4. =Discharge Observations.=--For a large stream it is necessary to observe the discharges by taking cross-sections and measuring the velocity. If there is a sufficient range of water-levels, it will be possible to make actual observations of a sufficient number of discharges. If soundings cannot, owing to the depth or velocity, be taken at high water, they must be inferred from those previously taken, but this does not allow for changes in the channel, which are sometimes considerable and rapid. If there is not a sufficient range of water-level, the discharges for some water-levels must be calculated from those at other water-levels. In this case observations of the surface slope will be required, and the discharge site should be so selected that no abrupt changes in the channel will come within the length over which the observations are to extend. This length should be such that the fall in the water surface will be great enough to admit of accurate observation. If the cross-section of the stream is nearly uniform throughout the whole of this length, or if it varies in a regular manner, being greatest at one end of the length and least at the other end. the differences in the areas of the two end sections being not more than 10 or 12 per cent., then the velocity and cross-section of the stream can be observed in the usual manner at the centre of the length; but otherwise they should be observed at intervals over the whole length, or at least in two places, one where the section is small and one where it is great, and the mean taken. Or the velocity can be observed at only one cross-section and calculated for the others by simple proportion and the mean taken. The coefficient C can then be found from the formula C = V/√(RS). To find the discharge for a higher or lower water-level, the change in the value of C corresponding to the change in R can be estimated by looking out the values of C in tables, and the discharge calculated by using the new values of C and R and the new sectional area, S remaining unaltered. But if the channel is such that, with the new water-level, a change in S is likely to have occurred, this change must be allowed for. Any such change will be due to the changed relative effects of irregularities, either in the length over which the observations extended or downstream of that length. The effect of irregularities in the bed is greatest at low water. The effect of lateral narrowings is greatest at high water. Since a change of 10 per cent. in S causes a change of only 5 per cent. in V, it will usually suffice to draw on the longitudinal section the actual water surface observed and to sketch the probable surface for the new water-level. If the whole channel is fairly regular for a long distance downstream of the discharge site, no slope observations need be made nor need several sections be taken in order to find V. The changed value of C should, however, be estimated in the manner above indicated.