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In all cases therefore, provided one of two, either p’ or m be
small, or if they are both small, we have
7. This formula for the retardation on which depends the explanation of the coloured lemniscates, is true it would appear even if the angle between the optic axes were considerable. I do not know whether this be true experimentally or not.
I forbear from proceeding further in the development of the lemniscates, as that has been already effected with a formula coincident with my own, or nearly so. As to the experimental verification of formulae such as these, they involve so much of calculation that there is considerable difficulty in being able to form a correct judgment on their coincidence; as far as I am aware, Sir J. Herschel and Sir D. Brewster calculate the angles between the optic axes (see Phil. Trans. 1820.) from assuming the law of refraction to be the Snellian law; this is evidently not treating of rays but of waves; and consequently any law of velocity which would be by this means established, would be one relating to the velocity of a wave; and in the same manner, the directions within the crystal can be no other than the normals.
So that M. Biot's law when translated into the language of the undulatory theory, is precisely that which I have enunciated above. Indeed as far as I can collect, Sir J. Herschel appears to state it so in one place. (Ency. Met. 1812.)
Many writers make M. Fresnel's beautiful law of the reciprocals of the squares of the velocities of the rays, to be the same thing as this of Biot and Brewster. The cause appears to lie in the confusion of language which naturally has been fallen into by different writers, the one denoting by ray what the other denotes by wave, and so on.
I have dwelt a long time on this subject, from a wish rather to obtain information on the subject than to communicate it. It is no slight matter of astonishment to me, that a law so elegant as is that which we have been discussing, and one too, the necessity of which (or something analogous) must have been felt at every step which was taken in the development of the Biaxal Theory, has never been mentioned in connexion with this theory, in any writers that I have seen, whilst others apply M. Fresnel's law in its stead without stating their reasons. I do not presume to suppose that it had not been established, my object will be fully attained if I shall have succeeded in exhibiting its importance, and in obtaining for it its proper place in the theory which has been usurped by the no less elegant Theorem of M. Fresnel.
Note. The figure referred to in (18) is constructed by drawing three rectangular axes Pr, Py, P2, and Pri, Py, inclined to these; PN being the line in which y, z,
The figure of (4) in Supplement, is a broken line AB, BC, CD; as an incident, proceeding and emergent ray of common optics.
AB is produced to G
That of (6) is a series of spherical triangles, SR 207" being a large arc, S2 = z T, R2 = 2 O.
TPQ, PR, PO, QS, QT all arcs.
XVI. A Statistical Report of Addenbrooke's Hospital, for the Year 1836. By HENRY J. H. Bond, M.D.
[Read March 18, 1837.]
NUMBER of Beds:
12 in the Fever Wards.
Number of Patients in the Hospital:
Maximum .... 78
Minimum ..... 49
Admissions from January 1st, 1836, to January 1st, 1837:
Male Patients 337
Total ... 597
Previous Residence of the Patients:
226 (38 per cent.) in the Town of Cambridge. 371 (62 per cent.) in the Country, principally in Cambridgeshire and the Isle of Ely.
Description of In-Patients:
180 (53 per cent.) Labourers, chiefly agricultural.
20 - - - - - - - - - Boys of ten years of age or under. 8 . . . . . . . . . Grooms.
7 - - - - - - - - - Tailors.
7 - - - - - - - - - Watermen.
6 ......... Carpenters.
6 ......... Servants.
6 - - - - - - - - - Tramps.
97 . . . . . . . . . Of forty-five different occupations, four being the largest number belonging to any one of them.
100 (38 per cent.) Servants.
90 - - - - - - - - - Women occupied at home with the care of their families, or children above ten years of age, residing likewise at home. 22 - - - - - - - - - Girls ten years of age or under, living at home. - - - - - - - - - Dressmakers. - - - - - - - - - Laundresses. 42 - - - - - - - - - Occupations of, not registered.