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the earth reached G and the planet O, the latter would be seen among the fixed stars at 0, and would, consequently, have appeared to have performed a backward, or retrograde motion. At an intermediate point between the real advance and the apparent retrogression, the appearance of a short cessation of motion would be presented. The view that would be afforded of a racecourse from a station considerably remote presents a familiar illustration of the apparent motions of the planets whose orbits are without ours.
2. “On what causes do the variation of brightness in the planet Venus depend?"
We see more or less of the illuminated disc of Venus according to the part of her orbit in which she is advancing. When she is in her greatest elongation she appears like a half moon; in her progress thence to her inferior conjunction (i.e., intermediate position between the sun and earth) she becomes a crescent; but, within certain limits, affords greater light than at her elongation, from the fact of being much nearer the earth, and giving light from a portion of an illuminated disc of greater apparent diameter.
3. “What is meant by parallax ? To what uses is the consideration of parallax applied, and what conclusions have been drawn from it?"
Parallax is the apparent angular change in the position of a heavenly body as viewed from different points of observation. In journeying along a railway we observe the bearing of distant objects to vary with our change of place. At one time, for instance, we see a church due east from us ; and after going some miles to the north the same church would be seen in a southeasterly direction. The angle between two points in which the church appears in the horizon is the parallax of the church as seen from the two supposed stations. The more remote the object the less the parallaxtic displacement due to a given distance between the places from which parallax is observed. Astronomically speaking, parallax is limited to the different apparent positions of the heavenly bodies when viewed from the surface of the earth, and as they would appear from its centre. Now it can be determined in what part of the heavens any heavenly body, as the moon, would appear if viewed from the earth's centre ; and actual measurement informs us of the position in which
the same body appears from the earth's surface. For instance, in the above figure, suppose the moon M to be viewed from P on the earth's surface, and also from P', the point through which a line from C, the earth's centre, would pass to the moon; and let it be supposed that the moon is in the horizon of P. at the time of observation. From P the moon would appear among the stars at p, and from P' at p. Under the circumstances assumed, the angle p' M p, which is the angle of parallax, and equal to angle P M С, would be found to be 57' 5. But the angle M P C is a right angle, as we have supposed the moon to be in the sensible horizon of P. Hence, the three angles of the triangle MP C are known; for 2 PCM = 90° — 57' 5" =
89° 2' 55"; and P C = radius of the earth = 3965 miles. From these data, M C, the distance of the moon from the centre of the earth may be found; for if MC be radius, P C is the sine of angle P MC = .016605 to unity as radius. And M C exceeds unity as many times as 3965 exceeds sine of angle P M C to unity as radius ; that is, radius MC = 3965 = .016605 = 238,800, nearly. In round numbers we usually say the moon is 240,000 miles from the earth, and, in reality, she is sometimes more than, and sometimes less than the result of our calculation, as her orbit is elliptical. Similarly, the parallax of other heavenly bodies has been the means by which astronomers have determined their distances from the earth. The fixed stars obtain their appellation from the circumstance that they never change their relative positions inter se; and the nicest observations, with our most perfect instruments, and made at all parts of our orbit, fail to indicate any increase or diminution in the angle which one of the fixed stars makes with another. As the result of some astronomical observations, it may be remarked, that the nearest of the fixed stars cannot be so near the earth as 100,000 times the earth's diameter. This is a deduction from the fact that none of the stars have any parallax from the earth's diameter as the basis of observation.
SECTION 1. 1. Give the names of the notes, as commonly employed
in instrumental and vocal music respectively. 2. Write down the shapes of the notes, and explain
their relative value. 3. Explain the Diatonic scale, and show what are the
intervals between each successive note, in the major mode.
1. Write down the different rests, and show their re
spective value. 2. Write down the treble, tenor, and bass clefs, and
explain their meaning. 3. Explain what is meant by a unison, an interval, a
sharp, a flat, a dotted note, and a bar.
1. What is meant by time, and what is the distinction
between common and triple time? Explain the
meaning of compound time? 2. What is meant by accent, and what does it differ
SECTION IV. 1. What is tranposition ?
sary by it?
2. How is the use of sharps and flats rendered neces3. Explain the order in which the scales follow each
other, and how they give rise to the use of the
different semitones on the chromatic scale. | Write short passages of music in the time indi
3 3 cated respectively by C, each in a different key.
1. “Give the names of the notes as commonly employed in instrumental and vocal music respectively.
The shape-names of notes employed in both instrumental and vocal music are, Breve, Semibreve, Minim, Crotchet, Quaver, Semiquaver, Demisemiquaver, and Hemidemisemiquaver: the last two, however, are confined to instrumental music. The sound-names are of two kinds, the one now beginning to be generally applied to vocal, and the other, the old terms, mostly retained in instrumental music. They are as follows:
Vocal, Do, Re, Mi, Fa, Sol, La, Si.
Instrumental, C, D, E, F, G, A, B. The eighth sound from any particular note is termed its octave, and receives the same name as that note. The former of these designations for the sounds of a musical scale have, in England even, long been familiar to musicians, especially those who have completed their course of study on the Continent; but the unparalleled success of Wilhem's system, under the direction of Mr. Hullah, and the scarcely less indefatigable exertions of Mr. Mainzer, have given such an impetus to