(4.) 240: 308=cos. 51° 16': cos. of the lat. sought.

Ar. co. Log. 240

= 7.619783

Log. 308

= 2.488551

Log. cos. 51° 16'

= 9.796364

.. lat. sought=36° 35′ 8′′

= 9.904698

Page 58.

(1.) Dif. lat. =14° 46′-10° 30′=4° 16′=256 miles. Middle lat. (14° 46′+10° 30′)=12° 38'.

R: sec. course 3 pts. dif. lat.: dist.

Log. sec. 3 pts.-R

Log. dif. lat. 256

.. distance 307-9

=

=080154

=2.408240

=2.488394

Cos. mid. lat. tan. course = dif. lat: dif. long. (7)

Ar. co. Log. cos. = - Log. sec. 12° 38′

=10010644

Log. tan. 3 pts.
Log. 256

= 9.824893

= 2.408240

.. dif. long. =175.7

Hence the difference of longitude was 2° 56' nearly, which is east, since the course is east, and since the longi

= 2.243777

tude sailed from was west, their difference is the latitude

in 21° 50'.

(2.) Dif. lat. =49° 54′-45° 8'=4° 46′ 286 miles.

Middle lat. (49° 54′+45° 8')=47° 31'.

320: 286-R: cos. of the course.

Ar. co. Log. 320

Log. 286
Log. R

=7.494850

=2.456366

10.000000

..the course 26° 39' 6" W. =9.951216
cos. mid. lat. sin. course = dist. : dif. long.

Ar. co. Log. cos.

:

Log. sec. 47° 31'

Log. sin. 26° 39′ 6′′
Log. 320

.. the dif. long. =212-54 W.

This dif. long. being W., and that sailed from is also W., and W. is the longitude in.

(3.)

=10-170455
= 9.651825
=2.505150

= 2.327430

(1.)

3° 33′ nearly, whilst 6° 19′, their sum, 9° 52′

280: 186-R : sin. of the course.

Ar. co. Log. 280

.. The course=41° 37′ 39′′ E. 9.822355

=7.552842

Log. 186
Log. R

=2.269513

=10.000000

Half sum 41° 47' 30" the middle latitude.

cos. mid. lat. : sin. course Dist.: dif. long. (1.)

Ar. co. cos. Log. sec. 41°47′ 30′′

Log. sin. 41° 37' 39"

Dist. dif. long. cos. mid. lat. : sin. course. (4.)

.. The course=39° 28′ 14′′= 9.803239

.. Dif. lat. 6° 26'=386 = 2.586560 Now, since the latitude sailed from was N., and the difference of latitude made was S., the latitude sailed from will be the middle latitude increased by half the difference of latitude made, and the latitude arrived at will be the middle latitude diminished by half the difference of latitude made; hence

NOTE. It may be remarked here that in multiplying feet and inches by feet and inches, the denomination in the product next to feet, though commonly called inches, does not represent square inches, but a surface that is 12 inches long and 1 inch broad, being the 12th part of a square foot, whilst the second denomination from feet, commonly called parts, represents square inches.

(3.) 25 x 17 437 square feet, which being divided by 9, the number of square feet in a square yard, gives 4811 the Ans.

£2 12 6=2=£%, and 134=40, hence
£21 × 40=£35. Ans.

Or 1 rood: 133 roods :: £2 12 6 ; £35.