CH. X] ON GEODETICS 489 



menon is often witnessed in the splitting of a glass tube. If a 

 crack appear in a thin tube, such as a test-tube, it has a tendency 

 to be prolonged in its own direction, and the more perfectly 

 homogeneous and isotropic be the glass the more evenly will the 

 split tend to follow the straight course in which it began. As 

 a result, the crack in our test-tube is often seen to continue till 

 the tube is spht into a continuous spiral ribbon. 



In a right cone, the spiral geodetic falls into closer and closer 

 coils as the diameter of the cone narrows ; and a very beautiful 

 geodetic of this kind is exempUfied in the sutural line of a spiral 

 shell, such as Turritella, or in the striations which run parallel 

 with the spiral suture. Similarly, in an elUpsoidal surface, we 

 have a spiral geodetic, whose coils get closer together as we 

 approach the ends of the long axis of the elhpse ; in the sphtting 

 of the integument of- an Equisetum-spore, by which are formed 

 the spiral "elaters" of the spore, we have a case of this kind, 

 though the spiral is not sufficiently prolonged to shew all its 

 features in detail. 



We have seen in these various cases, that our original definition 

 of a geodetic requires to be modified; for it is only subject to 

 conditions that it is "the shortest distance between two points 

 on the surface of the sohd," and one of the commonest of these 

 restricting conditions is that our geodetic may be constrained to 

 go twice, or many times, round the surface on its way. In short, 

 we must redefine our geodetic, as a curve drawn upon a surface, 

 such that, if we take any two adjacent points on the curve, 

 the curve gives the shortest distance between them. Again, 

 in the geodetic systems which we meet with in morphology, it 

 sometimes happens that we have two opposite systems of geodetic 

 spirals separate and distinct from one another, as in Fig. 236, c ; 

 and it is also common to find the two systems interfering with 

 one another, and forming a criss-cross, or reticulated arrangement. 

 This is a very common source of reticulated patterns. 



Among the cihated Infusoria, we have in the spiral lines along 

 which their ciha are arranged a great variety of beautiful geodetic 

 curves; though it is probable enough that in some complicated 

 cases these are not simple geodetics, but projections of curves 

 other than a straight line upon the surface of the solid. 



