FIELDS OF PRESSURE AND MASS IN THE ATMOSPHERE. 93 



To find the correlative representation of the distribution of mass, we have to 

 remember that the difference of pressure from one standard equipotential surface 

 to another is equal to the average density of the air in the sheet between them. 

 By arithmetical or graphic subtraction of the fields of pressure in the level sur- 

 faces limiting an equipotential sheet we therefore get a chart representing the 

 average distribution of density in this sheet. Such charts are given in figs. 16 and 

 23. The figures added to the curves give the mutual pressure differences in m-bars. 

 As they refer to level sheets of 1000 dynamic meters interval they will, after divi- 

 sion by io 5 , give the average densities of the sheets. 



A valuable complement to these charts of absolute pressure and of pressure dil- 

 ference are vertical sections like those of figs. 18 or 24. These are obtained by 

 means of verticals like the third of fig. 4. A set of such verticals being drawn at 

 proper mutual distances, points representing the same dynamic height are united by 

 curves, and in like manner points representing the same value of density. In this 

 way we obtain the profile curves of the equipotential and isopycnic surfaces, those 

 of the equipotential surfaces being drawn simply as horizontal equidistant lines. 



An important relation between these vertical sections and the corresponding 

 charts will be developed below (section 73). 



66. Construction for Lower Levels of Charts of Absolute and of Mutual 

 Topography from Observations Made at the Earth's Surface. In drawing the 

 charts described in principle in the preceding articles, it is important to make as 

 complete a use as possible of the observations from the stations at the earth's sur- 

 face. For these observations are abundantly at hand, while those from the open 

 air will always remain relatively scarce. By means of the method of extrapolation 

 developed in sections 58 and 59, it will be possible from the observations at the 

 earth's surface to draw charts for the lower sheets of the atmosphere. 



From stations near sea-level the heights of the three lowest standard surfaces 

 may be found, and from many mountain stations the heights also of the fourth and 

 fifth and even higher surfaces may be determined with satisfactory accuracy. The 

 common meteorological observations will therefore enable us to draw topographic 

 charts of the three, four, or even five lowest standard isobaric surfaces. The three 

 first charts of fig. 19 are obtained in this way, only slightly corrected and extended 

 afterwards by the results obtained by ascents in the air. It is important to remark 

 that charts of this kind can be obtained every day from the regular meteorological 

 observations, and with the same ease as the charts for sea-level now in use. 



It is of course always desirable to derive the charts directly from the original 

 observations, and not from these observations after they have been " reduced to 

 sea-level." But often, when past atmospheric states must be worked out from 

 published observations, these are accessible only in the distorted form of isobaric 

 charts for sea-level. Re-reductions to higher levels are thereby made more 

 troublesome and less trustworthy. But it is important to notice that it is very easy 

 to change an isobaric chart for sea-level into a topographic one for the 1000 

 m-bar surface, provided the isothermic chart be known besides the isobaric. 



To perform this change when the isobaric chart is drawn for millimeters of 

 mercury and the isothermic for degrees of the centigrade thermometer, table 18 a 



