Lars pr

to AN, and let AN b, At = x, latus rectum of the parabola

Draw Pt and Arx', and 4 a then PQ Pp + pq = b- x + a + x + a + x + b x' =2(a + b) which is constant, therefore the length of the path will be the same from whatever point in the ordinate the ray proceeds.

8. In some person's eye the radius of the cornea is too great; consequently light coming from a near point will be refracted by the cornea to a point beyond the retina; but that coming from a distant point will be refracted to a point on the retina. This is called longsightedness. While in some other eyes the curvature of the cornea is too great; that is its radius is too small, and light coming from a distant point will not be refracted to a point in the retina, but will converge to a point nearer than the retina. This is called short-sight

Let O be the centre of the cornea; then in the first case as represented in figure (1) light coming from a near point will converge to a point q, beyond the retina, and will cover a small circle at q on the retina, and will therefore cause indistinct vision. If now a convex lens of focal length be applied to the proper it will converge the rays to a eye, point in the retina, and there will be distinct vision. And in the 2nd as represented in the 2nd figure, light coming from a distant point will

converge to a point q, nearer than the retina and will cause indistinct vision. If therefore a concave lens of proper focal length be applied, it will cause the rays to fall on the retina in a state of greater divergence, and will cause them to converge at a point in the retina, and there will be distinct vision.

9. Let A be the centre of the spherical surface, then

10. Let A be the centre of the mirror, and CD the eye-lens, placed on the axis of the mirror. Here the telescope is supposed to be without the plain mirror, which makes no difference in the result. Then if the telescope be directed to a distant object, it will form an inverted pq of the object in its principal focus. Let q be the point in the image which is cut by the reflected ray AD, such that AD just touches the eye-lens CD; then the point D of the image will be by half-light; for the light coming from the portion AA" will not enter the eye-lens, but those rays only will enter which come from the portion AA. If we join A" D, the point of the image which is cut by A" D will be seen by full-lights. The portion between this point of the image and the q is called the ragged edge. Let the semi

diameter of the eye-lens be b, then if S and S. denote the focal

e

lengths of the object glass and the eye-lens; the field of view

b

= 2 POQ 2 qAp=2 ▲ DAC = 2 So + Se

11. The magnifying power of the Galilean telescope to an eye that can see at the distance of 12 inches = (1⁄2 + ) —'

ASTRONOMY.

Afternoon Paper.

1. That the earth is of the globular form is rendered probable from the following reasons: 1st, when a ship approaches a port, the mast becomes first visible, and the hull afterwards, whereas if the earth's surface were a plane, the hull being the larger body would appear first; 2nd, that the horizon of a person standing on the deck of a ship in the sea, is not seen to lose itself in distance and mist, but is a sharp, clear and well-defined circle, such as would be produced by the revolution of a tangent to a sphere; 3rd, from the analogy from the sun and planets, which are all known to be round bodies; and 4th, that in lunar eclipses, when the earth comes between the moon and the sun, the shadow on the disk is seen to be circular in all positions of the earth, which would not be the case, if the earth be of any other form. But though from these reasons we conclude that the earth is nearly a spherical body, still we do not know its exact form. From the measurements of a degree in various quarters of the earth, it is found that the length of an arc subtending one degree in the centre of the earth increases as we proceed northwards in the northern hemisphere, and by comparing the different lengths in different latitudes of the earth, it is found that the equatorial diameter exceeds the polar by

about

1

(230)th part of its length. However for general purposes

we may assume the earth to be of the globular form.

Let D be the length of a degree on this supposition, and r the radius of the earth, then

1° : 360° :: D: 2 π r

360 D

·λ= 2 π

The distance of the earth from the sun is determined by means of

the horizontal parallax of the body.

Let P be the horizontal parallax of the and r and

R the radius

of the and its distance from the then.. P" =

, we get

R

H

X number of seconds contained in an arc to the

2. Let Ho be the horizon of any place, P the pole, M S, S the ecliptic, and ES the Equator; then when the S is at S, the intersection of the ecliptic and the Equator, the days and nights will be equal over the whole earth; as the sun moves in the direction S, S on the Ecliptic a greater portion of the diurnal Ole of the sun become visible every successive day, till when the sun is at the solsticial point when the longest day will happen to the place.

As the sun moves further and further from the last point, the length of the days diminishes every successive day, till the sun is again at the other equinox, when the days and nights are again equal. Afterwards as the sun moves in the Ecliptic the days become shorter, till the sun is in the tropic of Cancer, when the shortest day happens to a place in the northern hemisphere. As the sun moves from the last point towards the equinox, the length of the day increases till the sun is in the equinox, when the days and nights are equal.

If the latitude of the place be such that the whole diurnal circle for a particular day lies above the horizon; then the day will last 24 hours,