INVESTIGATING ORGANIC FORMS. 211 



form of a turbinated shell was produced by the revolution of 

 the perimeter of the figure round the axis of the shell. In 

 the Nautilus the figure was that of an ellipse, which revolves 

 round its minor axis, and increases in geometrical progression 

 without ever changing its form as it revolves. A turbinated 

 shell revolving round its axis shows the figure carried forwards 

 along the axis of revolution, from the apex of the spire to its 

 termination. They might do this by cutting a piece of paper 

 to the figure of the turbinated shell. It would be found that the 

 figure was always the same, but increased. Professor Moseley 

 ascertained this in two ways 1st, after the curve had been 

 ascertained ; and 2dly, by a very curious investigation of the 

 operculum. He had ascertained that the spiral possessed the 

 peculiar properties of a logarithmic spiral; hence the oper- 

 culum was found to form a very convenient measure of the 

 shell itself and all its parts. The operculum being fixed, as 

 the shell increased in size it underwent a gradual increase 

 the size of the mouth gradually increased with the size of the 

 operculum. Now, if the operculum were merely pushed 

 forward by the animal, one of two circumstances would occur 

 it would either require new calcareous shelly matter (but it 

 was not so), or there would be, as indeed was the case, a much 

 more precise method of extension by the deposition of addi- 

 tional matter along the lower margin of the shell which formed 

 the tangent of the curve. 



There were other examples of a similar kind. Take one 

 of the Goniums, a little animal or vegetable structure existing 

 amongst the polygastria, and consisting of four cellules in 

 a square plate, as also the Sarcina Yentriculi. The Goniums 

 and others were rectangular forms. They were all squares. 

 And why ? They reproduced themselves in a geometrical pro- 

 gression, and that because each individual consisted of four 

 cells, and four only, until it was reproduced by other four. 

 The law of its reproduction was by a geometrical series 



