62 DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



Setting aside on the one hand frictional resistance, and on the other hand the 

 acceleration of the particles of air, we get a motion determined dynamically by the 

 equilibrium between pressure-gradient and deviating force of the earth's rotation. 

 Recent observations have shown that the true motion in the higher strata is usually 

 not very different from that determined by this equilibrium condition.* The ideal 

 motion existing when this condition is fulfilled is directed along the level curves 

 on the isobaric surfaces and goes on with a velocity represented by the formula 



v = 



2 w a sin ip 



to is the angular velocity of the earth, measured in radians per second (* = 0.000073) J 

 <p is the latitude, and a the distance in meters between level lines corresponding to 

 unit difference of level (one dynamic decimeter). The difference of level between 

 the successive curves being on some of our charts 10, on others 50 dynamic meters, 

 we can use the formula 



v 2 : > or > f r t ne greater interval, v = 



1 .46 a sin ip ' 1 .46 a sin <p 



measuring the distance a between the curves in millimeters on our chart in the scale 

 1 : 10 000 000. 



To use this principle to complete the observations on the charts, we have first 

 constructed the level curves for the isobaric surfaces representing a pressure equal 

 to the arithmetical mean of the pressures at the upper and the lower limits of the 

 sheet. These curves are easily found by the principle of graphic addition, by 

 drawing the diagonal curves through the parallelograms formed by the curves of 

 absolute topography of the lower and the relative one of the upper bounding surface 

 of the sheet, after having left out every second of the last curves. 



The accordance of these curves with the direction of the arrows is never com- 

 plete, and should be complete only in exceptional cases. Drawing the lines of 

 flow (fig. b of the plates LVII-LX) we have made them cut the level fines under 

 angles similar to those under which the arrows cut them (fig. a of the same plates). 

 Further, the numbers representing the observed wind-intensities are never in full 

 accordance with the formula. We have drawn the curves of equal wind-intensity 

 (fig. b of the mentioned plates) so as to get departures from the theoretical value 

 similar to those presented by the observations as seen by fig. A of the same plates. 



Of course, many different drawings of the lines of flow and curves of intensity 

 can be produced which are in accordance with these elastic rules. To what degree 

 we have succeeded in reconstructing by plates LVII-LX, the true horizontal motion 

 within each sheet will therefore remain an open question. We can not therefore too 

 strongly recommend further work to produce satisfactory direct observations of 

 atmospheric motions. Provisionally, the synoptic representations in higher strata 

 which we have obtained will serve our nearest aim, viz, that of illustrating formally 

 the further steps in the work of kinematic diagnosis. 



*E.jGold: Barometric gradient and windforce. London, 1908. 



