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THIS HIS treatise, which was presented in the first instance to the Academy of Sciences of Paris in 1903, is divided into two parts, the first theoretical and the second practical, to which a paper has been appended, mainly of a practical nature, on the curves of the discharge of springs and the abatement of river floods. The book is addressed to mathematicians, physicists, geologists, geographers, meteorologists, engineers, and all who are interested in the motion and the distribution of rainfall, both on the surface of the land and underground; and its object is to investigate theoretically and practically the variations in the discharge of springs, and the low-water flow of rivers, in order to be able to foretell the amount of this minimum flow, precisely as the height of the floods of rivers is predicted, as already effected in certain cases by French hydraulicians, such as Dupuit, Belgrand, Lemoine, de Preaudeau and others, and also recently by the author with respect to two of the sources of the River Vanne. M. Maillet believes that he is the first to have indicated a method by which exact quantitative discharges can be systematically predicted, such as a graphic curve, based upon Dausse's law concerning the permeable strata of the Seine basin, enabled him to determine the yearly minima discharges of two sources of the Vanne several months beforehand. Later on, by means of the hypothesis of a particular form of the free water-surface, he succeeded in obtaining a law which proved to be in accordance with experience, as indicated in the first half of the theoretical portion of the book. In the second half of this portion, the stability, or the nature of the motion of underground waters, under different conditions, is investigated, allowing for the increase in volume produced by rain; and assuming a simple form for the impermeable bed over which the water flows, it is shown that where the line of the bed is convex upwards the maximum height of the flood will be rapidly attained, and where concave, the flood will rise slowly, and that the influence of a part of the stream on the maximum will be greater in proportion to the fall of the bed. The connection, also, between the low-water levels, or minima discharges, at any point of a watercourse or spring and the rainfall, is considered in as general a form as possible; and it is proved that, in practice, the lowest discharge may often be regarded as a function of the combined rainfall of the preceding hot and cold seasons, and experiences very slight variations from year to year, especially in large river basins, unless the warm season is very rainy and impermeable strata intervene. The results of the theoretical investigations comprised in the first six chapters are summed up in the three following laws :-(1) A certain number of hydrological facts, corresponding to the low stages, or minima discharges, of springs or watercourses, in many cases depend almost exclusively on the total rainfall of several preceding warm and cold seasons. It is only in the case of restricted watersheds that the rainfall of the last one or two cold seasons exercises a predominating influence, the number of preceding years on which the results depend increasing in proportion to the size of the basin. The preceding warm seasons have less influence than the following cold seasons; and they both have less influence in proportion as they date further back, though this loss of influence varies inversely with the size of the basin. The immediately preceding spring and summer rainfalls may introduce an element of disturbance if they are heavy and widespread, supposing that the permeable strata predominate in the basin; but where the basin is almost wholly permeable, the rainfall of the preceding warm seasons may often be neglected. (2) The lowest level at a given point of a watercourse in any year is approximately a function of the minimum level of the preceding year, and of the amount of rain during the preceding cold season, and some preceding months of the warm season if very wet or very dry, provided the proportion of impermeable strata in the basin is small. In the case of many watercourses, the minimum yearly level varies little from year to year; and a succession of several years, or several cold seasons, more rainy or more dry than the average, is needed to produce modifications, which, moreover, are slow and progressive with the lapse of time. (3) In the Seine basin, the low-water levels at given points of many of the watercourses draining almost wholly permeable strata, differ little from their mean secular height. These variations cannot be abrupt, except under the immediate influence of rainy summers on the impermeable strata of the basin; and in any case they would be progressive, as a result of a gradual increase in the mean rainfall for a certain number of years. Subject to these reservations, an appreciable variation in the low-water level must be due to other than meteorological causes. The second, practical, part of the book occupies little more than a third of the space devoted to theoretical considerations, though divided into ten chapters, which are, consequently, very short for the most part. It contains some practical applications of the views and theories developed in the first part, to the prediction of various hydrological phenomena, and also some experimental verifications; and the works of Belgrand, and the observations and publications of the hydrometric service of the Seine basin, form the basis of this inquiry. After a very brief introduction, the chapters deal successively with proportion of rainfall which feeds underground waters, prediction of the drying up of the sources of the Somme from the rainfall, prediction of the discharges of Cérilly spring, a source of the Vanne, prediction of the minima discharges of the sources of the Vanne, application to the sources of the Dhuis, prediction of the low-water levels of the Marne at La Chaussée, drying up of the Laignes, remarks on springs supplying Havre, and |