Recent Progress in Theoretical Physics. 251 



that the undulation lengths for the two ra3's are not equal. The 

 annexed figure may serve to illustrate the mutual action of these 

 rays. Suppose M A D B, to be the orbit in which a force P tends 

 to urge a molecule M, to revolve around the center C, to which it 

 is drawn by the force M C. Suppose the equal force Q to urge 

 the same molecule to describe the same orbit in the opposite 

 direction. These forces holding each other iii equilibrio, the mole- 

 cule will follow the direction of the third force, M C. 



Now suppose the force Q suspended, the molecule will take 

 the direction of the circle A D B, and will continue to revolve in 

 it so long as the force P (supposed always tangential) continues 

 to act. But its movemehts will impart to the molecule next 

 below it a similar motion, and that to the next, and so on; so that, 

 as these successive molecules take up their movements later and 

 later, there will be a series in different degrees of advancement in 

 their several circles, forming a spiral ; and when the molecule M 

 shall have returned to its original position, the series will occupy 

 a position like the curve M F L N' R. If, now, P be supposed 

 to be in turn suspended, while the force Q continues to act, the 

 effect of Q will be to produce a contrary spiral, which may be 

 represented by M S K T V. If M D be a diameter of the circle 

 M A D B, drawn from M, and D H JST' be a line parallel to the 

 axis C G of the cylindrical surface, which is the locus of the 

 spirals, then, if the undulating lengths are the same for both 

 movements, the two spirals will intersect D H in the same point, 

 the intersection marking the completions of a half undulation for 

 each. But if these lengths be unequal, the intersection with D H 

 will take place at different points as IST and N'. 



Let now a plane intersect the cylinder at any distance below 

 M A D B, as at E, parallel to M A D B. It is conceivable that 

 this plane may be made to pass through the point where the 

 spirals intersect each other. If I mark the point of intersection, 

 and we draw the tangents I P' and I Q' in the plane of the circle 

 E H I, then there will be a molecule at the point I which will be 

 in the circumstances of the molecule in [Fig. 12 at the point a] — 

 that is to say, solicited by three forces, of which two, I P' and I Q' 

 are equal and opposite, and the third is directed in the line I Gr 



