PAPER BY PROF. OBERBECK. 185 



Moreover the two constants A and A', which occur in the combina- 

 tion 



ABf + % 



can be expressed in terms of the temperatures of the earth's surface at 

 the equator, T aJ and at the pole, T p . We have 



Finally we put 



I {T a -T p )=AR*+^ 3 



D=^'2e. H T a -T p ). 



The numerical value of these two last constants can not be given, 

 since, as before remarked, the coefficient of friction, ;*, will not agree 

 with that determined from laboratory experiments. In any case D is 

 considerably larger than C, since in D the fourth power of the radius 

 of the earth occurs, but in C only the second power. The components 

 of motion of the atmosphere are, therefore : 



V=G (1-3 cos 2 0).f{e) 

 N= —G.Q cos 6 sin d.cp (ff) 



0=1) sin | (L-3 cos 2 6) g {a) + 6 cos 2 y (g)\ 



If we take R.li for the altitude of the atmosphere as above defined, 

 then the four functions,/, cp, g, y, are to be so determined that they 

 satisfy the prescribed boundary conditions for ff=0 and a=h. I have 

 executed this computation for the most general case, namely, that in 

 which at the upper limit slipping occurs without friction, but at the 

 lower limit sliding with friction. Undoubtedly however the condi- 

 tion of the atmosphere on the earth's surface is much more nearly that 

 of adhesion than that of free slipping, so that I will here communicate 

 only the solutions for this latter case. For this case the motion at the 

 earth's surface is everywhere zero. But for this motion one can easily 

 substitute the motion at a slight altitude, that is to say, for small 

 values of <7. For the four functions we find the following expressions : 



f((f)=^h— a)(3hff— 2& 2 ) 



■ (p(o)=^ | 67i 2 -15/i(r+8o- 2 } 



g (<y)=jL I -9/l 5 +15/i 2 (7 3 -15/K7 4 + 4ff 5 } 



