1892.] Mr Willis, On Gynodicecism in the Labiatae. 351 



maphrodite flowers is thus to some extent compensated for by the 

 greater number of the females. 



Abnormalities in the flowers of Nepeta, like those observed in 

 Origanum, &c, are comparatively few and far between, but were 

 yet fairly often encountered. 



During the course of these observations upon Nepeta an 

 interesting point was noticed. The protandry of the flowers 

 appears to vary according to the season : at the beginning of the 

 flowering season the stigmas begin to separate very soon after 

 the dehiscence of the anthers, while towards the end of the 

 season these processes are separated by a considerable time. I am 

 conducting further observations upon this point. If it should 

 prove general, it would, taken together with the negative results 

 of the above observations on Origanum, have a tendency to dis- 

 prove Ludwig's view of the origin of gynodicecism. This point 

 however I hope to discuss in a future paper, when I shall have 

 concluded the further observations on Origanum, &c, which are 

 now beins conducted. 



(3) On the Steady Motion and Stability of Dynamical Systems. 

 By A. B. Basset, M.A., F.R.S., Trinity College. 



1. The object of the present paper is to develop a method for 

 determining the steady motion and stability of dynamical systems, 

 by means of the Principle of Energy, and the Theory of the 

 Ignoration of Coordinates. The subject has already been discussed 

 by Routh*, but is treated in the present paper in a slightly 

 different manner. 



Let the coordinates of a dynamical system consist of a group 0, 

 and a group of ignored coordinates ^ ; and let k be the constant 

 generalized momentum corresponding to %. Then if the velocities 

 <% be eliminated by means of the equations 



dT_ 



dx~ K ' 



it is well known that the kinetic energy of the system will be of 

 the form 



T=% + ®, 



where X is a homogeneous quadratic function of the velocities 6, 

 and $ is a similar function of the constant momenta k. 



Also if © be that portion of the generalized component of 

 momentum corresponding to 6, which does not involve 6, and 



* Treatise on Stability of Motion. 



