 22	46 13	16 37	45 27	18 75	49
50	48 50	12 14	47 85	14 51	47 08	16 85	46 19	19 13	50
51	49 47	12 39	48 80	14 80	48 01	17 18	47 12	19 52	51
52	50 44	12 63	49 76	15 09	48 96	17 31	48 04	19 89	52
53	51 41	12 87	50 72	15 38	49 90	17 85	48 97	20 28	53
54	52 38	13 12	51 67	15 67	50 84	18 19	49 89	20 66	54
55	53 35	13 36	52 63	15 96	51 78	18 53	58 01		55
56	54 32	13 60	53 59	16 26	52 73	18 87	51 73	21 15	56
57	55 29	13 85	54 55	16 55	53 67	19 20	52 66	21 43	57
58	56 26	14 09	55 50	16 84	54 61	19 54	53 58	22 81	58
59	57 23	14 33	56 46	17 23	55 55	19 87	54 21	22 20	59
60	58 20	14 57	57 42	17 42	56 49	20 21	55 43	22 58	60
70	67 90	17 00	66 90	20 31	65 90	23 58	64 67	26 78	70
80	77 60	19 43	76 55	23 22	75 32	26 95	73 91	30 61	80
90	87 30	21 86	86 10	26 12	84 73	30 39	83 14	34 44	90
100	97 00	24 29	95 69	29 02	94 15	33 68	92 38	38 26	100.
200	194 00	48 58	191 38	58 04	188 30	67 36	184 76	76 52	200
	E W	N S	E W	N S	E W	N S	E W	N S
	6 Points ¾	6 Points ½	6 Points ¼	6 Points.
	75 deg. 56 m.	73 deg. 7 m	70 deg. 19 m.	67 deg. 30 m.
The 6 Points Quarters.

A Traverse-Table for every Point, Half-Point, and Quarter-Point of the Compass, to the 100 part of a League or Mile; which gives the Difference of Lat, and Departure from the Meridian.

