PART II. POLAR MAGNETIC PHENOMENA AND TERRELLA EXPERIMENTS. CHAP. VI. 695 



Let us look for a little at the last case. The expression 



r a v a sin a a F(r] 







ill then remain positive during the in-going motion; but if we compare 2 points with the same value 

 f r, one on the out-going, and one on the in-going path, then 



(r a v sin - /) in <(r a v lt sin /) oll t , 

 id 



out 

 id consequently 



d(f> 

 ~dr 



In 



dr 



out 



The particle will thus return to the globe again by a steeper path than that by which it went out 

 om it. 



Setting aside the case in which the particle recedes indefinitely, only those cases are left in which, 

 ith negative direction of revolution, it either changes to an in-going motion again, or approaches a 

 jimdary-circle. 



We will look at the former of these cases. 



If we compare the value of -J- in 2 points with the same value of r, one on the out-going and 

 ic on the in-going path, it is evident that 



dr[> dip 



dt in ttt out 



It might then happen that - . became positive when the particle came in sufficiently near to the 

 <>be again; but then ,-- would certainly also be positive for smaller values of r. Then as -/- and 



W in dt in 



would both be positive for these sufficiently small values of r, we may prove in the same way as 



'out 



;iove that 



/I if 

 dr 



in 



dff 



it then the particle must return to the globe again. On the other hand, if it does not end in the globe, 



en, with negative value of -j. , it will either turn out again, or approach a boundary-circle. It is then 



drr 

 < rtain, however, that -' will continue to be negative for all time. Along an eventual out-going path, 



t r 



. will certainly remain negative; and if it turns in again, will also, by virtue of the relation 



dcp dcp 



dt i n * dt ou t ' 



I: negative along the in-going path, and so on. 



In conclusion we will see whether the particle with negative direction of revolution can approach 

 ; boundary-circle from within, when a a > 0. If we call the radius of the circle r, , then 



