Gershom Bradford

“ The system of laying off the heavens just described is well enough for the momentary locating of a body, which is a very important feature in navigation, but for some purposes a more stable point than the zenith, which on shipboard is ever changing, is needed, from which to form a system that is constant the world over. To meet this demand we take the point in the sky penetrated by the prolongation of the earth’s northern axis—the celestial pole—and from this point meridians and parallels are developed upon the celestial sphere as has been done on the earth. ”

“ It is always advantageous to get an observation of a star near twilight or dawn, in order that a well-defined horizon may be available; but, in taking a sight of Polaris, another important feature is to be considered. When the star’s hour angle is at or near 6 or 18 hours, that is, near that part of its orbit cut by a line passing through the pole and parallel to the horizon, it is rising or falling most rapidly, with the result that a small error in time will produce a considerable error in the hour angle, an error of 3 minutes introducing a difference of 1 ́ in the latitude. ”

“ A good guide is to never allow the number of degrees in the zenith distance to be exceeded by the number of minutes from noon. In very high altitudes circum-meridians are not to be recommended, and the higher the altitude, the more accurate must be the time used. This is plain when it is realized that the lower the sun’s altitude at noon, the more nearly its diurnal path approaches the line of the horizon; with the lessening curve of its course, comes a lessening rise near noon, hence less accuracy is needed in the exact time of sight from that of transit. ”

“ An amplitude, unlike an azimuth, is restricted as to time of observation, for the body must be on the horizon either rising or setting; and should be observed when the sun is about its own diameter above the horizon and with a not excessive height of eye. The amplitude is measured from the east or west point through 90° to the north or south point. If the body observed has a south declination and is rising, the amplitude will be East so much South; if declination is north, East so much North, for a body rises in the East point when its declination is 0°—on the equator. ”

“ While we are unconscious of the earth’s rotation, its effect is seen in the apparent daily course of the sun across the heavens, caused by our turning past it, yet in common practice the sun is assumed to revolve around the earth, and is usually thus spoken of for the purpose of simpler explanation.
The time at each meridian is necessarily different from that of every other, as only one of them holds the same position relative to the sun at the same time or putting it in another way, only one meridian can cross the sun at the same time, determining local noon for those places located upon it. ”

“ A circle may be a great circle of either the celestial sphere, the earth, or even of a baseball. The poles of a great circle are the points on the surface of its sphere, penetrated by the diameter perpendicular to the plane of the great circle. As for example, the poles of the earth are connected by the diameter that is perpendicular to the plane of the equator. An angle at any pole is measured on the great circle which subtends it. For instance, angles at the poles of the earth are measured on the equator; angles at the zenith on the horizon. ”

“ The angle of parallax subtended by the radius of the earth is then an acute angle of a right-angled triangle and is as large as it can possibly be with the body at the same distance. As the body obtains altitude above the horizon, the right angle of the triangle (at the observer) becomes obtuse and our acute angle of parallax becomes smaller and smaller until the body reaches an altitude of 90°—in our zenith, when the obtuse-angled triangle has resolved itself into the perpendicular line that passes through our position and the earth’s center. ”

“ Sidereal time is the bedrock of all time; for it is by converting it into solar time and sending it throughout the country by telegraph and radio that the people of [Pg 44] the world get the standard by which to set their clocks and chronometers. Sidereal time is not practicable for every day use as its noon occurs, without regard to light or darkness, at every hour of day or night during a year. In March, at the time of the vernal equinox, it agrees with the solar clocks, but in September at the autumnal equinox, its noon occurs at the solar midnight. ”

“ All the meridians on a Mercator chart are parallel and cut the equator at right angles. They all lie in a true north and south direction. The parallels of latitude all lie east and west and are parallel to each other and at right [Pg 149] angles to the meridians. The degrees of longitude on the globe grow smaller and smaller as the pole is approached due to the actual convergence of the meridians, but as all meridians are parallel on the Mercator chart the length of a degree must be shown the same length at the top as well as at the bottom of the chart. ”

“ At two points (the equinoxes) on opposite sides of the earth, and at right angles to the direction of its inclination, the equator and terrestrial ecliptic cross each other at the “water’s edge.”
The sun is always exactly overhead for that point of the earth which is nearest to it. This is an essential fact to remember in navigation. Bearing in mind that the sun is stationary and ignoring for a time the rotation of the earth, each advance in its orbit brings about a change of bearing of the sun and a new position becomes the nearest point, and thereby directly beneath the sun. ”

“ Every mariner who has reached a position in the profession where he is intrusted with the responsibilities of navigating a vessel is under obligation to the late Capt. Thomas H. Sumner, of Boston. This shipmaster discovered and developed the principle of the so-called Sumner or Position Lines, a principle which has proved of inestimable value and which, with its subsequent improvements, has well-nigh revolutionized the methods of navigation. ”

