Prof. Tait on Listing's Topologie. 35 



round with the sun (secundum solem), that of the vine tendril 

 against the sun (contra solern). 



Thus the vine tendril forms an ordinary or (as we call it) 

 right-handed screw, the hop tendril a left-handed screw. 



Now, if a point move in a circle in the plane of yz in the 

 positive direction, and if the circle itself move in the direction 

 of x positive, the resultant path of the point will be a vine-, or 

 right-handed screw. But if the circle's motion as a whole, or 

 the motion of the point in the circle, be reversed, we have a 

 left-handed screw; while if both be reversed, it remains right- 

 handed. Every one knows the combination of the rotatory 

 and translator^ motions involved in the use of an ordinary 

 corkscrew; but there are comparatively few who know that a 

 screw is the same at either end — that it has, in fact, what is 

 called dipolar symmetry. 



With a view to assist the botanists, Listing introduced a 

 fancied resemblance between the threads of the two kinds of 

 (double-threaded) screws and the Greek letters A, and S, for 

 the latter of which he also proposed the longy used as a sign of 

 integration; thus AAAA and 555S, °^ffff' 



The first, which is our vine- or right-handed screw, he calls 

 from his point of view (which is taken in the axis of the screw) 

 laeotrop, the other dexiotrop. He also proposes to describe 

 them as lambda- or delta- Windungen. But it is clear that all 

 this " makes confusion worse confounded/'' Every one knows 

 an ordinary screw. It is right-handed or positive. Hence he 

 can name, at a glance, any vegetable or other helix. 



(5) A symmetrical solid of revolution, an ellipsoid for 

 instance (whether prolate or oblate), has, if at rest, dipolar 

 symmetry. But if it rotate about its axis, we can at once 

 distinguish one end of the axis from the other, and there is 

 dipolar asymmetry. 



This distinction is dynamical as well as kinematical, as every 

 one knows who is conversant with gyroscopes or gyrostats. 



A flat spiral spring, such as a watch- or clock-spring, or 

 the gong of an American clock, if the inner coils be pulled 

 out to one side, becomes a right-handed screw; if to the other, 

 a left-handed screw. In either case it retains the dipolar 

 symmetry which it had at first, while plane. 



But when we pass an electric current round a circle of 

 wire, we at once give it dipolar asymmetry. The current 

 appears, from the one side, to be going round in the positive 

 direction; from the other, in the negative. This is, in fact, 

 the point of Ampere's explanation of magnetism. 



A straight wire heated at one end has dipolar asymmetry, 



1>2 



