. Carnegie Institution of Washington publication. ii4 DYNAMIC METEOROLOGY AND HYDROGRAPHY. This outflow has a simple additive property. Let the considered area be divided by a line into two parts (fig. 93). The transport through the dividing line will then appear in the expression for the outflow out of each part. But in the sum of these two outflows this transport will drop out, as it represents the transport out of the one and into the other area. The sum of the outflows out of the two parts will therefore be equal to the outflow out of the total area. As each part can be divided again, and
. Carnegie Institution of Washington publication. ii4 DYNAMIC METEOROLOGY AND HYDROGRAPHY. This outflow has a simple additive property. Let the considered area be divided by a line into two parts (fig. 93). The transport through the dividing line will then appear in the expression for the outflow out of each part. But in the sum of these two outflows this transport will drop out, as it represents the transport out of the one and into the other area. The sum of the outflows out of the two parts will therefore be equal to the outflow out of the total area. As each part can be divided again, and so on, we get the general result that the outflow out of all the parts into which an area can be divided will be equal to the outflow out of the total area. We sym- bolize this result by the equation (b) fA„ds = VJAnds the first member being extended to the contour of the total area, and the integrals in the second member being extended to the contours of all the parts into which the total area has been divided. The division may be continued indefinitely. The areas of which the contours appear in the second member of equation (b) may therefore be considered as elemen- tary areas da. As they can have any form let them be limited by the two elements ds and ds' of two vector-lines, and by the two elements dn and dn' which are normal to these lines (fig. 94). The outflow will be the difference between the transport^ 'dn' and A dn through the latter elements, (c) A'dri - Adn Here A' will vary as we proceed along a vector-line s, and the same will be the case with the normal distance dn' between the two vector-lines. We may then consider these quantities as functions of 5 and use the developments. A' = A+9-^ds 3s dn' = dn-\--—~ds 2s. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Carnegie Institution of Washi
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