In preparing the rating curves special consideration is given to the class of stations represented. (See below.) The discharge measurements for all classes of stations, when plotted with gage heights in feet as ordinates and discharges in second-feet as abscissas, define rating curves more or less parabolic in form. For many stations curves of area in square feet and mean velocity in feet per second are also constructed to the same scale of ordinates as the discharge curve. These curves are used mainly to extend the discharge curves beyond the limits of the plotted discharge measurements and give a check to the form of the discharge curve and to determine and eliminate erroneous measurements.

For every rating table the following assumptions are made for the period of application of the table: (a) That the discharge is a function of and increases gradually with the stage; (b) that the discharge is the same whenever the stream is at a given stage, and hence such changes in conditions of flow as may have occurred during the period of application are either compensating or negligible, except that the table is not applicable for periods during which ice, log jams or other obstructions existed in the channel; (c) that the increased and decreased discharge due to change of slope on rising. and falling stages is either negligible or compensating.

The gaging stations in Minnesota may be divided into two general classes:

The stations of class 1-that is, the stations located at points 'where the conditions that control the flow at the gage are comparatively permanent-represent the most favorable conditions for accurate determination of stream flow and are also the most economical to maintain. The bed of the stream is usually composed of rock and is not subject to the deposit of sediment and loose. material. This class includes also many stations located in a pool below which is a permanent rocky riffle that controls the flow like a weir. Provided the control is sufficiently high and close to the gage to prevent cut and fill at the gaging point from materially affecting the slope of the water surface, the gage height will for all practical purposes be a true index of the discharge. Discharge measurements made at such stations usually plot within a few per cent of the mean discharge curve, and the rating table developed. from that curve represents a very high degree of accuracy. (See Plate III.)

The stations of class 2-those located where conditions of flow change only during periods of extreme high water-include many of those maintained in Minnesota. If sufficient measurements could be made at stations of this class, results would be obtained nearly equaling those of class 1, but owing to the limited funds at the dis

posal of the Survey this is manifestly impossible, nor is it necessary for the uses to which discharge data are applied. The critical points are as a rule at relatively high or low stages. The percentage error, however, is greater at low stages. No absolute rule can be laid down for stations of this class. Each rating curve must be constructed mainly from the measurements of the current year, the engineer being guided largely by the past history of the station and the following general law: If all measurements ever made at a station of this class are plotted on cross-section paper, they will define a mean curve which may be called a standard curve. It has been found in practice that if after a change caused by high stage a relatively constant condition of flow occurs at medium and low stages, all measurements made after the change will plot on a smooth curve which is practically parallel to the standard curve with respect to their ordinates or gage heights. This law of the parallelism of ratings is the fundamental basis of all rating tables and estimates at stations with semipermanent and shifting channels. It is not absolutely correct but, with few exceptions, it answers all the practical requirements of estimates made at low and medium stages after a change at a high stage. This law appears to hold equally true. whether the change occurs at the measuring section or at some controlling point below. The change is, of course, fundamentally due to change in the channel caused by cut or fill, or both, at and near the measuring section. For all except small streams the changes in section usually occur at the bottom.

Slight changes of an oscillating character at low or medium. stages are usually averaged by a mean curve drawn among them parallel to the standard curve, and if the individual measurements do not vary more than 5 per cent from the rating curve the results are considered good for stations of this class.

The computations have, as a rule, been carried to three significant figures. Computation machines, Crelle's tables, and the 20inch slide rule have been generally used. All computations are carefully checked.

After the computations have been completed they are entered in tables and carefully studied and intercompared to eliminate or account for all gross errors so far as possible. Missing periods are filled in, so far as feasible, by means of comparison with adjacent streams. The attempt is made to complete years or periods of discharge, thus eliminating fragmentary and disjointed records. Full notes accompanying such estimates follow the daily and monthly discharge tables.

ACCURACY AND RELIABILITY OF RECORDS.

