NA TURE 



THURSDAY, MAY ii, 1905. 



FLOW OF UNDERGROUND AND RIVER 

 WATERS. 

 Essais d'Hydraidiquc souterraiiie ct fluvialc. By 

 Edmond Maillet, Ingenieur des Fonts et Chaussees. 

 Pp. vi + 2iS. (Paris : Librairie scientifique, A. Her- 

 mann, 1905.) Price II francs. 

 THIS 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 in- 

 dicated a method by which e.\act quantitative dis- 

 charges 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 obtain- 

 ing a law which proved to be in accordance with ex- 

 perience, as indicated in the first half of the theoretical 

 portion of the book. In the second half of this por- 

 tion, the stability, or the nature of the motion of 

 underground waters, under different conditions, is 

 investigated, allowing for the increase in volume pro- 

 duced 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 up- 

 wards 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 water- 

 course 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 im- 

 permeable strata intervene. 



The results of the theoretical investigations com- 

 prised in the first siS chapters are summed up in the 

 NO 1854, VOL. 72] 



three following laws : — (i) A certain number of hydro- 

 logical 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 pro- 

 portion 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 propor- 

 tion as they date further back, though this loss of 

 influence varies inversely with the size of the basin. 

 The immediately preceding spring and summer rain- 

 falls may introduce an element of disturbance if they 

 are heavy and widespread, supposing that the per- 

 meable 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 mini- 

 mum 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 in- 

 fluence of rainy summers on the impermeable strata 

 of the basin ; and in any case they would be pro- 

 gressive, 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 meteor- 

 ological 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 rain- 

 fall which feeds underground waters, prediction of the 

 drying up of the sources of the Somme from the rain- 

 fall, prediction of the discharges of C^rilly spring, a 

 source of the Vanne, prediction of the minima dis- 

 charges of the sources of the Vanne, application to 

 the sources of the Dhuis, prediction of the low-water 

 levels of the Marne at La Chauss^e, drying up of the 

 Laignes, remarks on springs supplying Havre, and 



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