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placing a slice of rock crystal in the polarised ray rs, fig. 64. The uniform colour in the interior of the image depends upon the thickness of the slice; but whatever that colour may be, it will alternately attain a maximum brightness and vanish with the revolution of the glass B. It may be observed, that the two kinds of quartz, or rock crystal, mentioned in the text, are combined in the amethyst, which consists of alternate layers of right-handed and left-handed quartz, whose planes are parallel to the axis of the crystal.

NOTE 215, p. 193. Suppose the major axis AP of an ellipse, fig. 18, to be invariable, but the excentricity CS continually to diminish, the ellipse would bulge more and more; and when CS vanished, it would become a circle whose diameter is A P. Again, if the excentricity were continually to increase, the ellipse would be more and more flattened till CS was equal to CP, when it would become a straight line AP. The circle and straight line are therefore the limits of the ellipse.

NOTE 216, p. 194. The coloured rings are produced by the interference of two polarised rays in different states of undulation, on the principle explained for common light.

NOTE 217, p. 225. According to Mr. Joule, that heat is produced by motion, and that it is equivalent to it, Mr. Thompson of Glasgow investigates from whence the sun derives his heat, since he shows that neither combustion nor his primitive heat could have supplied the waste during 6000 years. He concludes that the solar heat is maintained by myriads of minute bodies that are revolving at the edge of his dense nebulosity or atmosphere, some of which are often seen by us as falling stars. These, vaporized by his heat, and drawn by his attraction, meet with intense resistance on entering the solar atmosphere as a shower of meteoric rain; through it they descend in spiral lines to the sun's surface, producing enormous heat by friction during their fall, and serving for fuel on their arrival.

NOTE 218, p. 252. The class Cryptogamia contains the ferns, mosses, funguses, and sea-weeds; in all of which the parts of the flowers are in general too minute to be evident.

NOTE 219, p. 254. Zoophytes are the animals which form madrepores, corals, sponges, &c.

NOTE 220, p. 254.

and lizard kind.

The Saurian tribe are creatures of the crocodile

NOTE 221, p. 266. If heat from a non-luminous source be polarised by reflection or refraction at r, fig. 64, the polarised ray rs will be stopped or transmitted by a plate of mica M under the same circumstances that it would stop or transmit light; and if heat were visible, images analogous to those of figs. 65, 67, &c., would be seen at the point s.

NOTE 222, pp. 275, 329, 357. The foot-pound, or unit of mechanical force established by Mr. Joule, is the force that would raise one pound weight of matter to the height of one foot; or it is the impetus or force generated by a body of one pound weight falling by its gravitation through the height of one foot.

Impetus, vis viva, or living force, is equal to the mass of a body multiplied by the square of the velocity with which it is moving, and is the true measure of work or labour. For if a weight be raised 10 feet, it will require four times the labour to raise an equal weight 40 feet. If both these weights be allowed to descend freely by their gravitation, at the end of their fall their velocities will be as 1 to 2; that is, as the square roots of their heights; but the effect produced will be as their masses multiplied by 1 and 4; but these are the squares of their velocities: hence the impetus or vis viva is as the mass into the square of the velocity.

Thus impetus is the true measure of the labour employed to raise the weights, and of the effect of their descent, and is entirely independent of time. Now heat is proportional to impetus, and impetus is the true measure of labour. In percussion the heat evolved is in proportion to the force of the impetus, and is thus measured by labour.

Travail is a word used in mechanics, to express that work done is equal to the labouring force employed. The work done may be resistance overcome or any other effect produced, while the labouring force may be a horse, a steam-engine, wind, falling water, &c.

NOTE 223, p. 313. When a stream of positive electricity descends from P to n, fig. 72, in a vertical wire at right angles to the plane of the horizontal circle A B, the negative electricity ascends from n to P, and the force exerted by the current makes the north pole of a magnet revolve about the wire in the direction of the arrow-heads in the circumference, and it makes the south pole revolve in the opposite direction. When the current of positive electricity flows upwards from n to P, these effects are reversed.

NOTE 224, p. 314. Fig. 73 represents a helix or coil of copper wire, Fig. 72.

Fig. 73.

