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INDEX TO THE PHILOSOPHICAL TRANSACTIONS FOR THE YEAR 1853. A. Adams (J. C., Esq.). On the Secular Variation of the Moon's Mean Motion, 397. Agathocles, eclipse of, 187. Airy (G. B., Esq., Astron. Roy.). On the Eclipses of Agathocles, Thales and Xerxes, 179. Allman (Dr. James). On the Anatomy and Physiology of Cordylophora, a contribution to our history of Tubularian Zoophytes, 367. Amphibia, on the impregnation of the ovum of, 233. 1. Comparison of the vitality of the ovum and the spermatozoon, 234. 2. Evolution of vitality in the spermatozoon and ovum, 237. 3. Vitality of the ovum, 239. 4. Endosmosis of the egg in reference to its vitality, 242. 5. Quantity of spermatozoa essential to fecundation, 245. 6. Tests of fecundation, 246. 7. Partial or incomplete fecundation, 247. 8. Deficiency of fecundatory influence, ibid. 9. Portion of the yolk most susceptible of fecundation, 251. 10. Excess of fecundatory influence, 253. 11. Deficiency and excess of fecundatory influence compared, 256. 12. The motion of the spermatozoon in relation to its function, 259. 13. Penetration by the spermatozoon in effecting fecundation, 266. 14. Nature of the influence of the spermatozoon, 281. Archetype of the Cephalous Mollusca, 44. Atlanta, anatomy of, 36. B. Bakerian Lecture, 549. Balloon ascents, meteorological observations in, 312. Birds, structure and development of the liver in, 11. Bone, on the structure and development of, 109. Haversian and other canals of bone, 110. Laminæ, 112. Lacunæ, 115. Haversian systems, 117. Ossified cartilage of joints, 118. Ossified lacunal cells, 119. Bone tissue, 120. Development of bone, 123. Growth of bone, 130. C. Calculi, urinary, on the dissolution of, 201. Cephalous Mollusca, anatomy and morphology of, 29. Archetype of, 44. Clarke (J. Lockhart, Esq.). On certain Functions of the Spinal Chord, with further investigations into its Structure, 347. Cœnosarc, definition of the term, 368; description of, in Cordylophora, 371. Common measure, on the quotients resulting from the process of continuous division ordinarily applied to two algebraical functions in order to determine their greatest, 467. Continued fraction, on the complete and simplified residues generated in the process of developing an ordinary rational algebraical fraction under the form of \(a\), 415. ———, improper, on the quotients arising from the expansion of \(\frac{f'x}{fx}\) under the form of, 469. ———, on an unlimited arbitrary algebraical rational integral, 535. Cordylophora, on the anatomy and physiology of, 367. D. Decomposition of rubian, products of, 67. De Morgan (Campbell, Esq.) and John Tomes, Esq. Observations on the Structure and Development of Bone, 109. Development of bone, 123. E. Eclipses of Agathocles, Thales, and Xerxes, on the, 179. Section I. On the elements of the lunar table, 179. Section II. Method of computation adopted by the author, 185. Section III. Eclipse of Agathocles, 187. Section IV. Eclipse of Thales as recorded by Herodotus, 191. Eclipse recorded by the Persian historians, 197. Eclipse of Xerxes, 198. Ectoderm, definition of the term, 368; description of, in Cordylophora, ibid. Embryology of Cordylophora, 373. Endoderm, definition of, 368; description of, in Cordylophora, 370. Equations having equal roots, a theorem concerning, 467. ———, algebraical, on the theory of intercalations of the real roots of two, 486. Equation, on a new method of finding superior and inferior limits to the real roots of an, 490. Development of the method, 496. F. Fecundation, tests of, in the Amphibia, 246; partial or incomplete, 251. Deficiency and excess of fecundatory influence, 247, 253, 256. Firoloides, anatomy of, 30. Fishes, structure and development of the liver in, 3, 6. Fluids in motion, thermal effects of, 357. H. Heat, on the transmission of, through organic substances, 217. Heteropoda, anatomy and morphology of, 30. Hobarton, on the influence of the moon on the magnetic declination at, 557. Huxley (Thomas Henry, Esq.). On the Morphology of the Cephalous Mollusca, as