368 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



uniform throughout such a long distance, it would be more correct 

 to put this equation in the form 



dp 13.6 s 



r =-77- g ( lb ) 



at p 



where d /? expresses the change of pressure for the elementary dis- 

 tance d I in the direction of the greatest barometric change. Hence 

 the value of G should be deduced from the equation 4 



dp = G 

 dl ' 111 111 



Finally for many points of view it is very advantageous to write 



di i 



where A /? indicates some definite change of pressure and / the dis- 

 tance in the direction of the greatest gradient to which one must go 

 until a difference of pressure J p is attained, assuming a uniform baro- 

 metric gradient. 



Thus the formula assumes the form 



Ap 13.6 , 



r = • g ( lc ) 



1 p 



Instead of these three formulae which I will speak of collectively 

 as the formulae (i) since they are in fact only different forms of the 

 same fundamental formula, one may also use the following very 

 different form 



T - g tg a (2) 



where a is the angle that a surface of constant pressure makes with 

 the horizon, and always in the direction of the steepest gradient. 



The formulae (i) and (2) are closely associated with thetwo above- 

 mentioned geometrical methods of presentation that we used to 

 express the distribution of atmospheric pressure. 



Since we can easily lay off a distance of 1 1 1 , 1 1 1 meters or 1 1 1 kilo- 

 meters on any map, no matter what its style of projection may be, 

 therefore the formula (ia) is specially appropriate to such investiga- 

 tions as those based on the ordinary synoptic charts. 



For this reason also in using formula (ia) one should not, as is 

 often done, speak of the length of one degree of the equator, since 



4 Compare C. M. Guldberg and H. Mohn: Etudes sur les Mouvements de 

 1'Atmosphere, p. 18. Christiania, 1876. [Supra XI. p. 146.] 



