in rising, encounter obstacles which tend to pond the water and hold back the flood so that the discharge will not increase in relation to height of water at so rapid a rate as at a medium stage. This condition of affairs has, however, not been actually encountered.

The construction of this curve is similar in all respects to that of the rating line for the meters, noted on a previous page. As in that case, the analytic method of obtaining the curve can be employed to advantage in connection with the plot of discharge, but for most practical purposes the graphic methodif only one is used-is preferable, as its accuracy is far within the probable error of the observations. Thus, for rapid work, as in preparing estimates of discharges, the purposes of this survey were best accomplished by the use of the sketched rating line.

The question now arises, for how long a period will this rating curve be true, or its values fall within the range of allowable error? Every river is constantly modifying its channel to some extent, alternately scouring and filling its bed to suit the everchanging conditions of velocity and volume. The station is, in the first instance, selected at a point where this action will be at a minimum, but usually there is an appreciable change, especially during and after floods or protracted periods of low

water.

The rating curve is founded, however, on measurements made, as far as possible, under all the varying conditions of water depth, and is in itself of the nature of an average or compromise between all these conditions. Thus it is evident that for any one height of water at a particular stage, the discharge as given by the rating table may not be as accurate as the result of a direct measurement made on that particular day, but the value given by the rating table should be the average value of the discharge (for that particular height), whether the river be rising, falling, or stationary. In other words, it is assumed that for a given height of water the discharge varies within certain limits, depending upon circumstances, such as amount of silt carried, condition of channel above and below, and other modifying features, and that the rating tables can not be

brought to the refinement of discriminating between all these conditions, but must represent an approximation at their mean. It is interesting to observe, however, that there is, taking a season through, a general return to former conditions, even in certain quite sandy channels, where the change from day to day is noticeable, the deep portion shifting from side to side, while the relation of gauge height to discharge takes a wider and more irregular range, the plotted points being scattered on each side of the average line. Thus it has been found practicable to rate certain stations and obtain mean discharges whose probable error is within an allowable limit at places where at first sight it would seem hopeless.

The above remarks apply particularly to places where the material of the bed is continually rearranged and replaced; but if the action of the stream is to build up the bed as a whole and then to wash this out bodily, height of water alone can have no meaning-the bed of the stream itself is rising or falling. It has been proposed to meet such exigencies by neglecting the arbitrary height of water surface and considering the hydraulic mean radius in its place; that is to say, instead of having the river height read daily at the shore, to have the observer make soundings at definite points of the cross-section.

Rating tables are usually made as soon as possible after six or eight observations of discharge have been obtained, if these are well distributed along the path of the curve, and subsequent points are plotted when obtained. The curve is modified, if necessary, to take account of these new data, and corrections are made in the rating table. The experience of the last year has shown, however, that after six or eight well distributed gaugings have been made subsequent measurements during that season are not in general of sufficient value to justify the expense of obtaining them. In other words, the corrections in the rating table are not worth what they cost.

This Survey has not been in operation for a sufficient time to be able to determine whether these rating tables can be used a second or third year without material change. It is probable, however, that they can be used to give approximate values in case they can not be checked by observations in later years.

RAINFALL.

At the beginning of the operations of the Hydrographic Survey the necessity of rainfall measurements was appreciated, and an examination was made of the methods in use by the Signal Service of the Army, which had that subject in charge. It appeared at that time that the Signal Office was not in condition to extend its observations to the points at which measurements were most needed for the Hydrographic Survey, and therefore the attempt was made to supply this deficiency by establishing a system of volunteer observers, in general details fashioned after that already in operation under the direction of the Chief Signal Officer. Standard rain gauges were placed in the hands of observers, wherever these could be found, in the basins in which the hydrographic work was at first begun. In the Rio Grande basin, for example, about forty rain gauges were thus located at accessible points; nearly the same number in the Gila basin, principally around the headwaters of the river and its tributaries; and a few in the basin of the Arkansas in Colorado and that of the Truckee River in Nevada.

The principal difficulty is to secure measurements at points. where they are most needed. As is well known, the greater portion of the population is in the lower valleys, and at these points observers of rainfall can be found with comparative ease, but it is from the high mountains that the principal water supply comes, and there the measurements should be made. Unfortunately it is almost if not quite impossible to obtain volunteer observers in those places, and it is evidently impracticable to hire men to reside at these high altitudes for the sole object of noting precipitation. Thus it happens that all the data concerning rainfall and snowfall relate mainly to the low valleys where the precipitation is least, and estimates based upon these figures are in general below the truth.

The results obtained from the measurements of precipitation carried on by this Survey were transmitted from time to time. to the Chief Signal Officer and by him published in the Monthly Weather Review in connection with the results from his own observers. The relation which exists between the rainfall and