In their search for others things, Von Osten, Krall, and the Moekels have brought out clearly among various other facts, without exactly accounting for it, the fundamental fact of the existence in the animal of a psychic substratum predisposed in some manner to arithmetic. I say "in some manner," and by that I do not wish to prejudge any particular view of the argument; and above all I do not make of this predisposition or mathematical permeability, a criterion of intelligence. I do not forget either the mentally deficient or the prodigies among child calculators, etc. But likewise I cannot forget another thing: that all organisms are already throughout permeated with mathematics, and that the more we descend the scale, from man down to the most "simple" biological fact, the more nearly we approach to physics, which is nothing but mathematics. I have not the space here to digress on the intermediate gradations. Besides, I have already done so, in part at least, elsewhere. But I wish to recall the curious coincidence that the mathematical achievements of the Elberfeld horses were much more brilliant and much more prodigious than those of the dogs which have up to now been experimented on. And horses in the phylo-genetic line are more ancient than dogs: they are lower in the zoologic scale. Much lower still, i.e. among the Arthropoda, occur many other mathematical wonders. I only mention in a cursory way the logarithmic spiral of the spider's web, the precise curves realized without instruments of any kind by the Coleoptera and Hymenoptera in cutting leaves, the stereometry of the aphides. Then, as it were, at the bottom of the scale (if one may still speak of a descent and a bottom) the marvellous plancton filters of the Appendiculata; the geometrical spots of the Amoebae; the cases of perfect forms of so many other Protozoa; and, finally, think of the constructive technic of the static organs, or of those of movement either in man or animals or plants; think of the complex mathematics of the mitosi, or of any cell proceeding to its own indirect division. It seems to me clear that the mathematical faculty--assuming always, let it be understood, that it may give rise to more or less conscious phenomena in the biological subject--may be amongst the most natural of imaginable causes, and that even the smallest amount of consciousness may help this existing capacity in the animal to express itself. That we are concerned with an expression by raps or not, does not seem to me as important as a proper estimation of the importance of the central fact constituted by this mathematical capacity.