I may add that the name of the reviewer is kept a profound secret, and yet is perfectly well-known, as everybody who reads the article finds it out when he reaches those parts which describe Dr. Carpenter’s important physiological researches and discoveries. MATHEMATICAL FICTIONS. (BRITISH ASSOCIATION, 1871.) The President’s inaugural address, which was going through the press in London while being spoken in Edinburgh, has already been subject to an unusual amount of sharp criticism. For my own part I cannot help regarding it as one of the least satisfactory of all the inaugural addresses that have yet been delivered at these annual meetings. They have been of two types, the historical and the controversial; the former prevailing. In the historical addresses the President has usually made a comprehensive and instructive survey of the progress of the whole range of science during the past year, and has dwelt more particularly on some branch which from its own intrinsic merits has claimed special attention, or which his own special attainments have enabled him to treat with the greatest ability and authority. A few Presidents have, like Dr. Huxley last year, taken up a particular subject only, and have discussed it more thoroughly than they could have done had they also attempted a general historical survey. Every President until 1871 has scrupulously kept in view his judicial position, and the fact that he is addressing, not merely a few learned men, but the whole of England, if not the whole civilized world. They have therefore clearly distinguished between the established and the debatable conclusions of science, between ascertained facts and mere hypotheses, have kept this distinction so plainly before their auditors that even the most uninitiated could scarcely confound the one with the other. In Sir William Thomson’s address this desirable rule is recklessly violated. He tells his unsophisticated audience that Joule was able “to estimate the average velocity of the ultimate molecules or atoms” of gases, and thus determined the atomic velocity of hydrogen “at 6225 feet per second at temperature 60 degs. Fahr., and 6055 feet at the freezing point;” that “Clausius took fully into account the impacts of molecules upon one another, and the kinetic energy of _relative_ motion of the matter constituting an individual atom;” and that “he investigated the relation between their diameters, the number in a given space, and the mean length of path from impact to impact, and so gave the foundation for estimates of the absolute dimensions of atoms.” Also that “Loschmidt, in Vienna, had shown, and not much later Stoney, independently, in England, showed how to reduce from Clausius and Maxwell’s kinetic theory of gases a superior limit to the number of atoms in a given measurable space.”