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terminated by two cups containing a little quicksilver. When the positive wire of a Voltaic battery is immersed in the cup p, and the negative wire in the cup n, the circuit is completed. The quicksilver ensures the connection between the battery and the helix, by conveying the electricity from the one to the other. While the electricity flows through the helix, the magnet S N remains suspended within it, but falls down the moment

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it ceases. The magnet always turns its south pole S towards P, the positive wire of the battery, and its north pole towards the negative wire.

NOTE 225, p. 316. A copper wire coiled in the form represented in fig. 73 was the first and most simple form of the electro-dynamic cylinder. When its extremities P and n are connected with the positive and negative poles of a Voltaic battery, it becomes a perfect magnet during the time that a current of electricity is flowing through it, P and n being its north and south poles.

NOTE 226, p. 344. It is to Halley we are indebted for the first declination chart and the theory of 4 poles of maximum magnetic intensity, since confirmed by observation, as well as the earliest authentic values of the magnetic elements in London and St. Helena, where he went on purpose to make observations on terrestrial magnetism. Since that time M. Gauss has formed charts of the magnetic lines, and published a theory which very nearly represents the magnetic state of the globe. The mass of observations daily making by our cruizers and our Government surveys in every part of the earth is enormous.

NOTE 227, p. 360. In fig. 74 the hyperbola HPY, the parabola pPR, and the ellipse A EPL, have the focal distance SP, and coincide

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through a small space on each side of the perihelion P; and, as a comet is only visible when near P, it is difficult to ascertain which of the three curves it moves in.

NOTE 228, p. 363. In fig. 75, E A represents the orbit of Halley's

E

Fig. 75.

comet, ET the orbit of the earth, and S the sun. very nearly exact.

A

The proportions are

NOTE 229, p. 382. Fig. 74 represents the curves in question. It is evident that, for the same focal distance SP, there can be but one circle and one parabola p PR, but that there may be an infinity of ellipses between the circle and the parabola, and an infinity of hyperbolas HPY exterior to the parabola p P R.

NOTE 230, p. 387. Let A B, fig. 26, be the diameter of the earth's orbit, and suppose a star to be seen in the direction A S' from the earth when at A. Six months afterwards, the earth, having moved through half of its orbit, would arrive at B, and then the star would appear in the direction B S', if the diameter AB, as seen from S', had any sensible magnitude. But A B, which is 190,000,000 of miles, does not appear to be greater than the thickness of a spider's thread, as seen from 61 Cygni, supposed to be the nearest of the fixed stars.

NOTE 231, p. 389. Stars whose parallax and proper motions are

known.

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The space run through in one second by these stars is therefore

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There are three great discrepancies in the parallax of the star Argelander or 1830 Groombridge. M. Otto Struve makes it 0" 034, which gives it a velocity of 251 leagues per second, while M. Faye finds the parallax to be between 0" 03 and 0" 01, which makes its velocity from 30 to 85 leagues per second.

These are all minimum velocities, because we can only determine on the celestial vault a projection perhaps much foreshortened of the real motions of the stars.

NOTE 232, pp. 398, 401. The following are the binary systems whose orbits have been accurately determined :

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NOTE 233, p. 403. The mass is found in the manner explained in the text; but the method of computing the distance of the star may be made more clear by what follows. Though the orbit of the satellite star is really and apparently elliptical, let it be represented by CDO, fig. 14, for the sake of illustration, the earth being in d. It is clear that, when the star moves through CDO, its light will take longer in coming to the earth from O than from C, by the whole time it employs in passing through O C, the breadth of its orbit. When that time is known by observation, reduced to seconds, and multiplied by 190,000, which is the number of miles light darts through in a second, the product will be the breadth of the orbit in miles. From this the dimensions of the ellipse will be obtained by the aid of observation; the length and position of any diameter as Sp may be found; and as all the angles of the triangle d Sp can be determined by observation, the distance of the star from the earth may be computed.

NOTE 234, p. 405. The mean results of MM. Argelander, Otto Struve, and Luhndahl for stars in the northern hemisphere and the epoch 1790, places the point to which the sun is tending in 259° 5' of right ascension and 55° 23' of north polar distance. Mr. Gallaway computed from stars in the southern hemisphere, at the same epoch, the point to have been in 260° 1' right ascension and 550° 37' north polar distance, results nearly identical, though from very different data.

NOTE 235, p. 414. One of the globular clusters mentioned in the text is represented in fig. 1, plate 8. The stars are gradually condensed towards

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