About the 31st August the two globes will be in the line S C, on which day their right ascensions will be equal, each being about 10:37; and because of this equality, there will be no equation of time: hence, on that day the hour-hand of a well-adjusted clock will correspond with the horary shadow of a correct sun-dial. As the two globes advance from C to D, the right ascension of a will be less than that of e; and therefore the real globe will come to the meridian earlier than the imaginary one; and thus its dotted meridian lines S a XI., S a XII., &c. fall to the left hand of the black meridian lines Sell, S e 12, &c. belonging to the imaginary globe* :—hence, the equation of time, indicated by the solar angle comprehended between the two meridian lines, is subtractive from apparent time, and additive to mean time. The two globes will be in the line S D about the 24th December; on which day their right ascensions will be equal, each being about 1810"; and because of this equality the equation of time vanishes. During the time that the two globes are moving from D to A, the right ascension of a being now greater than that of e, the real globe will not come to the meridian until after the imaginary one :—hence, its dotted meridian lines S a XIX., S a XX., &c. fall to the right hand of the black meridian lines Se 19, S e 20, &c. belonging to the imaginary globe; and therefore the equation of time, expressed by the solar angle e Sa, is additive to apparent time, and subtractive from mean time. From the above it is evident, that the equation of time is the angular distance in time, or the solar angle which is contained between the places of the real globe and the imaginary one. In the above diagram, the spaces comprehended between the points A and B, B and C, C and D, and D and A, are as proportional to the intervening times as the nature of the projection would admit of:-Thus, since A represents the 15th April, B, the 15th June, C, the 31st August, and D, the 24th December: therefore, the first space comprehends an interval of 61 days; the second, an interval of 77 days; the third, an interval of 115 days; and the fourth, an interval of 112 days making in the whole 365 days. During the 61 days that are included between A and B, and the 115 days betwixt C and D, viz. between the right ascension 1:33, and 5:33", and between the right ascension 10:37 and 18:10", the true globe precedes the imaginary one; and, therefore, as it comes to the meridian first, the equation of time is subtractive from apparent time. But, during the 77 days that are included between B and C, and the 112 days betwixt D and A, viz. between the right ascension 5:33", and 10:37, and between the right ascension 1810" and 25:33" (viz. 133"), the real globe is behind the The eye of the reader is to be directed from the centre S to the circumference. imaginary one; and, therefore, since it comes to the meridian later, the equation of time is additive to apparent time ;-hence, it is manifest that the equation of time is subtractive for 61+115= 176 days, and additive for 77+ 112 189 days in every year. 36. As the above expressions are adapted to apparent time, therefore, whenever mean time is under consideration, the equation of time is to have a contrary sign; that is, for subtractive read additive, and vice versa, for additive read subtractive. Hence it will appear evident, that between the 15th April and the 15th of June, and between the 31st August and the 24th of December, the equation of time is additive to mean time. But, between the 15th June and the 31st of August, and between the 24th December and the 15th of April, the equation of time is subtractive from mean time. 37. Since the generality of astronomers have adapted their language to the senses, or to the ideas immediately resulting from celestial appearances; it is therefore usual in astronomical expressions, to apply that motion to the sun which nature has impressed upon the earth. This is to be regretted, because it tends to perpetuate that optical illusion under which the uninformed in astronomy have ever laboured; and which has been the means of leading them into numberless extravagant speculations in relation to the heavenly bodies. However, whether the earth be in motion and the sun at rest (as they actually are); or the earth at rest and the sun in motion, the appearance of the heavens will be always the same: for, in whatever part of the ecliptic the earth moves, the sun will be posited in that point of the firmament which is diametrically opposite; and therefore if we notice what point of the ecliptic comes to the meridian at midnight on any given day, the sun (then apparently under the earth), will be exactly 180 degrees distant from that point :Hence, so far as calculation is in question, it is perfectly immaterial whether the sun be at rest or in motion, because the result will be always the same. And, in consequence of this, we may change the terms used in the diagram, Article 35, at pleasure :-And, therefore, if we allow S to represent the earth ;—a I., a II., a III., &c., to represent the real sun moving with a variable degree of velocity round the earth along the circular plane of the equinoctial indicated by the points a, a, a, &c., and e 1, e2, e 3, &c. to represent an imaginary sun moving with an invariable degree of velocity along the dotted equinoctial marked e, e, e, &c.; we will have the true meaning of the second paragraph in page 497 of the Nautical Almanac for 1836, where it is said, “An imaginary sun, called the mean sun, is conceived to move uniformly in the equator with the real sun's mean motion in right ascension." Now, since the mean motion of the real sun is at the rate of 59:8733 per day (Article 6, second paragraph), which in time answers to 356:5554; this, therefore, is the equable diurnal rate at which the imaginary sun is conceived to move round the equator: and it is the accumulation of this equable rate that constitutes the element called "Sidereal Time" which is given in page II. of the month in the Nautical Almanac. 38. The imaginary, or mean sun, and the imaginary first point of Aries may be esteemed as the synonymies of each other; they are precisely of the same import; and, therefore, the right ascension of the mean sun expresses the right ascension of the first point of Aries:-And hence it is that the right ascension of the mean sun is called sidereal time in the Nautical Almanac; and hence, also, that the interval of time between two consecutive returns of the imaginary or mean sun to the same meridian, which consists of 24 hours, 3 minutes, 56. 5554 seconds, is called a mean solar day in sidereal time, Article 9. 