METEOROLOGY. 535 



fluid masses, the principal resistances are those that arise from the ac- 

 celeration of the fluid and especially in consequence of the formation 

 of dividing surfaces (on either side of which independent movements 

 simultaneously take place). These resistances increase with the square 

 of the velocity until that due to friction only is proportional to the first 

 power of the velocity and is specially apparent only in experiments with 

 quite small tubes and inclosures. (Z. 0. G. M., xvm, p. 100.) 



Sprung gives a critical review of the three important memoirs by Fer- 

 rel on the mechanics of motions in the atmosphere; he deduces Ferrel's 

 fundamental equations in a more general manner, but as his equation 

 cannot be conveniently reproduced here it suffices to state that by an 

 almost entirely independent course of reasoning he is led to a general 

 system of atmospheric circulation and to special systems of cyclonic 

 circulation entirely similar to that which was published by Ferrel. As 

 to the origin of areas of high and low pressure, the inclination of the so- 

 called axis of the cyclone and the causes of the progressive movements 

 of the storms he also adopts Ferrel's views. (Z. 0. G. M., xvn, p. 

 161.) 



Sprung makes the following remarks in respect to Hadley's principle 

 i. e., that a body that is relatively at rest on the earth's surface at the 

 latitude q) , and revolviug about the earth's axis with the absolute 

 velocity proper to this latitude, R co cos cp , has the same absolute ve- 

 locity at any other latitude to which it may attain by virtue of some 

 impulse, ■», in a meridional direction. 



(1.) On arriving at the latitude cp, the body is found to have a rela- 

 tive east and west velocity of E = R go (cos <p» — cos q>). If we con- 

 sider this to be the result of a steady deflecting force, continuously act- 

 ing like the force of gravity, then E is the integral of the differential 



expression -^5- = R iS-co sin cp: where R -£-= v is the above uni- 

 1 dt dt ri dt 



form meridional velocity due to the initial impulse. 



(2.) If we consider the earth and meridians as stationary, then, at 



the end of the time t two bodies starting from <p A , one moving east 



and the other polewards as well as east, will have respectively arrived 



at the two points (cp and A), and (cp and A x ) where 



A] = R oo cos cp t and A = R go cos (p 1 



The difference of longitude will be 



y = R go (cos cp — cos cp) 



The difference of latitude 



vt = R {cp — cp ) 



whence 



whence 



T>2 co 



y = (cp — (p ) x (cos cp — cos <p ) 



rfE = d?y = qi sin 

 dt dt ^ 



This second value is twice the preceding, and is that also deduced 



