N

It may in this case be considered as made up of two tele

scopes, by the first of which an inverted image is formed, and by the second of which the erect position is restored.

This is completed by substituting for the eye lens, G H, an achromatic eye-piece of either of the forms which have been described. Uhe improved achromatic terrestrial telescope is therefore now composed of five lenses. The achromatic object

E

A

lens is adapted to a large tube. To this the smaller tube, represented in the figure, which contains the remaining four lenses, is adapted. The lens B sends on the rays, which have crossed after forming an image in the focus of the object lens, in parallel directions. These are caused to form an image in the focus of the lens D, which will be erect; and this image is viewed almost free from colours by the eye-piece composed of the lenses A C.

The size of the achromatic refracting telescope was long limited by the difficulty of obtaining pieces of flint glass of suffi cient size. In the hands of its inventor its length was therefore limited to ten feet, and of this length no more than a single good one was constructed. A few have been made eight feet in length, but the greater part of the English instruments do not exceed five feet. Of late years the Swiss and German artists have succeeded in making flint glass of much greater size, and thus in increasing the length of the achromatic telescope. The most celebrated instrument in which this has been employed is that constructed by Frauenhoffer for the Observatory at Dorpat in Russia, which has a length of twenty-eight feet.

In the reflecting telescope of Newton, a concave mirror is placed at the end of a tube most distant from the object. By this an image would be formed in the position n' m'. Before the rays meet to form this image, they are interecpted by a plane reflecting surface placed at an angle of 45° to the axis of the

T

B

tube. By this the rays are bent at right angles, and the image is formed at n m. This image is viewed by an eye lens at E. In the reflecting telescope of Gregory, the image formed by the great mirror at n m serves as an object to a smaller concave

E

TTU

D

M

mirror. This, therefore, forms a second image at m' n', which will be erect. A hole is pierced through the great mirror, to which a tube containing an achromatic eye-piece is adapted, by which this second image is viewed and seen erect.

In the telescope of Cassegrain, the rays which are reflected from the great mirror are intercepted by a small convex mirror, C D, before they can form an image at n' m'. The place of the

image is thus transferred to n m, where it appears inverted. This inverted image is viewed in the same manner as in the telescope of Gregory.

The elder Herschel constructed many Newtonian reflectors. He also modified their structure by removing the plane reflector, and bringing the image near to the side of the tube by placing the mirror oblique to the axis of the tube. This image was

423. We have referred (§ 000) to the theory which holds that light is conveyed by means of undulations, excited in a medium which occupies all space. It is not our intention to enter into the consideration of the truth or falsehood of that theory, as such discussion would be foreign to our object. We recur to it at present in order to state that this theory derives its strongest evidences from the well-known phenomena of the propagation of sound. The mathematical investigations of the undulatory theory of light are therefore in close connexion with the subject of acoustics, with which we shall close our views of the physical sciences.

ACOUSTICS.

§ 424. We have, in a preceding section, stated some few of the facts in relation to the cause and the manner of the propagation of sound. The origin of sound in the oscillations of elastic bodies may be illustrated by means of a steel plate screwed into a vice. When thus held, it will vibrate if struck. If it be of considerable length, the vibrations will be so slow that they may be counted; and when the efficient length of the plate is altered by drawing it through the vice, it will be found experimentally, as may be also demonstrated mathematically, that there is a fixed relation between the length of the part of the plate which projects from the vice and the number of vibrations it performs. This relation is the same as that between the lengths and the numbers of the oscillations of pendulums. So long as the vibrations of the plate are so slow that they may be easily counted there is no audible sound. The power of counting them ceases

viewed by an eye-piece. The light in which the original Newtonian instrument, is lost at the second reflection, is bere saved, One of the instruments constructed on the last plan had forty feet focal distance. The best made by Herschel is twenty right feet, and is equal in its powers to the telescope of Dorpat

(000) when they become more frequent than eight or ten in a second; but the law which has been referred to will enable us to calculate their numbers when the lengths of the plates are known. The inference which has been stated (§ 000) is thus made, that at least sixteen vibrations of the sounding body per second are necessary for an audible sound, while, if they exceed twelve thousand per second, the sound becomes inaudible at the other extreme of the scale. Within these limits, then, a are included all the sounds audible by human ears. Nor does it appear that any one ear is capable of hearing every sound even within these limits. By experiments made by Wollaston, it appeared that the ear of every person on whom it was made had an imperfection which rendered some sound or other inaudible.

It does not appear that the limits are exactly the same in different individuals of the human race; and other animals have different limits to their auditory scale from those of man. Thus the lion and elephant were found to receive the impression of sound from oscillations too infrequent to affect the human ear, while small animals did not hear the sounds of the lower part of the human scale, and appeared to be affected by oscillations more rapid than any of those which convey the sensation to the human ear.

That the vibrations of sounding bodies are capable of raising waves in liquids, may be shown by the familiar experiment of producing sound in a drinking glass by rubbing the finger over its rim. Series of waves will then be distinctly seen at the surface of the liquid contained in the glass. From facts of this description Newton inferred that the propagation of sound in air resembled that of waves in a liquid. In the latter case no progressive motion is produced, but the waves are formed by an oscillation up and down, resembling the motion

of a liquid in a bent tube. The progress of the waves may be illustrated by reference to what takes place in a field of grain, over which waves formed by the wind may be often seen to pass, while each stalk remains firmly rooted to its place.

Taking up this view of the subject, Newton inferred that sounds ought to be conveyed in air at the rate of about 900 feet per second, while the actual velocity, ascertained by careful experiment, is more than 1100 feet.

The cause of discrepancy has been detected by Biôt and La Place, who have shown that the compression of the air which forms the wave changes its capacity for specific heat, and thus renders it more elastic by an increase of its temperature. When this circumstance is taken into account, the theoretic velocity of sound in air is raised from 900 to 1100 feet per second, which agrees almost exactly with experiment.

§425. Sound is conveyed by liquids with a greater velocity than in air; thus it passes through water at the rate of 4750 feet per second. In solids the velocity is still greater, being in cast iron ten times as great as in air.

426. The pulses in the air which convey sound are capable of being reflected when they meet with obstacles in their course. These reflected waves will produce separate audible sounds, when they follow the original sound at a sufficient interval of time. If several reflected waves cross each other at the same point within a similar interval, they may produce a sound louder than the original one. This interval, from the constitution of the human ear, is the eighth part of a second, and is therefore equivalent to the passage through a space of about 136 feet.

If, then, there be a vertical obstacle in front of the person who utters a sound, at a distance of about 70 feet, he will hear a distinct repetition of a single