to consider, and the conditions by which they are at least partially defined.
Among the several possible, or conceivable, types of microscopic skeletons let us choose, to begin with, the case of a spicule, more or less simply linear as far as its intrinsic powers of growth are {440} concerned, but which owes its now somewhat complicated form to a restraint imposed by the individual cell to which it is confined, and within whose bounds it is generated. The conception of a spicule developed under such conditions we owe to a distinguished physicist, the late Professor G. F. FitzGerald.
Many years ago, Sollas pointed out that if a spicule begin to grow in some particular way, presumably under the control or constraint imposed by the organism, it continues to grow by further chemical deposition in the same form or direction even after it has got beyond the boundaries of the organism or its cells. This phenomenon is what we see in, and this imperfect explanation goes so far to account for, the continued growth in straight lines of the long calcareous spines of Globigerina or Hastigerina, or the similarly radiating but siliceous spicules of many Radiolaria. In physical language, if our crystalline structure has once begun to be laid down in a definite orientation, further additions tend to accrue in a like regular fashion and in an identical direction; and this corresponds to the phenomenon of so-called ãorientirte Adsorption,ã as described by Lehmann.
In Globigerina or in Acanthocystis the long needles grow out freely into the surrounding medium, with nothing to impede their rectilinear growth and their apôÙproxôÙiôÙmateôÙly radiate distribution. But let us consider some simple cases to illustrate the forms which a spicule will tend to assume when, striving (as it were) to grow straight, it comes under the influence of some simple and constant restraint or compulsion.
If we take any two points on some curved surface, such as that of a sphere or an ellipsoid, and imagine a string stretched between them, we obtain what is known in mathematics as a ãgeodeticã curve. It is the shortest line which can be traced between the two points, upon the surface itself; and the most familiar of all cases, from which the name is derived, is that curve upon the earthãs surface which the navigator learns to follow in the practice of ãgreat-circle sailing.ã Where the surface is spherical, the geodetic is always literally a ãgreat circle,ã a circle, that is to say, whose centre is the