The Traverse-Table, The 3 Points Quarter.
Dist. in Leagues or Miles sail'd	25 deg. 19 m.	28 deg. 07 m.	30 deg. 56 m.	33 deg. 45 m.	Dist. in Leagues or Miles sail'd.
2 Points ¼	2 Points ½	2 Points ¾	3 Points.
N S	E W	N S	E W	N S	E W	N S	E W
1	00 90	00 43	00 88	00 47	00 86	00 51	00 83	00 56	1
2	01 81	00 85	01 76	00 94	01 71	01 03	01 66	01 55	2
3	02 71	01 28	02 65	01 41	02 57	01 54	02 49	01 67	3
4	03 61	01 71	03 53	01 89	03 43	02 06	03 32	02 22	4
5	04 52	02 14	04 41	02 36	04 29	02 57	04 16	02 78	5
6	05 42	02 56	05 29	02 83	05 15	03 08	04 99	03 33	6
7	06 33	02 99	06 17	03 30	06 00	03 60	05 82	03 89	7
8	07 23	03 42	07 05	03 77	06 86	04 11	06 65	04 44	8
9	08 14	03 85	07 94	04 24	07 72	04 63	07 48	05 00	9
10	09 04	04 28	08 82	04 71	08 58	05 14	08 31	05 55	10
11	09 94	04 70	09 70	05 18	09 44	05 66	09 15	06 11	11
12	10 85	05 13	10 58	05 66	10 29	06 17	09 98	06 67	12
13	11 75	05 56	11 46	06 13	11 15	06 68	10 81	07 22	13
14	12 66	05 99	12 35	06 60	12 00	07 20	11 64	07 78	14
15	13 56	06 41	13 23	07 07	12 87	07 71	12 47	08 33	15
16	14 46	06 84	14 11	07 54	13 72	08 23	13 30	08 89	16
17	15 37	07 27	14 99	08 01	14 58	08 74	14 13	09 44	17
18	16 27	07 70	15 87	08 48	15 44	09 25	14 97	10 00	18
19	17 18	08 12	16 76	08 96	16 30	09 77	15 80	10 56	19
20	18 08	08 55	17 64	09 43	17 16	10 28	16 63	11 11	20
21	18 98	08 98	18 52	09 90	18 01	10 80	17 46	11 67	21
22	19 89	09 41	19 40	10 37	18 87	11 31	18 29	12 22	22
23	20 79	09 83	20 28	10 84	19 73	11 82	19 12	12 78	23
24	21 60	10 26	21 17	11 31	20 59	12 34	19 95	13 33	24
25	22 60	10 69	22 05	11 78	21 44	12 85	20 79	13 89	25
26	23 50	11 12	22 93	12 26	22 30	13 57	21 62	14 44	26
27	24 41	11 54	23 81	12 73	23 16	13 88	22 45	15 15	27
28	25 31	11 97	24 69	13 20	24 02	14 39	23 28	15 56	28
29	26 22	12 40	25 58	13 67	24 87	14 91	24 11	16 11	29
30	27 12	12 83	26 46	14 14	25 73	15 42	24 94	16 67	30
31	28 02	13 25	27 34	14 61	26 59	15 94	25 78	17 22	31
32	28 93	13 68	28 22	15 08	27 45	16 45	26 61	17 78	32
33	29 83	14 11	29 10	15 56	28 31	16 97	27 44	18 33	33
34	30 74	14 54	29 98	16 03	29 16	17 48	28 27	18 89	34
35	31 64	14 96	30 87	16 50	30 02	17 99	29 10	19 44	35
36	32 54	15 39	31 75	16 97	30 88	18 51	29 93	20 00	36
37	33 45	15 82	32 63	17 44	31 74	19 02	30 76	20 56	37
38	34 35	16 25	33 57	17 91	32 59	19 54	31 60	21 11	38
39	35 26	16 68	34 40	18 38	33 45	20 05	32 43	21 67	39
40	36 16	17 10	35 28	18 86	34 31	20 56	33 26	22 22	40
41	37 06	17 53	36 16	19 34	35 17	21 08	34 09	22 78	41
42	37 67	17 96	37 04	19 81	36 02	21 59	34 92	23 34	42
43	38 87	18 38	37 92	20 27	36 88	22 11	35 75	23 89	43
44	39 78	18 81	38 80	20 74	37 74	22 62	36 58	24 44	44
45	40 68	19 24	39 69	21 21	38 60	23 14	37 42	25 00	45
46	41 51	19 67	40 57	21 68	39 46	23 65	38 25	25 56	46
47	42 49	20 09	41 41	22 16	40 31	24 16	39 08	26 11	47
48	43 39	20 52	42 43	22 63	41 17	24 68	39 91	26 67	48
49	44 30	20 95	43 21	23 10	42 03	25 19	40 74	27 22	49
50	45 20	21 38	44 10	23 57	42 89	25 71	41 57	27 78	50
51	46 10	21 61	44 98	24 04	43 74	26 22	42 40	28 33	51
52	47 01	22 23	45 86	24 51	44 60	26 73	43 24	28 89	52
53	47 91	22 66	46 74	24 98	45 46	27 25	44 07	29 44	53
54	48 82	23 08	47 62	25 46	46 32	27 76	44 90	30 00	54
55	49 72	23 52	48 51	25 93	47 17	28 28	45 73	30 56	55
56	50 62	23 94	49 39	26 40	48 03	28 79	46 56	31 11	56
57	51 53	24 37	50 27	26 87	48 89	29 30	47 39	31 67	57
58	52 43	24 79	51 15	27 34	49 75	29 82	48 22	32 22	58
59	53 33	25 23	52 03	27 81	50 61	30 33	49 06	32 78	59
60	54 24	25 65	52 91	28 28	51 46	30 84	49 89	33 33	60
70	63 27	29 92	61 73	32 99	60 04	35 98	58 22	38 88	70
80	72 31	34 20	70 55	37 71	68 61	41 12	66 51	44 44	80
90	81 35	38 47	79 37	42 43	77 19	46 26	74 83	50 00	90
100	90 39	42 75	88 19	47 13	85 77	51 41	83 14	55 55	100
200	180 78	85 50	176 38	94 26	171 54	102 82	166 28	111 11	200
	E W	N S	E W	N S	E W	N S	E W	N S
	5 Points ¾	5 Points ½	5 Points ¼	5 Points.
	64 deg. 41 m	61. deg. 52 m	59 deg. 4 m.	56 deg. 15 m
The 5 Points Quarters.

A Traverse-Table for every Point, Half-Point, and Quarter-Point of the Compass, to the 100 part of a League or Mile; which gives the Difference of Lat. and Departure from the Meridian.

