Page images
PDF
EPUB
[blocks in formation]

Logarithms and logarthmic Sines and Tangents, to four decimal figures. To avoid an extra line of figures, the 10 in the index of the tangents and cotangents has been rejected, when the index exceeded 10.

[merged small][merged small][ocr errors][merged small]

obliquity of the ecliptic less log. of the difference of the moon's and sun's parallaxes, and log. Barith. comp. sine of difference of the parallaxes.Tangent of sun's semidiameter.

TABLE VI.

Latitudes of a number of places with their longitudes from the meridian of Greenwich.

The latitudes and longitudes of several of the places in the United States are given according to the determinations of R. T. Payne, the former editor of the astronomical part of the American Almanac, a valuable work, published annually in Boston.

TABLE VII.

Mean Refractions with the corrections due to given changes in the states of the barometer and thermometer.

TABLE VIII.

Sun's Parallax in Altitude.

TABLE IX.

Mean Right Ascensions and Declinations of 30 principal Fixed Stars for the beginning of the year 1840, with their Annual Variations; also, auxiliary quantities to facilitate the computations of their aberrations and

nutations.

TABLES X and XI.

These serve to convert intervals of mean solar time into equivalent intervals of sidereal time, and the contrary.

TABLES XII to XV, inclusive.

Auxiliary tables, for the computations of Solar Eclipses, and Occultations.

TABLE XVI.

Reductions of the moon's parallax and of the latitudes of a place, and also the logarithms of the earth's radius, according to the compression

[ocr errors]

TABLE XVII.

в

Logarithms to be added to the logarithmic cosine and sine of the geographic latitude of a place, to obtain the logarithms of e cos o' and sin '; in which ę is the radius of the earth at the place, and ' the geocentric latitude.

TABLES XVIII to XXI, inclusive.

These serve to find the time of New or full Moon in any imately, or within a few minutes of the true time.

month approx

The time of mean new moon in January of each year, as given in table XVIII, has been diminished by 15 hours. These 15 hours have been added to the equations in table XXI. Thus, 4h. 20m. has been added to

the first equations; 10h. 10m. to the second; 10 minutes to the third; and 20 minutes to the fourth. By this means, the equations are all made additive.

TABLES XXII to XXXI, inclusive.

These are approximate Solar Tables, by which the sun's true longitude, hourly motion, semidiameter and radius vector, and the apparent obliquity of the ecliptic, may be determined for a given time, very nearly.

The Sun's Mean Longitude, the longitude of the perigee, and Arguments for finding some of the small equations of the sun's place given in table XXII, are all computed for mean moon at the meridian of Greenwich, on the first of January for common years, and on the second of January for bissextiles. The sun's longitudes and the longitudes of his perigee have each been diminished by 2°. As each is diminished by the same quantity, the mean anomaly, which is obtained by subtracting the longitude of the perigee from the sun's longitude, and which is the argument for the equa. tion of the centre, is not affected. The Argument I., is for the equation depending on the action of the moon; Argument II., is for that depending on the action of Jupiter; Argument III., is for that depending on the action of Venus; and Argument N, is for the Nutation, or equation of the equinoxes. Of the 2° which has been subtracted from the sun's mean longitudes, 1° 59' 30" is added to the equation of the centre, and 10" to each of the small equations due to the actions of the Moon, Jupiter, and Venus.

TABLES XXXII to LXIV, inclusive.

Approximate Lunar Tables, by which the moon's true longitude, latitude, horizontal parallax, semidiameter and hourly motions in longitude and latitude for a given time, may be determined, very nearly.

The Epochs of the Moon's Mean Longitude, and of the Arguments for finding the Equations which are necessary in determining the True Longitude and Latitude of the Moon given in table XXXII, are all computed for mean noon at the meridian of Greenwich, on the first of January for common years, and on the second of January for bissextiles. The Argument for the Evection is diminished by 29', the Anomaly by 1° 59' the Argument for the Variation by 8° 59', the mean longitude by 9° 44'; and the Supplement of the Node is increased by 7'. This is done to balance the quantities which are applied to different equations to render them affirmative.

TABLE LXV.

Five pages of the Nautical Almanac, for the month of May 1836.

TABLES LXVI, LXVII, and LXVIII.

Tables of Second, Third, and Fourth Differences; useful in finding from the Nautical Almanac, the moon's longitude or latitude for any intermediate time between noon and midnight.

TABLES LXIX to LXXIX, inclusive.

Approximate tables for the planet Mercury; including also a small table containing the Heliocentric Longitude, Latitude &c. of the planet Venus at the times of transit over the sun's disc in 1874 and 1882.

TABLE LXXX.

Logistical Logarithms. This table is convenient in working proportions when the terms are minutes and seconds, or degrees and minutes, or hours and minutes.

PRELIMINARY OBSERVATIONS.

It is frequently convenient to regard quantities as separated into two classes; those of one class being called affirmative, and those of the other negative. Thus, a right line or an arc of a circle, taken in one direction, being regarded as affirmative, a line or arc taken in the opposite direction, is regarded as negative. An affirmative quantity is denoted by having the sign, called the affirmative or plus sign, prefixed to it, and a negative quantity by having the sign—, called the negative or minus sign, prefixed to it. Before an affirmative quantity the sign is frequently omitted, it being understood to be affirmative if neither sign is prefixed; but before a negative quantity the sign must always be expressed.

If an affirmative arc, and a negative arc, equal to the supplement of the former to 360°, both commence at the same point in the circumference of a circle, they must also both terminate at the same point. We may, therefore, denote the position of a point in the circumference with reference to a given or fixed point, either by an affirmative arc or by a negative one equal to its supplement to 360°. Thus, supposing the affirmative arc to be 294° 47', we may substitute in place of it,- 65° 13'.

To add quantities, having regard to their signs. When all the quantities have the same sign, add them as in common arithmetic, and prefix that sign to the sum. When the quantities have different signs, add the affirmative quantities into one sum, and the negative into another. Then take the difference between these two sums and prefix the sign of the greater.

When several arcs are to be added together, if the sum exceeds 360°, we may reject 360° or any multiple of it, and regard the result as the sum of the arcs.

« PreviousContinue »