676 ON CONCRETIONS, SPICULES, ETC. [ch. 



circles of latitude are not so, any more than in the sphere. But 

 a line which crosses the equator at an oblique angle, if it is to-be 

 geodesic, will go on so far and then turn back again, winding its 

 way in a continual figure-of-eight curve between two extreme 

 latitudes, as when we wind a ball of wool. To say, as we have done, 

 that the geodesic is the shortest Une between two points upon the 

 surface, is as much as to say that it is a trace of some particular 

 straight line upon the surface in question ; and it follows that, if any 

 linear body be confined to that surface, while retaining a tendency to 

 grow (save only for its confinement to that surface) in a straight line, 

 the resultant form which it will assume will be that of a geodesic. 



Let us now imagine a spicule whose natural tendency is to grow 

 into a straight Hnear element, either by reason of its own molecular 

 anisotropy or because it is deposited about a thread-Hke axis, and 

 let us suppose that it is confined either within a cell-wall or in 

 adhesion thereto ; its fine of growth will be a geodesic to the surface 

 of the cell. And if the cell be an imperfect sphere, or a more or 

 less regular elhpsoid, the spicule will tend to grow into one or other 

 of three forms: either a plane curve of nearly circular arc; or, 

 more commonly, a plane curve which is a portion of an eUipse; 

 or, most commonly of all, a curve which is a portion of a spiral in 

 space. In the latter case, the number of turns of the spiral will 

 depend not only on the length of the spicule, but on the relative 

 dimensions of the ellipsoidal cell, as well as on the angle by which 

 the spicule is inclined to the elhpsoid axes; but a very common 

 case will probably be that in which the spicule looks at first sight 

 to be a plane C-shaped figure, but is discovered, on more careful 

 inspection, to he not in one plane but in a more comphcated twist. 

 This investigation includes a series of forms which are abundantly 

 represented among actual sponge-spicules, as illustrated in Figs. 310 

 and 311. ^t^, 



Growth or motion, when confined to some particular curved 

 surface, may appear in various forms and in unexpected places. 

 An amoeba, creeping along the inside or the outside of a glass tube, 

 was found in either case to follow a winding, spiral path : it was 

 really doing its best to go straight — in other words it was following 

 a geodesic or loxodromic path, determined by whatsoever angle of 

 obhquity to the axis of the tube it had chanced to start out upon. 