The Traverse-Table, The 4 Points Quarter.
Dist. in Leagues or Miles sail'd.	36 deg. 34 m.	39 deg. 22 m.	42 deg. 11 m.	45 deg. 00 m.	Dist. in Leagues or Miles sail'd.
3 Points ¼	3 Points ½	3 Points ¾	4 Points.
N S	E W	N S	E W	N S	E W	N S	E W
1	00 80	00 60	00 77	00 63	00 74	00 67	00 71	00 71	1
2	01 61	01 19	01 55	01 27	01 48	01 34	01 41	01 41	2
3	02 41	01 41	02 32	01 90	02 22	02 01	02 12	02 12	3
4	03 21	02 38	03 09	02 54	02 96	02 69	02 83	02 83	4
5	04 02	02 98	03 86	03 17	03 70	03 36	03 54	03 54	5
6	04 82	03 57	04 64	03 81	04 44	04 03	04 24	04 24	6
7	05 62	04 17	05 41	04 44	05 18	04 78	04 95	04 95	7
8	06 43	04 76	06 18	05 07	05 93	05 37	05 66	05 66	8
9	07 23	05 36	06 96	05 71	06 67	06 04	06 36	06 36	9
10	08 03	05 96	07 73	06 34	07 41	06 72	07 07	07 07	10
11	08 83	06 55	08 50	06 98	08 15	07 39	07 78	07 78	11
12	09 64	07 15	09 28	07 61	08 89	08 06	08 49	08 49	12
13	10 44	07 74	10 05	08 25	09 63	08 73	09 19	09 19	13
14	11 24	08 34	10 82	08 88	10 37	09 40	09 90	09 90	14
15	12 05	08 94	11 60	09 52	11 11	10 07	10 61	10 61	15
16	12 85	09 53	12 37	10 15	11 85	10 74	11 31	11 31	16
17	13 66	10 13	13 14	10 78	12 70	11 42	12 02	12 02	17
18	14 46	10 72	13 91	11 42	13 34	12 09	12 73	12 73	18
19	15 26	11 32	14 69	12 04	14 08	12 76	13 44	13 44	19
20	16 06	11 91	15 46	12 69	14 82	13 43	14 14	14 14	20
21	16 87	12 51	16 23	13 32	15 56	14 10	14 85	14 85	21
22	17 67	13 11	17 01	13 96	16 30	14 77	15 56	15 56	2••
23	18 47	13 70	17 78	14 59	17 04	15 45	16 26	16 26	23
24	19 28	14 30	18 55	15 22	17 78	16 12	16 97	16 97	24
25	20 08	14 89	19 32	15 86	18 52	16 79	17 68	17 68	25
26	20 88	15 49	20 10	16 49	19 26	17 46	18 38	18 38	26
27	21 69	16 08	20 87	17 13	20 00	18 13	19 09	18 09	27
28	22 49	16 68	21 64	17 76	20 75	18 77	19 80	19 80	28
29	23 29	17 27	22 42	18 40	21 49	19 44	20 51	20 51	29
30	24 10	17 87	23 19	19 03	22 23	20 12	21 21	21 21	30
31	24 90	18 47	23 96	19 67	22 97	20 82	21 92	21 92	31
32	25 70	19 06	24 74	20 30	23 71	21 49	22 63	22 63	32
33	26 51	19 66	25 51	20 93	24 45	22 16	23 33	23 33	33
34	27 31	20 25	26 28	21 57	25 19	22 83	24 04	24 04	34
35	28 11	20 85	27 06	22 20	25 93	23 50	24 75	24 75	35
36	28 91	21 46	27 83	22 84	26 67	24 17	25 46	25 46	36
37	29 72	22 04	28 60	23 47	27 41	24 85	26 16	26 16	37
38	30 52	22 64	29 37	24 11	28 16	25 52	26 87	26 87	38
39	31 33	23 23	30 15	24 74	28 90	26 19	27 56	27 56	39
40	32 13	23 83	30 92	25 38	29 64	26 86	28 28	28 28	40
41	32 93	24 42	31 69	26 01	30 38	27 53	28 99	28 99	41
42	33 73	25 02	32 47	26 64	31 12	28 21	29 10	29 10	42
43	34 54	25 61	33 24	27 28	31 86	28 88	30 41	30 41	43
44	35 34	26 21	34 01	27 91	32 60	29 55	31 11	31 11	44
45	36 14	26 81	34 78	28 55	33 34	30 22	31 82	31 82	45
46	36 94	27 40	35 56	29 18	34 08	30 89	32 53	32 53	46
47	37 75	28 00	36 33	29 82	34 82	31 56	33 23	33 23	47
48	38 55	28 59	37 10	30 45	35 57	32 23	33 94	33 94	48
49	39 36	29 19	37 88	31 08	36 31	32 91	34 65	34 65	49
50	40 17	29 78	38 65	31 72	37 05	33 58	35 35	35 35	50
51	40 96	30 38	39 42	32 35	37 79	34 25	36 06	36 06	51
52	41 77	30 98	40 20	32 99	38 53	34 92	36 77	36 77	52
53	42 57	31 57	40 97	33 62	39 27	35 59	37 48	37 48	53
54	43 37	32 17	41 74	34 26	40 01	36 26	38 14	38 14	54
55	44 18	32 76	42 52	34 86	40 75	36 94	38 89	38 89	55
56	44 98	33 36	43 29	35 53	41 49	37 61	39 60	39 60	56
57	45 78	33 96	44 06	36 16	42 23	38 28	40 30	40 30	57
58	46 59	34 55	44 83	36 79	43 07	38 95	41 01	41 01	58
59	47 39	35 15	45 61	37 43	43 72	39 62	41 72	41 72	59
60	48 19	35 74	46 38	38 06	44 45	40 29	42 43	42 43	60
70	56 22	41 69	44 11	44 41	51 85	47 00	49 49	49 49	70
80	64 25	47 65	61 84	50 75	59 26	53 72	56 56	56 56	80
90	72 28	53 61	69 57	57 09	66 67	60 44	63 63	63 63	90
100	80 32	59 56	77 30	63 43	74 08	67 15	70 71	70 71	100
200	160 64	119 12	154 60	126 86	148 16	134 30	141 41	141 41	200
	E W	N S	E W	N S	E W	N S	E W	N S
	4 Points ¾	4 Points ½	4 Points ¼	4 Points.
	53 deg. 26 m.	50 deg. 37 m	47 deg. 49 m.	45 deg. 00 m.
The 4. Points Quarters.

