Description and use of the sector To find the logarithm of any num- The rule of three by logarithms To calculate compound interest To find the log. sine, tangent, &c. To find the degrees, minutes, and To find the arithmetical comple- Table of solutions of the various Right-angled plane trigonometry Questions to exercise the learner in right-angled plane trigonometry A short introduction to astronomy Explanations of the terms used in A table of the angles which every Theorems for solving the several 13 Table of solutions of the several 17 cases of middle latitude sailing 63 20 Questions to exercise the learner 26 29 Table of solutions of the various 32 Construction and use of Merca- 33 Of the log-line and half-minute To take an altitude by a fore ob- To take the sun's altitude by a 35 Advice to seamen in the choice of 36 Description and use of a sextant 40 To measure the angular distance To measure the angular distance Verification of the mirrors and co- Adjustments of the circle of reflec- 52 To observe the meridian altitude To find the distance of the land in To observe an amplitude or azi- To calculate the true amplitude Questions to exercise the learner Having the true and magnetic am- plitude or azimuth, to find the To calculate the variation by azi- tudes before and after passing On the dip of the magnetic needle To find the latitude by a meridian To find the time of the moon's To find the moon's declination To find the latitude by the moon's To find the latitude by the meri- To find the longitude at sea by lu- 114 General observations on the tak- Examples of lunar observations 115 Second method of working a lu- 119 Witchell's improved method of 120 Method of taking a lunar observa- of two different objects, taken at different times First method Second method SIGNS AND ABBREVIATIONS USED IN THIS WORK. Is the sign of addition, and denotes that whatever number or quantity follows the sign, must be added to those that go before it, thus 9+8 signifies that 8 is to be added to 9. Or A+B implies that the quantities represented by A and B are to be added. The sign + is called the positive sign. The sign of subtraction; and denotes that the number following it must be subtracted from those going before it, thus 7-5, signifies that 5 must be subtracted from 7. The sign — is called the negative sign. X Is the sign of multiplication, and shows that the numbers placed before and after it are to be multiplied, thus, 7 x 9 signifies 7 multiplied by 9, which makes 63; and 7× 8 × 2 signifies the continued product of 7 by 8 and by 2, which makes 112. Multiplication is also denoted by placing a point between the quantities to be multiplied; thus A.B signifies that A is to be multiplied by B. Is the sign of division, and signifies that the number that stands before it is to be divided by the number following it, as 72+12 shows that 72 is to be divided by 12. Division may also be denoted by placing two points between the numbers, thus, 72: 12 represents 72 divided by 12 72 or by placing the numbers thus, which signifies 72 divided by 12. () or 12 Either of these marks is used for connecting numbers to gether, thus, 3+4×6, or (3+4)×6, signifies that the sum of 3 and 4 is to be multiplied by 6. Is the sign of equality, and shows that the numbers or quantities placed before it are equal to those following it: thus & × 12=96. Or 8 mul tiplied by 12 are equal to 96, and 7+2×4=36. :::: Is the sign of proportion, and is marked thus, 7: 14 :: 10: 20, that is, as 7 is to 14, so is 10 to 20. Or A: B:: C: D, that is, as A is to B, so is C to D. • Signifies degrees; thus, 450 represents 45 degrees. . 'Signifies minutes; thus, 24' or 24 minutes, " Signifies seconds; thus, 44", or 44 seconds. Signifies thirds or sixtieth parts of seconds; thus, 44", or 44 thirds. S. Signifies sine. N. S. Signifies Natural sine. Sec. Signifies Secant. Tan. Signifies Tangent. Co-sine, Co-tangent, or Co-secant of an arch signifies the sine, tangent or secant of the complement of that arch respectively. <Signifies Angle; with an s at top Angles, <s Ad Angled, A Signifies Triangle. 's Triangles. Signifies a square. or the Sun. O or the Moon. *a Star. L. L. Lower Limb. U. L. Upper Limb. N. L. Nearest Limb. S. D. Semi-diameter. P. L. Proportional Logarithm. N. A. Nautical Almanac. Z. D. Zenith Distance. D. R. Dead Reckoning. |