Ixxx 
THE VOYAGE OF H.M.S. CHALLENGER. 
spicules by their accumulation produce. In the higher forms of the family the radial 
spicules alone are developed ; for this I am not prepared with an explanation. In many 
of the Stellettidse and the Geodiidee the same absence of transversely disposed spicules is 
also a constant characteristic. 
If instead of a sigmaspire we consider an aster situated in the interior of the sponge, 
and enlarging by growth into a megasclere, the results will be but slightly dijBferent, in 
some cases the radial tensions will lead to the overdevelopment of the two actines which 
lie in the line of growth and the remainder will be suppressed, so that an oxea will 
result ; and in other cases some of the actines will be developed under the action of the 
transverse tensions, or rather of tensions which are the resultants of the transverse and 
radial tensions, the result of this might be the development of a triaxon spicule with six 
actines, or of a calthrops ; in some sponges the triaxon and in others the calthrops is 
produced ; in the Tetractinellida it is characteristically a calthrops, as on d priori grounds 
might have been expected. Thus in this case there are not two sets of oxeas, developed 
one along lines of transverse, and the other along lines of radial strain, as in the Tetillidae, 
but the different actines of the same spicule are some directed radially and some trans- 
versely, as in the Pachastrellidse. 
The effect of the tangential strains at the surface of the sponge may be best 
considered by first studying the effects of a uniformly distributed strain on a thin 
pellicle which yields by fissuring. The fissures so produced are rectilinear and intersect 
either at right angles, producing a rectangular system of cracks, or at angles of 60° or 120°, 
producing a system of hexagons or equilateral triangles ; the hexagons, since they present 
the smallest perimeter in relation to the area, are the most likely to result. Triradiate 
fissures thus produced have given rise to the hexagonal form of basaltic columns. The 
rectangular cracks are common in the glaze of “ crackled ” pottery. Though in the skin 
of the sponge actual fissures are not produced yet the lines along which they tend to be 
produced are lines of least resistance, and if spicules or the actines of spicules tend as we 
maintain to develop along such lines, we should expect to find them symmetrically 
arranged so as to form rectangular, hexagonal, or triangular areas, and on the principle of 
least action as already suggested, we should expect rather to find a hexagonal system 
than either of the others. And this or the triangular system is actually that which is 
most commonly met with in the dermal skeleton, not only in the Tetractinellida, but in 
the simpler Calcisponges, in the horny Sponges, the Monaxonida, and outside the Sponges 
altogether in the Eadiolarian test {Haliomma, &c,), and in the spicules and skeletal 
network of the Echinodermata ; the rectangular system occurs both in the Eadiolaria 
and the Echinodermata, and in the Hexactinellid Sponges. 
The application of these conclusions to the interpretation of the forms of sponge 
spicules is obvious ; take the case of a rhabdus spicule growing under the infiuence of 
radial tensions within the interior of the sponge till it meets the skin ; here it meets an 