As for Example.

	100	9951	980
S. ½ West.	70	6966	686
	3	299	29
Leagues.	17:3	172:16	16:95

Beforegoing, if you take all the Numbers in the Table, they will stand as here appear∣eth, where the Southerly Distance is 172 16/100 Leagues, and the Westerly is 16 95/100 Leagues.

But I hold it more convenient to omit the last Figure to the right hand, and so take the Tenths, as in the second Example; and then in all things it will agree with the Tra∣verse-Scale, on which if you extend the Compasses from 100 to 73, the same Distance will reach from the first ½ Point next the Line of Numbers, to 172 1/10; and from the half Point of the Westing, to 16 9/10 Leagues, as before.

As also, If you extend the Compasses from 172 1/10 the Difference of Latitude, or from 72 1/10 to 6 8/10, which stands for 16 8/10 on this or the like occasion, and apply this Distance from 4 Points on the Tangent-Line of the Scale, and the other Point of the Compasses will reach to ½ Point, which is from the South Westerly, as before.

Now for the Point and ½ Points reckoned at the Bottom, it is thus.

Admit a Ship fails 57 Leagues or Miles North-West and by West, or the 5th Rhomb from the Meridian; I would know how much I am to the VVestward, and how much to the Southward.

Distance	3 Rhomb.	3
	N S	E W
57	474	317
Sailed	E W	N S
	5 Rhomb.	5

Therefore look in the bottom of the Ta∣ble for the 5th Rhomb, and in the Side for 57 Leagues or Miles; and in the Line of Meeting over the fifth Rhomb you have 47.39 or 47 4/10 for the Westing, and 31.67 or 31 7/10 almost for the Northing.

Now had you been to find the Northing and Westing of the third Rhomb from the Meridian, as N. W. b. N. to 57 Leagues di∣stance, the Northing would be 47 4/10, and the Westing 31 7/10, as you see signified by the Letters N. S. and E. W. at the head of the Table, and North N. S. under E. W. at the foot of the Table. This is so plain, it needs no further Precept.

