PATHS OF MOVING PARTICLES — SPRUNG 7 I 



easily deduced by a closer consideration of the expression for sin d 

 in the first of equations (16) ; if, for example, we introduce the con- 

 dition that sin d = o for r = r , and write 



• a (u I r o 2 

 sin = - ( — — r 



v \r 



If now we consider two places on the earth's surface at the same 

 distance r from the axis, one of which is in the northern hemisphere, 

 the other in the southern, then sin 6 is in both cases = o, that is to 

 say, the motion is to be a purely south-northerly one. In the far- 

 ther course of these motions, however, r becomes smaller in the 

 northern hemisphere and therefore sin d > o ; on the contrary in the 

 southern hemisphere r will become greater and therefore sin #<o; 

 the body therefore deviates from the meridian towards the right 

 in the northern hemisphere but towards the left in the southern 

 hemisphere. 



If the motion is followed still farther (in the northern hemisphere 

 for example) then we have 



v 

 for the value 6 = 90° the distance r £ = — + 



2w 



6 = 270° 



the value of 6 becomes 360 again for r = r and therefore in the 

 same geographical latitude in which d = o. But it can be easily 

 seen that in this case the body has not returned to the meridian of 

 the starting place but to one lying farther west; for since the curva- 

 ture of the path continually diminishes wdiile d passes through its 

 values from 90 to 270 , therefore the southernmost point of the 

 path must lie farther westward than the preceding northernmost 

 point. The motion is therefore enclosed between two definite par- 

 allels of latitude and carries the body in many nearly circular con- 

 volutions gradually toward the west. Presumably this progression 

 is connected with a peculiarity of the corresponding absolute motion 

 which the latter has in common with a peculiarity of the spherical 

 pendulum ; in this latter case it is known that the successive tempo- 

 rary highest positions show a regular advance in a determinate direc- 

 tion on a horizontal circle. 



The correct representation of the relative (or absolute) path in 

 the form of an equation between the geographical coordinates <p and 



