i6o 



PROBLEMS OF RELATIVE GROWTH 



ratio is always smaller than the median (if it were larger, it 

 would of course decide the main spiral, and the other would 

 become the subsidiary differential, concerned with distortion 

 of the main spiral). 



Whereas the value of the main or median growth-ratio 

 decides the tightness of the coiling of the main spiral, that of 



— c 



-- c 



© 



® 



Fig. 76. — Diagram to illustrate the growth-gradients operating to produce 

 the plane and the turbinate spiral shells of Molluscs. 



(a) and (6) Projections of the growing edge of the mantle ; (c) and (d) corresponding elevations, 

 the ordinates representing growth-intensities, the abscissae distance across the shell-opening, (a) and 

 (c) gradients operating to produce a plane logarithmic spiral shell. There is a centre of maximum 

 growth at A, of minimum growth at C. The growth-gradients between A and C are identical on both 

 sides of the mantle, through B and through D. 



(b) and (d) gradients operating to produce a turbinate spiral. The growth-gradient ABC is ofa 

 different shape from ADC ; thus a secondary growth-ratio is established between B and D. The 

 growth ratio AP/CS < BQ/DR. 



the secondary or lateral growth-ratio decides the degree of 

 distortion of this spiral, the proportionate amount by which 

 it is pushed out of its fundamental plane. When the lateral 

 ratio is unity, the shell is flat, in one plane, like that of Plan- 

 orbis. When it is low, the shell is low also, like the depressed 