Or by the Traverse-Scale, Extend the Compasses in the Line of Numbers from 10 or 100, to 57 Leagues; the same Distance will reach from 3 Points in the next Line, with 5 Points of the Easting and Westing, to 47.4 Leagues or Miles; that Distance will reach from 5 Points in the Line of N. and S. to 31.7 Leagues, as before.

And the Compasses extended from 47 4/10, to 31 1/10 on the Line of Numbers; the same Distance will reach from 4 Points in the Tangent-Line, to 5 Points from the Meridian, or 3 Points if the Case so required, as if it had been N. W. b. N. The like do in all such Questions.

Likewise by the Traverse-Scale, Let the Course be given N. W. b. W. and Departure 47 4/10, To find the Distance and Difference of Latitude.

Extend the Compasses from 5 Points in the Line of E. W. of the Scale, to the De∣parture; the same Distance will reach from 10 or 100 in the Line of Numbers, to 57 the Distance; And also from 5 Points in the Line of N. S. to 31 7/10 the Diffe∣rence of Latitude. I make this plain by the Scale, by reason the Compasses and the Scale, are more portable than the Book and Table.

A larger Example I will give you of the Tables and Traverse-Scale together, whereby you may perceive, That the Artificial Numbers, Points, and Quarters agree in all things with the Table; nay, I hold the Scale the best of the two, for the ready allowing for Variation, and for Currents, which is done by removing the Compasses from one Point or Distance to another. Now let the Question be this,

Suppose a Ship sail from the Island of Lundy, in Latitude 51 deg. 22 min. North, and Longitude 25 deg. 52 min. to the Island of Barbadoes, in Latitude 13 deg. 10 min. North, and Longitude 332 deg. 57 min. By the Plain-Chart, Difference of Latitude is 764 Leagues, and Longitude 1059 Leagues, and I sail these several Courses, (viz.) S. S. W. ½ W. from A to B 400 Leagues, S. W. b. S. ½ W. 125 Leagues, and S. W. 180 Leagues, and S. W. b. W. ½ Westerly 190 Leagues, W. S. W. 146 Leagues, and W. b. S. 159 Leagues, and South 8 Leagues 7 7/10: All these Courses and Distances I set down as followeth. In the first Column is expressed the Days of the Month, and Distance sailing upon each Course; The second, the Day of the VVeek; The third, the Course sailed; The fourth, the Distance from the Meridian; The fifth, the Place and Point of each Course by Letters; The sixth, the Distance sailed; The se∣venth, eighth, ninth, and tenth, the Northing, Southing, Easting, and VVesting, which is the Difference of Latitude and Departure from the Meridian in Leagues 1/10 Parts; The eleventh Column is the Latitude; The twelfth, the Longitude; The thir∣teenth, the Variation of the Compass.

Da. Month.	Da. Week.	Course sailed.	Distance from the Meridi∣an.	The Places.	Dist. sailed.	North∣ing.	South∣ing.	East∣ing.	West∣ing.	Latitud. D••gr. Min.	Longit. Degr. Min.	Variati∣on.
* 1.221	f	S. W. ¾ W.	S.W. 54 d. 12 m.	From A to K.	1306 Leagu.	764 Leagues	704 Leagu.	1058 Leag.	1058 Leag.	51 22	25 52	Easterly 5 m.
13 10	332 57
* 1.32	2	S. S. W. ½ W.	S. W. 2 Po. ½	From A to B.	200 200	Current sets E. S. E.	176 4/10 176 4		94 3/10 94 3	33 44	16 26	Cur. sets by estim. E. S. E.
6	G	S. W. b. S. ½ W.	S. W. 3 Po. ½	From B to C.	100 20 5		773 155 39		634 127 32	28 28	12 28	Variat. 00 m.
10	d	S. W. S. W. ¼ W.	S. W. 4 Points. S W. 3 ¾	From C to D.	100 80 12		707 566 87		707 566 80	22 06	5 42	Variat. 00 m.
15	b	S. W. by W. ½ W.	S. W. 5 Po. ½	From D to E.	100 90		471 424		882 794	17 38	35 19	Westerly 2 degr.
19	f	W. S. W.	S. W. 6 Points.	From E to F.	100 40 6		383 153 23		924 370 55	15 50	350 24	Westerly 4 degr.
24	d	W. by S.	S. W. 7 Points.	From F to G.	100 50 9		195 98 38		981 490 92	13 11	342 46	Westerly 5 degr.
		The Course made good.	S. W. 48 d. 34 m.		1212 3/10		763 8/10		862	13 11	342 46

