I may mention here that I have witnessed these phenomena myself under good observing conditions and that I am prepared to certify in the most unequivocal manner that they are absolutely authentic; that is to say the result neither of fraud--conscious or unconscious--nor of illusion. Indeed, I do not suppose that an intelligent person could suppose them to be due to anything of the sort after a careful study of Dr. Crawford's book, quite apart from any personal observation and I only add my own testimony as a small make-weight for what it may be worth. We are here confronted with a sort of mechanical paradox. How can we conceive that the structure manages to combine the contrary attributes of rigidity and impalpability? Rigidity means simply the power of resisting deformation under stress. That is to say that in order for a body to be rigid it must be capable of developing within itself forces which shall counteract those which tend to deform it. If we apply a stress--a deforming force--to a rigid body, then this force must be met by some opposing force; otherwise the body will be deformed. Normally this is a matter of molecular cohesion, etc. Now, this structure resists deformation under stress, and it therefore follows that the deforming forces must be counteracted by opposing forces. But the structure is impalpable, and we can pass a rod through it in any direction without encountering any resistance. This being so it is difficult to conceive how the forces resisting deformation can be applied from any direction in which we can move the rod, _i.e._, from any direction known and accessible to us. The more one tries to think out what is involved in the idea of an impalpable and yet rigid structure, the more hopeless it seems. But I think that the concept of four-dimensional space will help us even here. We know two things. First that the structure is rigid and therefore that the deforming stresses are counteracted by opposing forces and, second, that these opposing forces are apparently not applied from any direction with which we are acquainted. But is it not possible that they may be applied from some direction with which we are _not_ acquainted? From some direction, in fact, of which the hypothetical fourth rectangular axis of space is a component. Is it possible that the matter which is drawn from the body of the medium, and which forms the structure, is composed of molecules whose atoms are arranged not in space of three dimensions but in space of four dimensions? I do not say that this is necessarily so; but I must confess that to me it looks rather like it. Still less am I prepared to say that the atoms are arranged four dimensionally. We do not know enough for that yet. But it is, I think, a possibility, although for all I know to the contrary there may be many other ways in which forces operating in four space might act on three-dimensional atoms and molecules. Consider a two-dimensional analogy again.