THE FORCED VERTICAL MOTION AT THE BOUNDING SURFACES. 133 



construction of topographic maps of a completeness which can not be attained 

 Taking the case of the atmosphere, the chart should give the configuration of every 

 irregularity of the ground, every stone, every tree, every house. And the use of 

 the map would require wind-observations taken all around these irregularities. 



Just as we have been obliged to consider an idealized wind (section 97), we 

 must use an idealized topography, corresponding to the placing of the fanes and 

 the anemometers in open places, above that sheet of air which has the most irregular 

 motions. 



It will therefore be perfectly legitimate to use an idealized topography like that 

 which is represented by the common contour-lines. And in most cases it will be 

 not only legitimate, but necessary, to go still further in the idealization than on 

 common charts. Even the map of the world as we have drawn it on the plates I-XXIV 

 contains far too much detail for meteorological work as long as the phenomena are 

 to be studied on a large scale, and not in minute details. 



For our practical work we have therefore been obliged to derive from this map 

 special maps of idealized topography. All these special maps have been drawn on 

 a scale of i : 10 000 000. We have found this scale convenient for the performance 

 of our constructions, and all our graphical auxiliaries have been made with this scale 

 in view. All these special maps have been drawn in a conical projection corre- 

 sponding to the latitude. Our reasons for preferring this projection to one with 

 curved meridians have been given already; all kinds of auxiliary graphical instru- 

 ments (sections 143, 161, 163) are easily applied when the chart is in conical pro- 

 jection. The idealizations have been performed step by step. First we have drawn 

 a map where all the smallest irregularities of the contour-lines have been removed, 

 then a new map where greater irregularities have been removed, and so on. The 

 simplified curves are always drawn so that the volumes of the great mountain- 

 chains and of the continents have retained their value. In this manner correct 

 values will be found for the average intensity of the forced ascending or descending 

 motion, while the small irregular motions up and down, which are only of local 

 importance, will drop out. But it should be remembered that the drawing of the 

 idealized charts has no unique solution. The same degree of idealization can be 

 attained in different ways as regards details. It will be a question of experience to 

 find out the proper degree of idealization and the best solution of dubious questions 

 of detail. In practical work we have used two degrees of idealization, represented 

 by the "moderately idealized" charts of the United vStates and of Europe given on 

 plates XXV and XXVIII, and the "greatly idealized" charts of plates XXVI and 

 XXIX. We have used the moderately idealized charts more for qualitative pur- 

 poses, drawing on them the charts of the horizontal motion (section 135), while we 

 use the charts of greatly idealized topography for the rigorous quantitative work. 



We have given no examples of idealized bathymetric maps. As we have had 

 no observations from which we could work out a kinematic diagnosis of sea-motions, 

 we have had no opportunity of examining the question of such charts for hydro- 

 graphic purposes. It should be remembered, however, that the bottom of the sea 

 is, generally speaking, less irregular than the ground above sea-level, and at the same 



