been no penalty, no compensation has been given and very little litigation has resulted, probably owing to the difficulty of proving damages or the principal riparian owners being interested in the diversion. There are a few instances on record of the compensation water provided in an act being purchased by the diverting authority. In general, the custom works well, but the growing interests of riparian owners or their growing capability of establishing them makes water works undertakings expensive in the United Kingdom which introduces an incentive towards the reduction of the consumption of water.

WATERSHED YIELDS AND REQUIRED STORAGE

The object of the present writing is to give a short concise statement of a large subject. A book might be written, but it is not possible to boil down an adequate statement to the reasonable limits of this article.

Instead of attempting an obviously impossible task, an outline is presented to which the reader can add by reading certain articles and books, listed at the end of this paper, in which more complete information may be found. Some of the earlier ones are mainly interesting from an historical standpoint, but reading them is helpful and necessary because much later work takes for granted a knowledge of what went before.

In reading the papers in the Transactions of the American Society of Civil Engineers the discussions following the papers should not be overlooked for they often contain matters quite as important as those in the papers themselves.

The chapter in the American Civil Engineers Pocket Book will be the most useful starting point in making actual computations and estimates. It does not give reasons but states methods, and gives tables of data believed to be the best now available.

A knowledge of modern scientific statistical method is necessary to an adequate understanding of this subject. The study of one or more of the excellent text books mentioned at the end of this article, or their equivalent, will be helpful.

It may be added that this is a subject which is rapidly developing with increasing data and better methods for their analysis.

Basic conceptions

If a tin roof represents a catchment area, the runoff would occur at times of rainfall, and would be always almost in proportion to it. The time elapsed for water to flow from the most remote part of the roof to the water spout is small and practically inappreciable. After the rain stops the runoff stops and the down-spout goes dry. This is the simplest conception of a catchment area.

Consider now what happens when a pile of sand is put upon the roof. The rain that hits the sand is absorbed by it, and held, at least until the sand is saturated. Some of the water so held is lost by evaporation; another part seeps to the bottom of the sand, and slowly flows to the down-spout. This seepage will continue for a certain length of time after the rain has stopped. The flow is to some extent equalized and prolonged by the pile of sand. The element of ground storage is thus introduced.

If now the pile of sand is made larger and deeper, more of the rainfall will be held back by it, and the flow between rains will be larger and more continuous. A point will be reached, with some quantity of sand, in a given climate, where the flow will be continuous at all times and the stream will cease to go dry.

Carrying the matter further, if we suppose the roof to be covered with a deep layer of sand, say many feet deep, there may be complete equalization of flow. The flow will of course increase in wet seasons and decrease in dry ones. But, if the sand is deep enough and retentive enough it will absorb all of the rain at the time of rainfall and give it up gradually, at a more or less steady rate.

These examples may seem small in comparison with actual catchment areas, but they do give an accurate idea of what takes place in stream flow.

The naked tin roof represents a catchment area that is all bare rock, clay, or other impervious soil. Such catchment areas are said to be flashy; torrents come from them when it rains and the streams go dry if there is more than a short interval between rains. Soil and vegetation, including forests, always present in some degree, are represented by the pile of sand that somewhat reduces the fluctuations.

Catchment areas that are covered with deep deposits of sand and gravel have more ground storage. The flows of streams from them. are not flashy but are well maintained. There are great deposits

of glacial material in the North and of older sand materials in the South and West. Sandstone acts in this respect as fine grained sand.

If there are limestone formations with caverns or underground passages, water may flow off in directions not indicated by surface drainage. These may be compared to a leaky roof. There is no rule that can be applied to such cases. Actual conditions must be ascertained before safe estimates can be made.

The characteristics of the flows of the stream and the possibilities of storage depend upon many factors. The most important are (a) Seasonal distribution and frequency and regularity of rainfall; (b) Evaporation which carries off a large and by no means constant proportion of the rainfall; (c) Ground water storage which retards the flow of the remainder to a greater or less degree, according to its amount; (d) In the north and in the high mountains everywhere, much of the precipitation is in the form of snow, and there will be little runoff until the snow and ice melt in the spring.

These are only a few of the innumerable causes that result in irregularity in runoff. The whole matter is so complicated that it is best treated as a matter of statistics and probabilities.

A great deal of ingenuity has been spent in studying relations between rainfall and runoff. This has no doubt been necessary in early days in the absence of runoff data, but elaborate studies of this kind are not to be encouraged and seldom yield results of commensurate value. In nearly all cases the direct study of runoff data by statistical and probability methods will lead to more useful results. Rainfall data will be helpful as furnishing a general background to the study rather than as a direct basis of calculation.

Method of estimate

If the stream for which estimates are to be made has been gauged for a term of years the records of the stream itself are to be analyzed by methods described in the literature that is referred to, and the results are to be studied by statistical methods; and the amount of storage or runoff estimated by the use of these methods. If no such record is available, estimates based on known performances of other streams must serve as the starting points.

The variations in stream flow are incessant, and any particular cycle is never repeated. If there is an absolutely complete record

of a stream for 20 years it is certain that the record for the next 20 years will not be like it. The problem is to visualize with some degree of accuracy the characteristics of a thousand year record of the stream of which only a 20-year segment is at hand; and to lay out works that will reasonably meet requirements based on the thousand year conception. In doing this the record of all other streams in any degree comparable to the one under discussion may well be analyzed and made to contribute to the general conception of stream flow.

The mass curve is used to ascertain the storage required for an assumed rate of draft applied to the flow record of a particular stream. It gives the absolute facts with reference to that stream for that period. When numerous mass curve records are calculated the results may be analyzed by statistical methods, and certain normal curves or factors found to be used as a basis for estimates. Care must always be taken that data so derived are not applied in cases where climatic conditions are different.

It has been customary, in the past, to estimate runoff and storage, for streams where long records are available, on the basis of the dryest of record; or in cases where only meager records are available, by means of comparisons per square mile of watershed area with similar streams for which long records are available, making due allowance for factors of rainfall and evaporation.

Studies in the last fifteen years have developed more advantageous methods. The following rules give an idea of the way in which they are carried on.

1. Start with a record or estimate of the mean flow of the stream. That is the best starting point for all calculations of flow and storage. Do not make comparisons based on so much per square mile.

2. Estimate the water to be made available as a percentage of the mean flow.

3. State storage, actual or proposed, in terms of the mean annual flow.

4. The mean, in all things, is to be first ascertained, and the probable variations from it are to be then considered.

Mean flows

Mean flows are usually stated as inches of runoff per annum. This form of statement has the advantage of making them directly.

comparable to the rainfall figures with which they will naturally be compared. To obtain from this the mean flow in United States gallons, multiply the area in square miles by the inches of runoff and the product by 47,851 to obtain the mean flow in gallons per day, and by 17,380,000 to obtain the mean flow in gallons per annum.

Evaporation from the surface of the water in a reservoir must be allowed for, except that when the records represent conditions after reservoir construction no correction is necessary. The recommended procedure is as follows:

First. When the mean annual rainfall is equal to or in excess of the mean annual evaporation from water surface.

Two corrections are necessary:

(a) A reduction in the estimated mean flow equal to the excess