This done, add up the South Column, which Sum is 763 8/10 Leagues; which redu∣ced into Degrees,* 1.4 by dividing by 20 and multiplying the odd Leagues under 20 by 3, and adding the Minutes in the Tenths, you will find the Difference of Lati∣tude in Degrees to be 38 deg. 11 min. which substracted from 51 deg. 22 min. there re∣mains 13 deg. 11 min. the Latitude of Barbadoes.

* 1.5Add up the Sums of the West Column, which is 862 Leagues; that converted in∣to Degrees, is 43 deg. 6 min. Substract that from the Longitude of the Island of Lun∣dy; if you cannot, add to it 360 deg. So 25 deg. 52 min. added to 360 deg. makes 385 deg. 52 min. Then the Difference of Longitude substracted from it, 43 deg. 6 m. there remains 342 deg. 46 min. the Longitude the Ship is in.

You must note, The Degrees are such that 60 Miles or min. makes a Degree of Longitude or Latitude, or of a Great Circle.

Note, The day we set sail, we put down the day of the Month and VVeek, the di∣rect Course to the Port we are bound to, and the Place marked with two Letters, as

in this Table A for Lundy and K for Barbadoes; and also under Distance, the number of Leagues upon a straight Course; and under Northing and Southing, the Difference of Latitude in Leagues and Tenth Parts; and under Latitude, the Latitude of the two Places; and under Longitude, the Longitude of the two Places, and also the Va∣riation of the Compass from whence we set out first: which you may see all plain in the head of the Table, in the Common Angle of Meeting with the 21 of April.

And remember, You have the Latitude and Longitude given you; therefore by it you must find the direct Rhomb and Distance, as you have been shewed by the second and sixth Case of Plain Triangles.

Now if you would set down this Reckoning on the Plain Chart severally, you must extend your Compasses from one of the Parallels of Longitude, to the Latitude you are in; as also take off so many Leagues of the Meridian Line, as your Departure hath been, reckoning 5 Degrees for 100 Leagues, and every Degree for 20 Leagues.

As for Example.

Suppose we would set down the first Distance of South and West, Extend your Compasses from the Parallel of 40 deg. to your Latitude you are in 33 deg. 44 min. And also extend another pair of Compasses on the Aequinoctial, if there is one divided; if not, on the Meridian, which is all one; and take off 16 deg. 26 min. by one of the Parallels of the Meridian: or take off 188 Leagues 6/10, which is 9 deg. 26 min. the Difference to the Westward from your first Meridian; and so let the Compasses of the Difference of Latitude run upon the Parallel of 40 deg. and the other Compasses with 188 6/10 or 9 deg. 26 min. on one of the Parallels of North and South, until they meet in the Point B: (And so add the Meridian-difference of the second Place to the first; and the Difference of Latitude of the second Place, substract from the first,* 1.6 by reason you are going from the North Pole toward the South or Aequator.) As for your De∣grees of Longitude, you must know where you begin the first Meridian; and as you go to the Westward substract the Difference of Degrees of Meridians, and as you sail to the Eastward add the Difference of Degrees, and you have the Longitude in Degrees where you are.

So that this may suffice for a President, to lay down on your Draught or Blank Chart the Point of the Place of the Ship, by the Meridian-distance and Difference of Latitude; and as you have been directed, so are the Points C, D, E, F, G set down, So that you need not pester the Chart with Rhomb-lines, as formerly; but take the Difference between the Latitude and Meridian-distance off the Line of Numbers, and apply that Distance to the Tangent-line of Rhombs on the Traverse-Scale, and that will presently shew you the Point or Rhomb between any two Places assigned.

The drawing of the Plain Sea-Chart, and the way of sailing thereby, is the most easie and plainest of all others: And though it be fit to use only in Places neer the Aequinoctial, or in short Voyages, yet it will serve for a good Introduction to the other kinds of Sailing. Therefore we shall not lose our labour; for in all kinds of Sailing the same Work must be observed with some caution.