39. A mean solar day is 3′′56:5554 longer than a natural day, which consists of 24 hours in mean time: and therefore mean solar time is converted into sidereal time by the addition of an equation; and vice versa, sidereal time is converted into mean solar time by the subtraction of an equation; as particularly explained in the description of Tables XLV. and XLVI., between pages 117 and 119; to which the reader is requested to refer. 40. Having thus touched upon the conversion of solar into sidereal time, &c., it may be advisable to notice the "Tables of Equivalents,” which are given between pages 486 and 489 of the Nautical Almanac for 1836:-The first of these is for the conversion of mean solar time into sidereal time; the construction of which is as follows, viz.: As 360: 24::: 360:59:8733018 to 24:356:5554; which is the correct length of a mean solar day in sidereal time, Article 9. Now, the twenty-fourth part of this gives the value of 1 mean solar hour= 1:0:9:8565, sidereal time: hence, 2 mean solar hours 20" 19:7130, sidereal time ;-3 mean solar hours 3:029:5694 sidereal time, &c. &c. = Note. It is the excess of the minutes and seconds over the hours, obtained in the above manner, that is contained in the second and following columns of Table XLVI., volume II., page 597. 41. The second "Table of Equivalents" in the Ephemeris, or that for converting sidereal time into mean solar time, may be constructed in the following manner, viz.. As 360:59:8:33018: 24:: 360: to 23:56 4:0906; which is the correct length of a sidereal day, or the absolute space of time that the earth takes to revolve once round its axis in mean solar time, Article 10. Now, the twenty-fourth part of this gives the value of 1 sidereal hour =0:59:50:1704 in mean solar time:-hence, 2 sidereal hours = 1:59:40:3409 mean solar time ;-3 sidereal hours = 25930:5113 mean solar time, &c. &c, as in the Ephemeris, page 490. Note. If the equivalents thus found be subtracted from 24 hours, the remainder will be the equations in mean time, which are contained in the second and following columns of Table XLV., volume II., page 597. 42. The mean sun's right ascension (given in page II. of the month in the Nautical Almanac under the head "Sidereal Time"), and the "Mean Time of Transit of the First Point of Aries," page XXII. of the month in the Ephemeris, may be deduced from each other in the following manner, viz. :-Let the mean sun's right ascension be subtracted from 24 hours, diminish the remainder by the corresponding equation in Table XLV., volume II., page 597, and the result will be the mean time of transit of the first point of Aries. And, let the mean time of transit of the first point of Aries, in the Ephemeris, be increased by the corresponding equation in Table XLVI.; then, this being subtracted from 24 hours, the result will be "the sidereal time," or the mean sun's right ascension. 43. Since the equation of time is measured by the solar angle, which is contained between the two meridian lines that flow from the centre of the sun to the centres of the real globe and the imaginary one, as appears evident by the diagram, Article 35; and since those meridian lines express the right ascensions of two objects (a real one and a fictitious), which, by the substitution of terms, we may now call the true sun, and an imaginary or mean sun; therefore the equation of time, which is given in page II. of the month in the Nautical Almanac, is simply, and bona fide, the difference between the mean sun's right ascension, viz., "Sidereal Time," and the true sun's right ascension, as given in the same page. 44. Having thus shown the nature of the new and important element called "Sidereal Time;" having demonstrated that it is simply the mean sun's right ascension; and, moreover, having shown that it is essentially different from the sidereal time which is deduced from the diurnal revolution of the earth in relation to the fixed stars (Articles 10 and 32); I shall therefore conclude this article by observing that, as the element in question corresponds with the angular distance of the first point of Aries from the instant of the vernal equinox, it ought, by analogy, to be denominated either the right ascension of the first point of Aries, or the mean sun's right ascension: but, as the latter denomination is evidently the most appropriate (Article 37); therefore, throughout the rest of this work the "Sidereal Time," which is given in After arriving at the astronomical calculations. page II. of the month in the Nautical Almanac, shall be called the mean sun's right ascension: because this will conduce to obviate the perplexity which young computers experience in consulting the last column of the above-mentioned page in the Ephemeris. ON THE ADJUSTMENT AND USE OF NAUTICAL INSTRUMENTS. 45. In the foregoing explanatory articles the young navigator is presented with all the points of information that have any relation to the essentially important element called "Sidereal Time," as well as to the other species of time, viz. Apparent and Mean, that are familiar to nautical astronomers: and, on the supposition that he has a competent knowledge of the whole, we will now make a few remarks relative to the adjustment and use of the nautical instruments that are used for the purposes of celestial observation. 46. The instruments made use of at sea for determining the latitude and longitude of a ship, are quadrants and sextants. * But since space cannot be afforded in this work for giving descriptions of those well-known instruments, the reader is, therefore, respectfully referred to an ocular inspection thereof, and to a few explanatory hints from some person who is practically acquainted with them. A few words from an experienced navigator will convey more substantial information to a young gentleman, than if he were to spend a whole year in poring over the many treatises that have been written by different authors, relative to "the description and use of the quadrant and sextant." Every midshipman in the Royal Navy who has been about three weeks at sea, is just as well acquainted with the description of the quadrant and sextant as he is with that of his cocked-hat and sword; and full as familiar with the adjusting-screws of those instruments, as he is with the steps of the quarter-deck ladder. But there are few, even amongst the more experienced officers, who are so thoroughly acquainted with the nature of the adjustments as to be able to determine the absolute value of the index error: for there is a peculiarity in the index-bar which seems to have escaped the notice of its makers; and of this I shall endeavour to satisfy the reader in a subsequent article. Knowing, from the long experience of thirty years, that such descriptions are as useless and unnecessary as "the examination of a young sea officer" in certain books on navigation; I shall therefore skip over them, and enter at once upon the principal rectifications of which these instruments are susceptible: and this becomes the more necessary * And sometimes reflecting circles. |