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characteristic function of the optical system to which the problem belongs. From this function is deduced the surface of wave-slowness of the medium; and by means of this surface, the direction of the rays refracted into the medium. From this construction also Sir W. Hamilton was led to the anticipation of conical refraction, mentioned above.

The investigations of MM. Cauchy and Lamé refer to the laws by which the particles of the ether act upon each other and upon the particles of other bodies;-a field of speculation which appears to me not yet ripe for the final operations of the analyst.

Among the mathematicians who have supplied defects in Fresnel's reasoning on this subject, I may mention Mr. Tovey, who treated it in several papers in the Philosophical Magazine (1837-40). Mr. Tovey's early death must be deemed a loss to mathematical science.

Besides investigating the motion of symmetrical systems of particles which may be supposed to correspond to biaxal crystals, Mr. Tovey considered the case of unsymmetrical systems, and found that the undulations propagated would, in the general case, be elliptical; and that in a particular case, circular undulations would take place, such as are propagated along the axis of quartz. It appears to me, however, that he has not given a definite meaning to those limitations of his general hypothesis which conduct him to this result. Perhaps if the hypothetical conditions of this result were traced into detail, they would be found to reside in a screw-like arrangement of the elementary particles, in some degree such as crystals of quartz themselves exhibit in their forms, when they have plagihedral faces at both ends.

Such crystals of quartz are, some like a right-handed and some like a left-handed screw; and, as Sir John Herschel discovered, the circular polarization is right-handed or left-handed according as the plagihedral form is so. In Mr. Tovey's hypothetical investigation it does not appear upon what part of the hypothesis this difference of right and left-handed depends. The definition of this part of the hypothesis is a very desirable step.

When crystals of Quartz are right-handed at one end, they are righthanded at the other end: but there is a different kind of plagihedral form, which occurs in some other crystals, for instance, in Apatite: in these the plagihedral faces are right-handed at the one extremity and left-handed at the other. For the sake of distinction, we may call the former homologous plagihedral faces, since, at both ends, they have the same name; and the latter heterologous plagihedral faces.

The nomologous plagihedral faces of Quartz crystals are accompanied by homologous circular polarization of the same name. I do not know that heterologous circular polarization has been observed in any crystal, but it has been discovered by Dr. Faraday to occur in glass, &c., when subjected to powerful magnetic action.

Perhaps it was presumptuous in me to attempt to draw such comparisons, especially with regard to living persons, as I have done in the preceding pages of this Book. Having published this passage, however, I shall not now suppress it. But I may observe that the immense number and variety of the beautiful optical discoveries which we owe to Sir David Brewster makes the comparison in his case a very imperfect representation of his triumphs over nature; and that, besides. his place in the history of the Theory of Optics, he must hold a most eminent position in the history of Optical Crystallography, whenever the discovery of a True Optical Theory of Crystals supplies us with the Epoch to which his labors in this field form so rich a Prelude. I cordially assent to the expression employed by Mr. Airy in the Phil. Trans. for 1840, in which he speaks of Sir David Brewster as "the Father of Modern Experimental Optics."]

BOOK X.

SECONDARY MECHANICAL SCIENCES.

(CONTINUED.)

HISTORY

OF

THERMOTICS AND ATMOLOGY.

Et primum faciunt ignem se vortere in auras
Aeris; hinc imbrem gigni terramque creari
Ex imòri; retroque a terrà cuncta revorti,
Humorem primum, post aéra deinde calorem ;
Nec cessare hæc inter se mitare, meare,
De cœlo ad terram de terrà ad sidera mundi.

LECRETIUS. i. 783.

Water, and Air, and Fire, alternate run
Their endless circle, multiform, yet one.
For, moulded by the fervor's latent beams,
Solids flow loose, and fluids flash to steams,
And elemental flame, with secret force,

Pursues through earth, air, sky, its stated course.

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