illustrated by the Anatomy of certain Heteropoda and Pteropoda collected during the Voyage of Her Majesty's Ship Rattlesnake in 1846-50, 29. Hygrometric condition of the air, variation of, as observed in balloon ascents, 336. I. Impregnation of the ovum in the Amphibia, on the, 233. Intercalations, on the theory of, 480; applied to algebraical equations, 486; as applicable to two functions of the same degree, 510. J. Jones (C. Handfield, M.D.). Further Inquiries as to the Structure, Development, and Function of the Liver, I. Jones (Henry Bence, M.D.). On the Dissolution of Urinary Calculi in dilute Saline Fluids, at the Temperature of the Body, by the aid of Electricity, 201. Joule (J. P., Esq.) and Thomson (Wm., M.A.). On the Thermal Effects of Fluids in Motion, 357. L. Light, on the change of refrangibility of, 385; degraded, degradation of, 387; fluorescence of, ibid. Liver, further inquiries as to its structure, development, and function, 1. Structure in Fishes, 3. Development in Fishes, 6. Structure in Reptiles, 8. Development in Reptiles, 10. Structure and development in Birds, 11; in Mammalia, 14. Function of the parenchyma, 19. M. Magnetic declination, on the influence of the moon on the, at Toronto, St. Helena, and Hobarton, 549. Magnetic disturbances, on periodic laws in, 165. Mammalia, structure and development of the liver in, 14. Meteorological observations in four balloon ascents, account of, 312. Molecular influences, on. Part I. Transmission of heat through organic structures, 217. Construction of the instrument used in the investigation, 218. Table of substances submitted to experiment, and results, 223. Mollusca, the Cephalous, anatomy of, 29. Anatomy of Firolöides, 30; of Atalanta, 36. Anatomy of Pteropoda, 39. The archetype of the Cephalous Mollusca, 44. Moon's mean motion, on the secular variation of the, 397. Muscular system in Cordylophora and other Tubulariadae, 372. N. Nerves, spinal, on the posterior and anterior roots of, 348, 350. Nesodon, description of species of, with remarks on the primary group (Toxodontia) to which that genus is referable, 291; generic characters of, 299. INDEX. *Nesodon imbricatus*, 301. —*magnus*, 308. —*ovinus*, 291. —*Sulivani*, 304. NEWPORT (GEORGE, Esq.). On the Impregnation of the Ovum in the Amphibia (Second Series, revised), and on the Direct Agency of the Spermatozoon, 233. O. Observations, meteorological, made in four balloon ascents, 312. Organic substances, of the transmission of heat through, 217. Ova and ovigerous capsules in Cordylophora, 373. Ovum, impregnation in the Amphibia, 233. OWEN (Professor RICHARD). Description of some Species of the extinct Genus *Nesodon*, with Remarks on the primary Group (*Toxodontia*) of Hoofed Quadrupeds to which that Genus is referable, 291. Oxalate of lime calculi, on the solution of, 205. P. Parenchyma of the liver, function of, 19. Periodical and non-periodic variations of the temperature at Toronto, 141. Periodical laws in the larger magnetic disturbances, 165. Phosphatic calculi, on the solution of, 211. Platinocyanides, optical properties of, 395. Polypary, definition of the term, 368; description of, in Cordylophora, 369. Polype, definition of the term, 368. Pteropoda, anatomy of, 39. R. Refrangibility of light, on the change of, 385. Method of observing by absorbing media, *ibid.*; by means of a prism, 391. Examples of these methods of observation, 393. Comparison of their relative advantages, 394. Platinocyanides, 395. Reptiles, structure and development of the liver in, 8, 10. Rubian, and its products of decomposition, Part II., 67. Action of alkalies and alkaline earths on, 67. Rubiadine, 72. Action of ferments on rubian, 74. Rubiafine, 80. Rubiacine and rubiacic acid, 81. Rubiagine, 87. Rubiadipine, 89. S. SABINE (Colonel EDWARD, R.A., V.P. and Treas. R.S.). On the Periodic and Non-periodic Variations of the Temperature at Toronto in Canada, from 1841 to 1852 inclusive, 141. —On the Influence of the Moon on the Magnetic Declination at Toronto, St. Helena, and Hobarton, 549. SCHUNCK (EDWARD, Esq.). On Rubian and its