366 The Life of the Spider 



angle, would be neither more nor less than a 

 logarithmic spiral. Conversely, the groove of 

 the shell may be considered as the projection 

 of this spiral on a conic surface. 



Better still. Let us imagine a plane per- 

 pendicular to the axis of the shell and passing 

 through its summit. Let us imagine, moreover, 

 a thread wound along the spiral groove. Let us 

 unroll the thread, holding it taut as we do so. 

 Its extremity will not leave the plane and will 

 describe a logarithmic spiral within it. It is, 

 in a more complicated degree, a variant of 

 BernouiUi's * Eadem mutata resurgo : ' the loga- 

 rithmic conic curve becomes a logarithmic 

 plane curve. 



A similar geometry is found in the other shells 

 with elongated cones, Turritellae, Spindle-shells, 

 Cerithia, as well as in the shells with flattened 

 cones, Trochidae, Turbines. The spherical 

 shells, those whirled into a volute, are no excep- 

 tion to this rule. All, down to the common 

 Snail-shell, are constructed according to loga- 

 rithmic laws. The famous spiral of the geo- 

 meters is the general plan followed by the 

 Mollusc rolling its stone sheath. 



