78 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



Theoretically it is correct to use a logarithmic scale of pressure. Practically, 

 however, the common pressure-scale maybe used without introducing error of any 

 importance. Fig. 7 gives the same virtual-temperature diagram as fig. 5, but with 

 a difference of scale. It is seen that the average virtual temperatures deduced 

 from this diagram are practically the same as those deduced from fig. 5. 



In reality the temperatures will be found a little too high from the diagrams 

 with the common pressure-scale. The amount of error can be determined theo- 

 retically if we suppose the curve to be a straight line in the one of the two 

 diagrams. It will then run up to 0.008 (t, t 9 ) for the isobaric sheet between the 

 1000 and the 900 m-bar surfaces, and to 0.057 (t 2 tj) for the sheet between the 200 

 and the 100 m-bar surface, t 10 and r a respectively, t 2 and r l being the temperatures 

 at the limiting surfaces of the sheet. Thus a temperature difference of io between 

 the limiting surfaces will bring the error up to about 0.1 degree for the lower sheets, 

 and somewhat above 0.5 degree for the highest sheet. These errors will generally 

 be much smaller than the errors of observation from these different sheets. 



While the errors introduced are thus unimportant, many practical advantages 

 are gained. Common coordinate paper can be used, and we avoid the special 

 inconvenience of the logarithmic scale, namely, that the best observations, those 

 trom the lower strata, have to be worked out on a minute scale, and the inferior 

 ones, those from the higher strata, by constructions on a large scale. 



56. Examples of the Method of Calculation when the Pressure is Given in 

 Millimeters or Inches of Mercury. When the observations are given in irra- 

 tional units, the most direct method is to change at once all observations to rational 

 units using the tables of the Appendix. And this change will be necessary, if it 

 be desired to work out the results with the completeness of the examples given 

 above. But if it be only required to find the main result, viz, the height of the 

 standard isobaric surfaces, a shorter way can be followed, which is illustrated by 

 the two examples below. No example is given for the case when the observed 

 quantity is the height. For in this case the first step will always be a change irom 

 geometric to dynamic height, and it is immaterial whether the height is observed 

 in meters or feet. 



It is to be hoped that the time will soon come when all observations obtained 

 from the higher strata are recorded in rational units. But as a vast amount of such 

 observations has already been produced and recorded according to the different 

 systems of irrational units, it will for some time to come be a question of great 

 importance to be able to work out with as little waste of labor as possible the most 

 important results in rational units from the data given in irrational units. 



The simplest method of doing this, under the supposition that no other aux- 

 iliaries are at hand than our tables and common coordinate paper, is illustrated by 

 the examples 3 and 4 below. As will be seen immediately from these examples, 

 several operations will drop out, and no little amount of time will be saved, if 

 special blanks be prepared, containing, besides the common coordinate lines, also 



