34 General Dynamical Principles [CH. n 



nardly have been satisfactorily discussed without the help of such equations. 

 Now that this theory has been established we can discard equations (48). 

 We have found that stability can be lost at a turning point or a point 

 of bifurcation on a linear series. The characteristic feature of a turning 

 point is that the variable parameter attains a stationary value at such a 

 point ; the characteristic feature of a point of bifurcation is that correspond- 

 ing to a single value of the parameter, there shall not only be a single 

 configuration of equilibrium, say lt 2 , but also a small range of 

 configurations of the form 



0! + *!, 2 , 3,.-. 



for all values of e so small that e 2 maybe neglected. 



