SPHERICAL ASTRONOMY

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Continguts

Newtons formula for interpolation
20
Computation of numerical differential coefficients
27
G THEORY OF SEVERAL DEFINITE INTEGRALS USED
33
Determination of the relative place of two objects by means
34
The law of the errors of observation
42
Determination of the most probable value of an unknown quantity
48
Determination of the probable error in this case
57
E THE DEVELOPMENT OF PERIODICAL FUNCTIONS FROM GIVEN
63
SPHERICAL ASTRONOMY
70
Coordinate system of longitudes and latitudes
77
Parallactic angle Differential formulae for the two preceding cases
85
and declinations
88
Mean solar time Equation of time
96
Rising and setting of the fixed stars and moveable bodies
103
Transits of stars across the prime vertical
109
THE NUTATION
114
Annual motion of the equator on the ecliptic and of the ecliptic
115
Annual changes of the stars in longitude and latitude and in right
121
Nutation in longitude and latitude and in right ascension and
130
The ellipse of nutation
137
Parallax in altitude of the heavenly bodies
144
Example for the moon Rigorous formulae for the moon
152
Law of the decrease of temperature and of the density of
160
Computation of the refraction by means of Bessels and Ivorys
166
Reduction of the height of the barometer to the normal tempera
172
On twilight The shortest twilight
178
Tables for aberration
188
Analytical deduction of the formulae for this case
194
Expressions for the apparent place of a star Auxiliary quantities
202
vation of zones
223
B Determination of the constants of aberration and nutation and of
231
G Determination of the constant of precession and of the proper motions
239
Solution given by Cagnoli
301
Method of finding the time by the disappearance of a star behind
307
DETERMINATION OF THE ANGLE BETWEEN THE MERIDIANS
313
Determination of the difference of longitude by eclipses Method
322
Determination of the difference of longitude by occultations
336
Determination of the difference of longitude by lunar distances
344
Determination of the difference of longitude by culminations
350
ON THE DETERMINATION OF THE DIMENSIONS OF THE EARTH
357
DETERMINATION OF THE HORIZONTAL PARALLAXES OF
366
Effect of the parallax on the transits of Venus for different places
375
SEVENTH SECTION
389
Use of the vernier
401
Effect of the excentricity of the circle on the readings The
408
S Methods of arranging the observations so as to eliminate the effect
417
Determination of the periodical errors of the screw Examination
425
Effect of the errors of the instrument upon the observations
429
Observations of altitudes
437
Determination of the errors of the instrument
445
THE TRANSIT INSTRUMENT AND THE MERIDIAN CIRCLE
451
Reduction of an observation on a lateral wire to the middle wire
460
Determination of the errors of the instrument
466
Reduction of the zenith distances observed at some distance from
477
THE PRIME VERTICAL INSTRUMENT
484
Reduction of the observations made on a lateral wire to the middle
492
Determination of the errors of the instrument
498
INSTRUMENTS WHICH SERVE FOR MEASURING THE RELATIVE
512
Best way of making observations with this micrometer
522
The heliometer Determination of the relative place of two objects
532
Reduction of the observations if one of the bodies has a proper
539
METHODS OF CORRECTING OBSERVATIONS MADE BY MEANS
545
Effect of refraction for micrometers by which the difference
551
Change of the angle of position by the lunisolar precession
558

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Pàgina 375 - The cubes of the mean distances of the planets from the sun are proportional to the squares of their times of revolution.
Pàgina 105 - When the sun is north of the equator the days are longer than the nights in the northern hemisphere ; and when the sun is south of the equator the reverse of this is the case; and in the southern hemisphere, of course, similar changes take place. At the equator the day is always 12 hours long, but at 8° 34' north or south of it, the length of the day extends to 12 J hours.
Pàgina 5 - C cos a — cos B cos C and changing the letters we get the following three equations, which correspond to the formulae (2), biit again contain angles instead of sides and vice versa: cos A = sin B sin C cos a...
Pàgina 113 - The cause of this motion is shewn, by physical astronomy, to arise from the attraction of the sun and moon on the excess of matter at the equatoreal parts of the earth.
Pàgina 3 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Pàgina 196 - For since (—) and (c—} are the differential coefficients \dtJ \dtJ of a and cT, if the heliocentric place of the planet is changed whilst the place of the earth remains the same, the second members of the two equations give the places of the planet at the time T? but as seen from the place which the earth occupies at the time t. Note. The motion of the earth round the sun and the rotation on the axis are not the only causes which produce a motion of the points on the surface of the earth in space,...
Pàgina 161 - Atmospheric currents, in high latitudes, when undisturbed, are westerly, particularly in the winter season. If storms and gales revolve by a fixed law, and we are able, by studying these disturbing causes of the usual atmospheric currents, to distinguish revolving gales, it is likely that voyages may...
Pàgina 74 - ... remain fixed in the celestial sphere. If we lay a great circle through the pole and the star, the arc contained between the star and the equator is called the declination and the arc between the star and the pole the polar-distance of the star. The great circle itself is called the declination -circle of the star. The declination is positive, when the star is north of the equator and negative, when it is south of the equator. The declination and the polar -distance are the complements of each...
Pàgina 5 - A = cos B cos C — sin B sin C cos a ; and changing the signs of the terms, we obtain, cos A = sin B sin C cos a — cos B cos C.
Pàgina 324 - If then we substitute in place of the indeterminate co-ordinates a;, y, z the co-ordinates of a place on the surface of the earth, referred to the same system of axes, we obtain the fundamental equation for eclipses. For this purpose we must first determine the position of the line joining the centres of the two bodies. But if a and d be the right ascension and declination of that point, in which the centre of the more distant body is seen from the centre of the nearer body or in which the line passing...

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