434 SHORT MEMOIKS ON METEOROLOGICAL SUBJECTS. 



then from this definition follows 



and b}' substitution of this value we find 



7 * 



AB = - . - (2 « sin + u) v. 

 g a 



Let 

 B be the barometric pressure at a given place, 

 T the temperature expressed on the absolute scale, that is to say, 



T = 2730 + t, 

 then we have 



. ^ 1 ^ ^ 10333 

 ' V ILO' B T ' 



where 10,333 kilograms is the pressure of one atmosphere. 



If we substitute this value of 8, and insert the numerical values of 

 fj = 9.80G meters (for ^ = 45°), <t = 1359G kilograms, E = 29.3, then we 

 find 



I B 

 ^■^ = mA: ' T ^^ " sin ^ + u) V. (I) 



In this formula, I is expressed in meters, B in millimeters, 2 wand « 

 in terms of the radius, v in meters per second of mean time; 2 71 is a 

 constant whose numerical value, 



2n = TTT^ = 0.0001458, 



we have not inserted in the formula merely for tyi)ograi)hic reasons and 

 convenience. 



The equation (I) represents the gradient AB as a function of the 

 velocity of the wind in case that the air describes a purely central move- 

 ment, and has therefore no frictional resistance to overcome, as, also, 

 that no new masses of air are drawn into the movement. 



We will now illustrate the use of this formula by two numerical exam- 

 ples, whereby, however, it must be remarked that it is only as a first 

 approximation that it can find an application to actual conditions. For 

 numerical computations, our formula first acquires a more convenient 

 form when we put B = IGO"^"^, and T = 273°, or t equal to 0^ Centigrade 

 or E6aumur, wbich is always allowable, since the inaccuracies that result 

 from these assumptions are smaller than those that attend the imperfect 

 theory itself. We will put the distance I equal to one German mile, or 



7.42 kilometers. Finally, if we consider that w v = — , where r represents 

 the distance from the axis of rotation, then the formula becomes 



AB = 71.875 ('0.0001458 sm<p.v+~\ 



If we desire to refer the gradient AB (which will be given in milli- 

 meters) to the English unit of 50 nautical miles [instead of one German 