Practically all discharge measurements made under fair conditions are well within 5 per cent of the true discharge at the time of observation. Inasmuch as the errors of meter measurements are largely compensating, the mean rating curve, when well developed, is more accurate than the individual measurements.

The accuracy of stream-flow data depends primarily on the natural conditions at the gaging station and on the methods and care with which the data are collected. Errors of the first group depend on the degree of permanency of channel and of permanency of the relation between discharge and stage.

Errors of the second class are due, first, to errors in observation of stage; second, to errors in measurements of flow, and, third, to errors due to misinterpretation of stage and flow data.

With relatively few exceptions the observers perform their work honestly. Care is taken, however, to watch them closely and to inquire into any discrepancies. In general, observations are taken twice a day at 8 and 6, and the mean of these readings taken as the mean for the day. Where the flow is controlled to an appreciable extent, two or three additional readings are taken at such times as tend to give the true mean for the day. However, it is not feasible to do this in all instances. With a few exceptions, however, it is believed that the readings give a fair average for the day.

In order to give engineers and others information regarding the probable accuracy of the computed results, footnotes are added to the daily discharge tables, stating the probable accuracy of the rating tables used, and an accuracy column is inserted in the monthly discharge table. For the rating tables "well defined” indicates, in general, that the rating is probably accurate within 5 per cent; "fairly well defined," within 10 per cent; "poorly defined" or "approximate" within 15 to 25 per cent. These notes are very general and are based on the plotting of the individual. measurements with reference to the mean rating curve.

The accuracy column in the monthly discharge table does not apply to the maximum or minimum nor to any individual day, but to the monthly mean. It is based on the accuracy of the rating, the probable reliability of the observer, and knowledge of local conditions. In this column A indicates that the mean monthly flow is probably accurate within 5 per cent; B, within 10 per cent; C, within 15 per cent; D, within 25 per cent. Special conditions are covered by footnotes.

Even though the monthly means for any station may represent with a high degree of accuracy the quantity of water flowing past

the gage, the figures showing discharge per square mile and depth of run-off in inches may be subject to gross errors which result from including in the measured drainage area large noncontributing districts and they should therefore be considered as only approximate.

The table of monthly discharge is so arranged as to give only a general idea of the flow at the station and should not be used for other than preliminary estimates. The determinations of daily discharge allow more detailed studies of the variation in flow by which the period of deficiency may be determined.

RIVER SURVEYS.

The river surveys were made to obtain the information necessary to determine the water surface of the rivers at medium stage and to map the shore lines, adjacent topography and the more important artificial features, leaving detailed surveys to be made by those interested in the various projects. This information has been plotted on the published sheets to a scale of 1,000 feet or 2,000 feet to the inch.

The surveys were made with transit and stadia and included determinations of levels, a magnetic traverse, and sketches of shore topography. A surveying party consisted of a topographer, transitman, two rodmen and teamster. In the later work canoes were used. The topographer, who was chief of party, kept the transit notes and made the topographic sketches, using a small field drawing board and plotting the traverse shots as made. These sketches were invaluable when the final map was made in the office and were very much more satisfactory than the fragmentary sketches made in the transit notes, as they were plotted to scale, usually 1 inch to 1,000 feet. The transitman ran the transit and directed the rodmen in giving proper side and main shots. The transit was used to run not only the traverse but also the levels, the transit being used as a level. Main traverse elevations were never obtained by vertical angles except in surveying the streams. in the northeastern part of the state, where the fall is very great and many of the streams flow through gorges.

In order to illustrate the method of procedure let it be assumed that the transitman has just reached a station. (As azimuth is carried by the magnetic needle it is only necessary to occupy every other station.)

The transitman, having set up his instrument, backsights on the preceding station (which was the forward station at the last set up), and, by reading stadia distances and magnetic bearing, locates his present position in the traverse. He then levels the telescope and reads the intersection of the middle wire on the rear