[illustration] sea-chart

The Plaine Sea Chart.

folio 156

First make the Square ASTB, of what length and breadth you please, and divide each Side into as many equal Parts as your occasion requires; and then: draw straight Lines through these Parts, crossing one the other at Right Angles, so making many lit∣tle Geometrical Squares, each of which may contain one Degree: but I have made this, by reason of its largeness; to contain 10 Degrees. Note, That the Degrees of the Meridian at the Aequinoctial are all of equal distance to the Poles, which is a gross Error, which shall be shewn in the following Discourse. So that you may make the Meridian-Line in your Chart 25 deg. 52 min. to the Westward of the Meridian of Lundy: Or you may divide the two Sides into Degrees as far as you think fit, and every Degree into 60 Parts, which is the old way; and I know most Mariners will not be directed a new way of dividing the Degrees each of them into 10 Parts; so each Part will contain about 2 Leagues; and that division of double Leagues is near enough for the Mariners use. You may suppose each of these Parts to be sub∣divided into 10; so every Degree will contain 100 Parts, which is a very ready way if you keep your Account by Arithmetick, by Decimals or 10 Parts. This is so plain, it needs no further Precept; therefore we will proceed to the use of it.

Now your several Courses and Traverse-Points are laid down on your Chart, from

Lundy at A, to B the first, second to C, third to D, fourth to E, fifth to F, the sixth to to G, which is the Point the Ship is in when you cast up this Reckoning.

764	00
763	08
000	02

1058

862

196 Leagues short of Barbadoes at G.

Now to know how far you are short of the Island by the Plain Chart, substract the Sum of the South Column 763 8/10 from the Difference of Latitude 764 Leagues, and you will find you are but 2/10 parts of a League to the Northward of your given Latitude, which is not to be regarded; and also substract the Sum of the West Column, from the Difference of Longitude, and the Remainer is 197 Leagues, which you are short at G of the Barbadoes; and being in the Latitude of 13 deg. 11 min. the Island bears off you due West at K: So that you should sail 197 Leagues on that Point West, before you should be arrived at your Port by the Plain Chart.

But by the true Sea-Chart you are arrived at G, which is the Island of Barbadoes:* 1.7 For the true Meridian-distance is but 865 Leagues betw••••n Lundy and Barbado••s, and the Plain Chart makes it 1059 Leagues; and the true Course from Lundy to Barba∣does is but 48 deg. 34 min. which is S. W. a little above a quarter of a Point Westerly; and the Plain Chart makes it 54 deg. 12 min. S. W. which is above ¾ of a Point; And the true Distance is but 1152 Leagues, and by the Plain Chart it is 1366 Leagues. By this you may plainly perceive, that no Island, nor Cape, or Head-Land, can be truly laid down in the Plain Chart in its true scituation, but near the Aequinoctial only, and near about the same may be used without sensible Error, because there only the Meridians and Parallels are equal; but on this side or beyond the Aequino∣ctial, there is Error committed proportionally to the Difference of the Meridian and Parallel; that is, The true Difference of Longitude found out by the Plain Chart, hath the same proportion to the true Difference of Longitude, that the Parallel hath to the Meridian. But most Mariners will not be drawn from this plain easie way of Sailing, notwithstanding the have it plainly demonstrated to them by us: But those that take the true way of Sailing, find the Credit and Benefit of it, to the shame of those that are so obstinate, conceited, and grounded in Ignorance.

B••t in the following Discourse I will use my endeavour to make things so plain, that if the Ingenious Mariner will but spend half an hours time at the setting forth of his Voyage, to find by direction his true Course and Distance, and Meridian-di∣stance, and put it at the Head of his Journal, as you see in the Table, he shall use his Plain Sailing, all the rest of his Voyage; and he shall have direction how to use it by the Chart made according to the Globe. But something more of this way, accord∣ing to my Promise.

Notes

• * 1.1

  The Rule of keeping a perfect Sea-Reckoning is best set down in particular after the general true Sea-Chart, in Chap. 17. of Great Circle Sail∣ing.
• * 1.2

  Apr.
• * 1.3

  May
• * 1.4

  〈 math 〉〈 math 〉
• * 1.5

  deg.	min.
  51	22
  38	11
  13	11
  Latitude of Bar∣badoes.
• * 1.6

  But add the difference of Lati∣tude as you sail to the Northward
• * 1.7

  The Errors of the Plain Sea-Chart.