10.

M

The syphon is a bent tube MLQ, having both ends open, and one of them is capable of being placed in a vessel of fluid, the other end being lower than the surface of the fluid in the vessel. The vertical height MT corresponding to the part ML of the bent tube must be less than the height of the column of fluid in the vessel, which equals the atmospheric pressure. Then if the tube be filled with the fluid

by suction or other means, the fluid will continue to flow through the syphon tube as a natural fountain, until the surface of the fluid falls below G.

Suppose water is the fluid used.

Let HM be the height of the water barometer 34 feet nearly. Draw LT and PQ horizontal. Now the pressure of the atmosphere at M is the weight of a column of water whose height is HM, and the downward pressure at M on account of the weight of water in LM is proportional to MT, therefore the remaining pressure or the force with which water is impelled into the syphon is proportional to HT, and this is the force with which the water moves. If now a finger be placed at Q, the whole pressure at Q will be proportional to HT together with TP the vertical height corresponding to the column of water in the tube which is rushing out. That is, the downward at Q is the weight of a column of water whose height is HP. But the upward pressure at Q of the atmosphere is proportional to HM, therefore the pressure which the finger at Q really sustains is the weight of a column of water whose height is MP.

S'

Then producing DB to meet CE in E, the angle DEC will be equal to twice the angle BAC. For

This is the optical principle of Hadley's Sextant which is des

cribed as below.

12.6

B

E

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 case = Z BDA, for mirror M is parallel to AD. This

angle is readily found by the gradu

ated arc AB. A ray of light SQ from a distant object S falling on Q is reflected successively by the mirrors into to the eye 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 / SES1 will be by the preceding position = twice the inclination of mirrors = 2 ADB 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 mea

=

sured arc AB. a ray EG falling on the prism ABC at G, is refracted into GL, the angle n GL of refraction being less than 2 m GE of incidence. (m n is a perpendicular at G to the edge of the prism.) The ray GL is refracted into LN making

NLt greater

than GLn, the prism being supposed to be a denser medium

than air.

Dispersive power

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, AG the

B

green. The VAR is called the total dispersion,

and the ratio of VAR 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.

C

A, B, C, D are four positions of the earth with respect to the sun corresponding 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 com

plete darkness. At the winter solstice C, the opposite is the case, 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 darkness, and the other at others.

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.