PAPER BY PROF. OBERBECK. 183 



The constant b must also here be added for the same reason as above 

 given. 



The function K is to be computed from the equation 



j^+^:^(^.^"-^9. ^ \=o (8) 



dr \^y r ^U- r J ^ 



From this last equation it follows that the introduction of the func- 

 tion K can be omitted when the teuiperature of the atmosphere is as- 

 sumed symmetrical with reference to the earth's axis. In this case 

 tCi—i) and the [atmospheric] movement resulting from the rotation of 

 the earth consists exclusively in a movement of rotation depending on 

 the geographical latitude and the altitude above the earth's surface. 



In order to present in the ordinary manner the currents of air for a 

 given point in the atmosphere, the following components are to be in- 

 troduced instead of ii, v, w: 



V, the vertical component computed positivelj" upwards ; 



N and 0, the two horizontal components, of which the first indicates 

 movement toward the north, the latter, movement toward the east; 



6, the complement of the geograi)hical latitude of a given place; 



//', the longitude counted from an arbitrary meridian; 

 then we have 



V=-{-{u cos '/--fv sin tp) sin 6-{-iv cos 6 ^ 



]S' = — {u cos tf' + v sin ?/<) cos S-^ic sin 8 > .... (9) 



0=— w sin ?/'4-r cos ^•. ) 



The formulae (4, C, and 9) contain the general solution of the problem 

 so far as this is at present intended to be given, assuming the distribu- 

 tion of temperature to be given and that the functions jEJ, F, J, H, K 

 are determined in accordance with the boundary conditions. 



IV. 



When one attempts to represent the distribution of temperature on 

 the earth's surface by a series of harmonic functions then the most im- 

 portant term is a harmonic function of the second order. Therefore as 

 a first approximation we put 



Ti= (' Ar^ + ~J )(l-3 cos^ B). 



\ 



This function, with a proper determination of the constants, ex- 

 presses the great contrast in temperature between the equator and the 

 pole. If now one would take into account the variation with the sea- 

 sons one must next introduce harmonic functions of the first order. 

 The consideration of the various peculiarities of the earth's surface will 

 of course demand further terms that depend on the geographical longi- 

 tude also. 



