On the Connexion of the Physical Sciences

by Mary Somerville

Note 146, pp. [50], [80]. Let q ♈ Q, and E ♎ e, fig. 11, be the planes of the equator and ecliptic. The angle e ♈ Q, which separates them, called the obliquity of the ecliptic, varies in consequence of the action of the sun and moon upon the protuberant matter at the earth’s equator. That action brings the point Q towards e, and tends to make the plane q ♈ Q coincide with the ecliptic E ♈ e, which causes the equinoctial points ♈ and ♎ to move slowly backwards on the plane e ♈ E, at the rate of 50ʺ·41 annually. This part of the motion, which depends upon the form of the earth, is called luni-solar precession. Another part, totally independent of the form of the earth, arises from the mutual action of the earth, planets, and sun, which, altering the position of the plane of the ecliptic e ♈ E, causes the equinoctial points ♈ and ♎ to advance at the rate of Oʺ·31 annually; but, as this motion is much less than the former, the equinoctial points recede on the plane of the ecliptic at the rate of 50ʺ·1 annually. This motion is called the precession of the equinoxes.

Note 147, [p. 81]. Let q ♈ Q, e ♈ E, fig. 36, be the planes of the equinoctial or celestial equator and ecliptic, and p, P, their poles. Then suppose p, the pole of the equator, to revolve with a tremulous or wavy motion in the little ellipse p c d b in about 19 years, both motions being very small, while the point a is carried round in the circle a A B in 25,868 years. The tremulous motion may represent the half-yearly variation, the motion in the ellipse gives an idea of the nutation discovered by Bradley, and the motion in the circle a A B arises from the precession of the equinoxes. The greater axis p d of the small ellipse is 18ʺ·5, its minor axis b c is 13ʺ·74. These motions are so small that they have very little effect on the parallelism of the axis of the earth’s rotation during its revolution round the sun, as represented in fig. 20. As the stars are fixed, this real motion in the pole of the earth must cause an apparent change in their places.

Fig. 36.

Note 148, [p. 83]. By means of a transit instrument, which is a telescope mounted so as to revolve only in the plane of the meridian, the instant of the transit or passage of a celestial body across the meridian can be determined. The transits of the principal stars are used to ascertain the time, or, which is the same thing, the amount of the error of clocks. A system of equidistant wires, as represented in the figure, is placed in the focus of the eye-piece, so that the middle wire is perpendicular and at right angles to the axis of the telescope. It consequently represents a portion of the celestial meridian; and when a star is seen to cross that wire it then crosses the celestial meridian of the place of observation. A clock beating seconds being close at hand, the duty of an observer is to note the exact second and part of a second at which a star crosses each wire successively in consequence of the rotation of the earth. Then the mean of all these observations will give the time at which the star crosses the celestial meridian of the place of observation to the tenth of a second, provided the observations are accurate. Now it happens that the simultaneous impression on the eye and ear is estimated differently by different observers, so that one person will note the transit of a star, for example, as happening the fraction of a second sooner or later than another person; and as that is the case in every observation he makes, it is called his personal equation, that is to say, it is a correction that must be applied to all the observations of the individual, and a curious instance of individuality it is. For instance, M. Otto Struve notes every observation Oʺ·11 too soon, M. Peters Oʺ·13 too late; M. Struve noted every observation one second later than M. Bessel, and M. Argelander estimated the transit of a star 1ʺ·2 later than M. Bessel. All these gentlemen were or are first-rate observers; and when the personal equation is known it is easy to correct the observations. However, to avoid that inconvenience Mr. Bond has introduced a method in the Observatory at Cambridge in the United States in which touch is combined with sight instead of hearing, which is now used also at Greenwich. The observer at the moment of the observation presses his fingers on a machine which by means of a galvanic battery conveys the impression to where time is measured and marked, so that the observation is at once recorded and the personal equation avoided.

Note 149, [p. 84]. Let N be the pole, fig. 11, e E the ecliptic, and Q q the equator. Then, N n m S being a meridian, and at right angles to the equator, the arc ♈ m is less than the arc ♈ n.

Note 150, [p. 85]. Heliacal rising of Sirius. When the star appears in the morning, in the horizon, a little before the rising of the sun.

Note 151, [p. 87]. Let P ♈ A ♎, fig. 35, be the apparent orbit or path of the sun, the earth being in E. Its major axis, A P, is at present situate as in the figure, where the solar perigee P is between the solstice of winter and the equinox of spring. So that the time of the sun’s passage through the arc ♈ A ♎ is greater than the time he takes to go through the arc ♎ P ♈. The major axis A P coincided with ♎ ♈, the line of the equinoxes, 4000 years before the Christian era; at that time P was in the point ♈. In 6468 of the Christian era the perigee P will coincide with ♎. In 1234 A.D. the major axis was perpendicular to ♈ ♎, and then P was in the winter solstice.

Note 152, [p. 88]. At the solstices, &c. Since the declination of a celestial object is its angular distance from the equinoctial, the declination of the sun at the solstice is equal to the arc Q e, fig. 11, which measures the obliquity of the ecliptic, or angular distance of the plane ♈ e ♎ from the plane ♈ Q ♎.