To construct a Map on Mercator’s Projection.

On a sheet of cartridge paper, 38in. by 20in., it is proposed to construct a map on Mercator’s projection, on a scale of ten miles to an inch equatorial, i.e. 6in. to a degree of longitude.

Lat.	31° to 33° N.
Long.	34° to 36° E.

Draw a base line, find its centre, and erect a perpendicular to the top of the paper; the extremes of longitude 34° and 36°, added together and divided by 2°, give 35°, the central meridian, and which is represented by the perpendicular. On each side of it lay off 6in., and erect perpendiculars for the meridians 34° and 36°; divide the base line into ten mile divisions, and the part from 35° 50´ to 36° into miles for the latitude scale. From Table A take the following quantities:—

	°	°	°	´		°	°
Lat.	31	to 32	= 1	10·4	= the distance between parallels	31	and 32
Lat.	32	to 33	= 1	11·1	” ”	32	and 33
			= 2	21·5	” ”	31	and 33

Having thus obtained the distance between the required parallels, divide the map into squares of ten miles each way, and the map is ready for the projection of the route.

A.—Table to construct Maps on Mercator’s Projection.

	0°	1°	2°	3°	4°	5°	6°	7°	8°	9°
	° ´	° ´	° ´	° ´	° ´	° ´	° ´	° ´	° ´	° ´
0		1 00	1 00·1	1 00·1	1 00·1	1 00·2	1 00·3	1 00·4	1 00·5	1 00·6
10	1 00·9	1 01	1 01·2	1 01·5	1 00·7	1 02	1 02·2	1 02·6	1 02·9	1 03·3
20	1 03·6	1 04·1	1 04·5	1 04·9	1 05·5	1 05·9	1 06·5	1 07	1 07·7	1 08·2
30	1 09	1 09·6	1 10·4	1 11·1	1 12	1 12·8	1 13·7	1 14·6	1 15·7	1 16·7
40	1 17·6	1 19	1 20·1	1 21·4	1 22·7	1 24·2	1 25·6	1 27·1	1 28·8	1 30·6
50	1 32·4	1 34·3	1 36·4	1 38·6	1 40·8	1 43·4	1 45·9	1 49	1 51·4	1 54·8
60	1 58·3	2 01·8	2 05·8	2 09·9	2 14·5	2 19·14	2 24·7	2 30·5	2 36·8	2 43·8
70	2 51·3	2 59·8	3 09·1	3 19·6	3 31·3	3 44·6	3 59·8	4 17·1	4 37·4	5 01·1
80	5 29·5	6 03	6 46·4	7 40·3	8 51·1	10 27·7	12 47·9	16 29·6	23 14·3	39 42·2

Use of the table.—Find the required parallel; the tens at the side, and the units at the top. At their intersection will be found in degrees and minutes the distance of the required parallel from the next less degree, to be measured from the scale of longitude on the map in progress.

Given the parallel of 30°, required that of 31°. 30 at the side and 1 at the top intersects at 1° 09·6´, the required distance of the two parallels.

Given the parallel of 31°, required that of 33°:

°	°	´
32 =	1	10·4
33 =	1	11·1
	2	21·5	the distance between the 31° and 33° parallels.

B.—Given the Departure to find Difference of Longitude.

	0°	1°	2°	3°	4°	5°	6°	7°	8°	9°
0		1·0001	1·0006	1·0013	1·0026	1·0038	1·0055	1·0075	1·0098	1·0125
10	1·0154	1·0187	1·0224	1·0261	1·0306	1·0353	1·0403	1·0457	1·0514	1·0578
20	1·0642	1·0711	1·0785	1·0864	1·0946	1·1034	1·1126	1·1224	1·1326	1·1434
30	1·1547	1·1666	1·1792	1·1924	1·2062	1·2208	1·2361	1·2521	1·2690	1·2868
40	1·3054	1·3250	1·3456	1·3673	1·3902	1·4142	1·4395	1·4663	1·4945	1·5242
50	1·5557	1·5890	1·6242	1·6616	1·7013	1·7435	1·7883	1·8361	1·8871	1·9416
60	2·0000	2·0626	2·1301	2·2027	2·2812	2·3662	2·4586	2·5593	2·6695	2·7904
70	2·9238	3·0716	3·2361	3·4204	3·6280	3·8637	4·1337	4·4454	4·8097	5·2406
80	5·7587	6·3925	7·1856	8·2057	9·5664	11·475	14·334	19·108	28·653	57·307

Use of the table.—Find the required parallel, the tens at the side and the units at the top, at their intersection will be found a quantity, which, multiplied by the departure, gives the difference of longitude.

The departure from the meridian on the parallel of 34° was 25 miles, required the difference of longitude:

25´ × 1·20 = 30·00´ the difference of longitude.

In the parallel of 60° the departure was 30 miles:

30´ × 2 = 60 miles, or 1 degree.

In the parallel of 35° N. the route was N. 40° W. 37 miles distance.

By traverse table, 40° course, dist. 37° = dep. 23·8´ × 1·22 = 29·03 miles difference of longitude.

The following example will serve to show how the traveller’s record of progress may be conveniently kept. It was framed by S. W. Norie expressly for the use of navigators; but explorers and travellers will find it a simple and useful form for recording the day’s work:

Corrected Courses	Distance.	Difference of Latitude.		Departure.
Corrected Courses	Distance.	N.	S.	E.	W.
N.E.	36	25·5		25·5
N. by W.	14	13·7			2·7
N.E. by E. ½ E.	58	27·3		51·2
N. by E.	42	41·2		8·2
E.N.E.	29	11·1		26·8
	Difference of Lat.	118·8		111·7	2·7
				2·7
			Dep.	109·0

The difference of latitude 118·8 and departure 109·0 give the course N. 42° 32´ E., and distance 161·2.

	°	´				°	´
Latitude left	52	36 N.	Merc. prjctns.	3724	Longitude left	21	45 W.
Diff. lat.	1	59 N.			Diff. lon. 184 or	3	4 E.
Latitude in	54	35 N.	Merc. prjctns.	3925	Longitude in	18	41 W.
Sum of lats.	2)107	11	Merc. diff. lat.	201
Mid lat.	53	35