“ First, the earth travels in an ellipse, and, as the length of a degree varies in the different parts of the circumference, the motion would appear to be irregular, [Pg 57] that is, if the sun actually traveled at a uniform rate, it would, from the above fact, appear to us to be variable in its motion; furthermore, the laws of forces only allow a body traveling in a circle the privilege of a uniform speed so the earth, owing to its varying distance from the sun, experiences a corresponding change in the amount of attraction exerted upon it by the sun and its velocity, actually becomes variable. ”

“ In calculating a meridian altitude, an error in the dip directly affects the result by a corresponding amount, so extra care should be exercised in this respect. In this instance, we endeavor to locate the body relative to our zenith and anything that affects its altitude directly affects the latitude. In a time sight, a different principle is involved. Here the position of the body as defined by the latitude locates the apex of one angle of the astronomical triangle and hence a small error in the altitude will very likely cause a greater effect on the longitude. ”

“ In slow cargo steamers and sailing vessels, particularly when the course creates but little departure, the change of time due to difference of longitude is not sufficiently large to cause much inconvenience and can be taken care of by setting the clock back or ahead at noon. But with the development of the modern steamer, speed has increased to such an extent that the easting or westing of certain day’s runs correspond to a considerable amount of time, and to correct the clock to local time, all at once, would be a source of inconvenience and a bother. ”

“ We know Orion does not move, for he is composed of fixed stars, and this seeming westward movement of his is in reality the apparent eastward marching of the sun, which is due to the earth’s movement of revolution. ”

“ It is a good rule to remember in reckoning all kinds of time that the clock’s face shows earlier time to the westward, and from this it is easy to deduce the proper application of a correction.
There are two kinds of solar time used in navigation; the first to be considered is apparent time, the kind shown by the sun dial, or measured by the sun as we see it. It is noon of the apparent day when the sun is seen with the sextant to dip while taking a meridian altitude. ”

“ The time the sun or moon is above our horizon depends upon its declination and our latitude. As the sun moves northward in declination from March to June, our days lengthen by the sun rising earlier and farther in the northeast, and setting later and farther to the northwest. Similarly the moon in September is moving northward in declination very rapidly and would be rising earlier each evening were it not for its own eastward movement of revolution which causes her to slip eastward an average of 51 minutes daily and causes her later rising at night. ”

“ Circum- or Ex-meridian Altitude
It frequently happens, especially in the higher latitudes, that an aggravating mass of cloud drives over the sun or other objects that you are chasing, with the tangent screw, and it is lost from view together with all hope of a meridian altitude. But such an unfortunate occurrence as the loss of the mid-day latitude may be averted by employing the Circum-meridian sight or Ex-meridian, as our English cousins call it.
The mariner accustomed to its use “shoots” the sun and notes the time by chronometer or watch. ”

“ While the sun is employed as the object of reference in solar time, it may appear strange that no particular star is thus used in sidereal; but in lieu of a definite stellar object by which to measure the sidereal movement of the heavens, we refer to the celestial vernal equinox.
This point was located in the constellation of Aries centuries ago, and hence its popular name—The First Point of Aries; but this has become a misnomer, for the point has long ago moved westward into another constellation, as discussed under the Precession of the Equinoxes. ”

“ The one which cuts the north and south points is called the celestial meridian, and is evidently a projection of the terrestrial meridian. The vertical circle passing through the east and west points is called the prime vertical, and has a distinction above other vertical circles by virtue of its being the most favorable position for a body in observations for longitude. The heavens are further swept by an infinite number of parallels of altitude which are, as their name implies, parallel to the horizon. ”

“ So it becomes evident that refraction is caused by the rays of light passing obliquely from a rarer to a denser medium or vice versa. A ray of light coming from a heavenly body to the earth passes through a medium of gradually increasing density, from the thin outer air to the denser atmosphere at the surface of the earth. The ray of light consequently becomes curved downward and reaches the earth at a point nearer the heavenly body than would be the case if the light ray traveled in a straight line. The effect of this to the observer is that the body appears higher than it really is. ”

“ In order to facilitate a simple explanation of New Navigation it will be brought to mind that every heavenly body has a corresponding point on the earth directly beneath it, which bears the same relation in latitude and longitude to the earth, that the body does in declination and right ascension to the celestial sphere. To an observer at such a sub-celestial point the body is in the zenith with an altitude of 90° ”

“ During the forenoon as the sun passes toward the meridian, the northern end of the position line will move in direct proportion with the body’s change in azimuth to the eastward and the southern end to the westward, until at noon with the sun on the meridian we have an east and west position line.
It will be seen that at one moment of the day it is a very easy matter to establish a line of position; the mere working of a meridian altitude does this. ”

“ Every meridian carries a time of its own, and the instant of the click of a telegraph key may be recorded all over the world in the local time of each locality, yet the interval between this and a subsequent click has an absolute value which is the same at every place, regardless of whether it is expressed in solar, sidereal or lunar time, and its actual value is invariable. ”