856 THE SPIRAL SHELLS [ch. 



especially where the spire makes more than one visible revolution 

 about the pole), by its fundamental property of continued similarity: 

 that is to say, by reason of the fact that the big many-chambered 

 shell is of just the same shape as the smaller and younger shell — 

 which phenomenon is as apparent and even obvious in the nautiloid 

 Foraminifera, as in Nautilus itself: but nevertheless the* nature of 

 the curve must be verified by careful measurement, just as Moseley 

 determined or verified it in his original study of Nautilus (cf. p. 770). 

 This has accordingly been done, by various writers : and in the first 

 instance by Valerian von Moller, in an elaborate study of Fusulina — 

 a palaeozoic genus whose little shells have built up vast tracts of 

 carboniferous limestone in European Russia*. 



In this genus a growing surface of protoplasm may be conceived 

 as wrapping round and round a small initial chamber, in such a way 

 as to produce a fusiform or ellipsoidal shell — a transverse section 

 of which reveals the close- wound spiral coil. The following are 

 measurements of the successive whorls in a couple of species of 

 this genus: — 



F. cylindrica Fischer F. Bocki v. Moller 



Breadth (in miUimetres) 



In both cases the successive whorls are very nearly in the ratio 

 of 1 : 1-5; and on this ratio the calculated values are based. 



Here is another of von MoUer's series of measurements of F. 

 cylindrica, the measurements being those of opposite whorls — that 

 is to say of whorls 180° apart: 



The mean logarithmic difference is here 0-088, = log 1-225; or the 

 mean difference of alternate logs (corresponding to a vector angle 

 of 27T, i.e. to consecutive measurements along the same radius) is 

 0-176, = log 1-5, the same value as before. And this ratio of 1-5 

 between the breadths of successive whorls corresponds (as we see 



* V. von Moller, Die spiral-gewundenen Foraminifera des riissischen Kohlen- 

 kalks, Mim. de VAcad. Imp. Sci.f St Petersbourg (7), xxv, 1878. 



