88 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



simplification is possible. In such a case the virtual-temperature diagram must be 

 drawn. But limiting the problem to the determination of the heights of the lowest 

 standard isobaric surfaces, a convenient short cut is easily found. Instead of using 

 table i 6 m, giving the local values of the virtual temperatures, we use table 15 m, 

 which gives in a corresponding manner the average virtual temperatures for the 

 sheets of air between the station and the heights figuring as argument. This table 

 is deduced from the preceding one by a process of integration, the principle of 

 which will be clear in itself. 



This table being given, we may proceed as follows in order to find the heights 

 of the nearest standard isobaric surfaces : Using the observed pressure we find from 

 table 1 1 M approximate values of the heights of these surfaces above the station. 

 Using these approximate height values and table 15 m, we find the average virtual 

 temperatures of the corresponding sheets. These virtual temperatures enable us 

 to correct the approximate heights already found by means of table 12M. The 

 complete procedure is seen by the example annexed to the table. 



This method of calculating the height above or the depth below the earth of 

 standard isobaric surfaces is analogous to the method of " reduction to sea-level " 

 of the barometric observations taken at stations situated at heights above sea-level. 

 We emphasize some important differences however our aim is always to find the 

 heights of isobaric surfaces really existing in the air. The main reductions are 

 therefore made upward and not downward. Consequently the result of the reduc- 

 tion is capable of being controlled by actual observations made in the open air, 

 while reductions to the interior of the earth involved in the reduction to sea-level 

 can not be made the subject of any kind of test by actual observations made at the 

 place for which the pressure is calculated. Further, the reductions to sea-level are 

 made generally according to a schematic method, using under all conditions the 

 same temperature gradient. We have retained this gradient for small reductions 

 downwards, while in working out the part of table 15 m to be used for reductions 

 upwards, we have tried to introduce individual temperature gradients according to 

 the different types of weather. In this direction probably much progress could be 

 made by a statistical study of the results of ascents in the air, as remarked above. 



