Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/112

 Rh then, if the moment of the couple acting on a molecule is less than mL, there will be no permanent deflexion, but if it exceeds mL there will be a permanent change of the position of equilibrium.

To trace the results of this supposition, describe a sphere whose centre is O and radius OL = L.

As long as X is less than L everything will be the same as in the case already considered, but as soon as X exceeds L it will begin to produce a permanent deflexion of some of the molecules.

Let us take the case of Fig. 8, in which X is greater than L but less than D. Through S as vertex draw a double cone touching the sphere L. Let this cone meet the sphere D in P and Q. Then if the axis of a molecule in its original position lies between OA and OP, or between OS and OQ, it will be deflected through an angle less than β0, and will not be permanently deflected. But if the axis of the molecule lies originally between OP and OQ, then a couple whose moment is greater than L will act upon it and will deflect it into the position SP, and when the force X ceases to act it will not resume its original direction, but will be permanently set in the direction OP.

Let us put then all those molecules whose axes, on the former hypotheses, would have values of θ between θ0 and π - θ0 will be made to have the value θ0 during the action of the force X.

During the action of the force X, therefore, those molecules whose axes when deflected lie within either sheet of the double cone whose semivertical angle θ0 is will be arranged as in the former case, but all those whose axes on the former theory would lie outside of these sheets will be permanently deflected, so that their axes will form a dense fringe round that sheet of the cone which lies towards A.