PART II. POLAR MAGNETIC PHENOMENA AND TERRELLA EXPERIMENTS. CHAP. VI. 699 



we obtain by the aid of (2), (3) and (4) 



_ r 

 dt \dt ~^~ \~dt" ' r 



We thus have to study the following system of equations: 



d*z SL 



151 



dip _ IMR* -f- ar 3 

 ~ dt = ~7" ' 



If, for the sake of brevity, we put 



r _ 



r RW 



.he first equation in (5) may be written in the form 



(If- ~2r 3r 

 From the second equation in (5), 



ve obtain by derivation as regards /, 



inv t*- iv . uz ct z IVL - 01 \ d t\ 01 z dz 

 ~dl ~dft " ~di~dP~ \3R 9r' r) i/i *~ 9r r dt 



d-z 

 If we introduce the expression just found for -^ , we obtain 



O 7T T^~ ~ ' \ 'J^ 1 ~ I ' 



dt dt 2 \SR ' dr r I dt 

 md as often as - L ^ , we can from this again conclude that 



<f/? = 

 dft = ~2 



Owing to the continuity, however, this equation also retains its validity, even if -y- = for certain 



pecial values of t. 



We can also eliminate t and find a differential equation in only z and R; this determines a surface 

 >f rotation, upon which the particle will always remain. 

 We have 



dz dz dR , d^z d-z /rf/?V . dz d*R 



Tt^ dR' dt ~aJ~dR* \~di~) '^~~dR ~dP 



