producing DB to meet CE in E, the angle DEC will be equal to twice

the angle BAC. For

LACM-BCG

=

ZA+ZABC

= LA + LBD = A + MBE again BMC-2A+ ACM

=LA+LA+MBE=2A+MBE

.. BEM + MBE 2A+MBE

=

.. BEM-2 A

This is the optical principle of Hadley's Sextant which is described as

below.

12.

M

E

S'

AC is an arc of 60° nearly, and is graduated, the graduations beginning from A. M is a plane mirror fixed on the side CD of the instrument, Q is a mirror fixed on a moveable arm DB, the mirror Q being parallel to M, when DB coincides with AD. The inclination of the mirrors is in the present BDA, for mirror M is parallel to AD. This angle is readily found by the graduated arc AB. A ray of light SQ from a distant object S falling on Q is reflected successively by the mirrors into the E. Now if the last reflected ray be in the direction of a ray of light from another object S1, the two objects will appear together, and their angular distance at the eye which is measured by by the preceding position twice the inclination of mirrors

eye

=

case =

SES1 will be

=

=

2 LADB

- 2 AB.

If then by a proper adjustment of the mirror Q, the two objects appear to coincide, their angular distance will be double the measured arc AB.

NLt greater than GLn, the prism being supposed to be a denser medium than air.

A

AG the green.

Dispersive power

The

G

R

and the ratio of VAR

a ray CA falling on the prism at A, is decomposed into 7 (seven) distinct primary colours. AR the least refrangible represents the red pencil AV the

outermost represents the violet,

VAR is called the total dispersion,

BAR is called the dispersive power of

the violet rays. In like manner the ratio GAR: BAR is called

the dispersive power of the green rays.

An inverted image (b) of a distant object is formed by the mirror AB, and the image b is farther from the small speculum a than its · principal focus; an inverted image b', or an erect image of the real object will be formed somewhere between C and D. such that pencils diverging from the image b' are refracted by D so as to enter the eye parallel and give distinct vision of the image, to the eye E. The magnifying power is equal to the focal length of the mirror AB divided by the focal length of the eye piece CD.

14. That the earth really moves is rendered probable. 1st. From its greater simplicity when we consider the immense distance of the stars and the enormous rapidity with which they must revolve, in order to

move round the earth in 23h 56m. 2nd. From the analogy of the sun and planets, which although many of them are much larger than the earth, are found by observing spots on their disks to have such a rotation. 3rd. From the earth's figure being not exactly spherical, but nearly such as would be supposing the earth to have been originally fluid, and to have revolved round an axis; and from the diminution of gravity in proceeding towards the equator being such as would arise from the centrifugal force of the earth's motion. 4th. In all curvilinear motions, there must be a force tending towards the centre; but as the earth is indefinitely small, in comparison with the sun and the planets, the latter cannot move round the earth as a centre. But the strongest argument in favour of the rotation of the earth is, that a stone let fall from a high tower, falls a little to the east of the base of the tower.

There is reason also to believe that the earth moves round the sun. For from the distance of the earth from the sun and the period of the sun's apparent revolution round the earth, compared with the distances and periods of the planets which are known to revolve round the sun, it appears probable that the earth is a planet, and is subject to the same laws of motion as the others.

The aberration of light also and the stationary points of the superior planets can be simply explained on the hypothesis of the earth's motion round the sun, and have not been accounted for on any other hypothesis. But the strongest argument in favour of the earth's revolution round the sun is, the perfect agreement, which it establishes between observations and results deduced on that hypothesis. From these we conclude that the earth revolves on its axis in a day, and round the sun in a year.

Now the apparent diameter of the sun varies throughout the year, and as this cannot proceed from any change in the real magnitude of the sun, this must be caused by the varying distances of the sun from the earth in the course of the year. From an accurate comparison of the proportion of the distances throughout the year, deduced from observations of the apparent diameters, it appears that the path of the earth round the sun is elliptical. Newton by assuming the law of solar gravitation, proved that the orbits of all the planets (the earth being one of them) are elliptical.

A, B, C, D are four positions of the earth with respect to the sun correspondA ing to the summer solstice (A), autumnal equinox (B), winter solstice (C,) and vernal equinox (D.) The axis of the earth in moving round the sun is always parallel to itself, and its inclination to the orbit is constant. At the summer solstice, the north pole P is in sunlight, whilst the south pole p is in

complete darkness. the north pole P being in darkness, and the south pole enjoys sunlight. At the equinoxes the sun just appears on the horizon at the two poles. In this manner we see that one pole is sometimes in darkness, and the other at others.

At the winter solstice C, the opposite is the case,

The sun is for nearly six months above the horizon of every place on the earth. But the quantity of rays received depends on his altitude above the horizon, and to those places where he passes the meridian near the zenith, the quantity of rays, and consequently the heat, is very great but to those places where he attains only a smaller altitude, the heat is proportionally less. The heat is greater when the sun is nearer the zenith, because the rays then fall nearly perpendicularly, and the number that falls on any body is greater, than when his altitude is less. It is to this difference in the intensity of heat, that there are different climates both at different and same places.

15. The length of a true or apparent solar day is variable throughout the year, but the variations are contained within very narrow limits. If the lengths of all the apparent solar days in a year be added together, and the sum divided by the number of days in the year, the quotient will be an average or mean of all the apparent days, and it is in consequence called a mean solar day. The difference between the lengths of the mean solar day and the apparent solar day, is called the equation of time. It is defined to be additive when being added to the apparent it will produce mean time, and subtractive when it is to be subtracted from the apparent time to arrive at the mean time.

The equation of time arises from two causes, first, the variable motion of the sun in the orbit, and secondly, from the obliquity of the

ecliptic to the equator.

ရာ

N

Now from apogee to perigee the velocity of the sun in the orbit continually increases, and from perigee to apogee, it continually diminishes. If now a fictitious body S1 move with the mean motion in the ecliptic com

pleting a revolution at the same time with the real sun; then

from apogee to perigee, the mean sun will be continually

before the real sun, and the former will be later in coming to the meridian ; i. e. calling t that part of the equation due to the variable motion, t' will be subtractive from apogee to perigee. Again from perigee to apogee, the mean sun is behind the real sun, or comes on the meridian first, hence t' from perigee to apogee is additive.

Call t that part of the equation of time due to the obliquity.

Let y and z represent halves of the equator and ecliptic respectively. P is the pole of the equator.

Let us now suppose another fictitious body S2 to move uniformly in the equator, completing its revolution in the same time with that of the revolution of the real sun.

Let S1 be the position of S1 in the ecliptic at any time. Take y = 90°; draw (P v,) P S1 s a secondary to the equator through S1, PZY another secondary cutting the ecliptic in Z. Now by Napier's Rules

Cos

quity

=

if vs

Si s = Cosy s Sin S1 Y s = Sin Cos s' if w

w = obli

90°, Cos vs is positive, and Sin w is also positive, ..

or S1 is behind S2 (the equator mean sun) or Si comes

on the

meridian first, .. t is substractive from an equinox to solstice, when