Products of Decomposition, Part II., 67. Spermatozoa, capsules containing, in Cordylophora, 375. Spermatozoon, on the agency of, in impregnation, in the Amphibia, 233; vitality of, 234, 235; quantity of, necessary for fecundation, 245; motion of, 259; and penetration of, 266. Nature of its influence, 281. Spinal chord, on certain functions of, with investigations into its structure, 347. Of the posterior roots of the spinal nerves, 348. Of the anterior roots, 350. On the means by which impressions received by the chord are transmitted to the brain, 352. St. Helena, on the influence of the moon on the magnetic declination at, 555. Stokes (Professor G. G., Esq.). On the Change of Refrangibility of Light, No. II., 385. Structure and development of bone, 109. Sturm's theorem, on formulae relating to, 457. Further formulae connected with, 480. Sylvester (J. J., Esq.). On a Theory of the Syzygetic relations of two rational functions, comprising an application of the Theory of Sturm's Functions, and that of the greatest Algebraical Common Measure, 407. Syzygetic relations of two rational integral functions, on a theory of the, comprising an application to the theory of Sturm's Functions, and that of the greatest algebraical Common Measure, 407. Introduction, ibid. Section I. On the complete and simplified residues generated in the process of developing under the form of a continued fraction, an ordinary rational algebraical fraction, 415. Section II. On the general solution in terms of the roots of any two given algebraical functions of $x$ of the syzygetic equation, which connects them with a third function, whose degree in $x$ is given, but whose form is to be determined, 433. Section III. On the application of the theorems in the preceding section to the expression in terms of the roots of any primitive function of Sturm's auxiliary functions, and the other functions which connect these with the primitive function and its first differential derivative, 456. Supplement to Section III. On the quotients resulting from the process of continuous division ordinarily applied to two algebraical functions in order to determine the greatest common measure, 467. Section IV. On some further formulae connected with Sturm's theorem, and on the theory of intercalations whereof that theorem may be treated as a corollary, 480. Supplement to Section IV. Development of the method of assigning a superior and inferior limit to the roots of any algebraical equation, 496. Section V. On the theory of intercalations as applicable to two functions of the same degree, and on the formal properties of the Bezoutian with reference to the method of invariants, 510. General and concluding Supplement, 535. Glossary of new or unusual terms, &c., 543. Table of Contents, 548. T. Temperature, periodic and non-periodic variations of, at Toronto, 141. Epochs of the maxima and minima at Toronto compared with those at several places on the continent of Europe, 148. Temperature, variation of, with height, as observed in balloon ascents, 332. Thales, eclipse of, 191. Thermal effects of fluids in motion, 357. Thomson (Wm., M.A.) and Joule (J. P., Esq.). On the Thermal Effects of Fluids in Motion, 357. Tomes (John, Esq.) and Campbell De Morgan, Esq. Observations on the Structure and Development of Bone, 109. Toronto, on the influence of the moon on the magnetic declination at, 550. INDEX. *Tubularian zoophytes*, on the anatomy of, 367. *Tyndall (John, Esq.).* On Molecular Influences. Part I. Transmission of Heat through Organic Structures, 217. U. *Uric acid calculi,* on the solution of, 202. *Urinary calculi,* on the dissolution of, in dilute saline fluids, at the temperature of the body, by the aid of electricity, 201. Section I. On the solution of uric acid calculi, *ibid.* Section II. On the solution of oxalate of lime calculi, 205. Section III. On the solution of phosphatic calculi and of carbonate of lime, 211. Appendix to the paper, 214. V. *Variations, periodic and non-periodic, of the temperature at Toronto,* 141. 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