890 
MR, G. H. DARWIN ON THE SECULAR CHANGES IN 
The numbers written on the curves represent the values of z, viz., z— 0, 1, 2, 
3, 4, 5. 
The ends of the contour lines on the right are joined by dotted lines, because it 
would be impossible to draw the curves completely without a very large extension of 
the figure. 
The broken lines (-) marked “ line of maxima,” terminating at A, and “ line of 
minima,” terminating at B, represent the two roots of the biquadratic (y). 
The lines marked n=fl represent the two roots of (8), but computation showed that 
the right-hand branch fell so very near the line of minima, that it was necessary to 
somewhat exaggerate the divergence in order to show it on the figure. 
Contour lines of surface of energy. 
The chain-dot lines C, C, marked n=yf/2, represent the two roots of (e). 
For configurations of the system represented by points lying between these two curves, 
the ellipticity of orbit will increase; for the regions outside it will decrease. This 
statement only applies to cases of small ellipticity, and small viscosity of the planet. 
Inspection of the figure shows that the line of minima is an infinitely long valley of 
a hyperbolic sort of shape, with gently sloping hills on each side, and the bed of the 
valley gently slopes up as we travel away from B. 
The line of maxima is a ridge running up from A with an infinitely deep ravine on 
the left, and the gentle slopes of the valley of minima on the right. 
