The powder was simply pulverized vitriol, that is, ferric sulphate, or sulphate of iron.

There was another and probably an older method of using sympathetic powders and salves; this was to apply the supposed curative to the weapon which caused the wound, instead of the wound itself. In the "Lay of the Last Minstrel," Scott gives an account of the way in which the Lady of Buccleuch applied this occult surgery to the wound of William of Deloraine:

"She drew the splinter from the wound, And with a charm she stanched the blood.

She bade the gash be cleansed and bound: No longer by his couch she stood; But she has ta'en the broken lance.

And washed it from the clotted gore, And salved the splinter o'er and o'er.

William of Deloraine, in trance, Whene'er she turned it round and round Twisted as if she galled his wound.

Then to her maidens she did say, That he should be whole man and sound, Within the course of a night and day.

Full long she toiled, for she did rue Mishap to friend so stout and true."[4]

That no direct benefit could have been derived from such a mode of treatment must be obvious, but De Morgan very plausibly claims that in the then state of surgical and medical knowledge, it was really the very best that could have been adopted. His argument is as follows: "The sympathetic powder was that which cured by anointing the weapon with its salve instead of the wound. I have been long convinced that it was efficacious. The directions were to keep the wound clean and cool, and to take care of diet, rubbing the salve on the knife or sword. If we remember the dreadful notions upon drugs which prevailed, both as to quant.i.ty and quality, we shall readily see that any way of _not_ dressing the wound, would have been useful. If the physicians had taken the hint, had been careful of diet, etc., and had poured the little barrels of medicine down the throat of a practicable doll, _they_ would have had their magical cures as well as the surgeons. Matters are much improved now; the quant.i.ty of medicine given, even by orthodox physicians, would have been called infinitesimal by their professional ancestors. Accordingly, the College of Physicians has a right to abandon its motto, which is, _Ars longa, vita brevis_, meaning, _Practice is long, so life is short_."

As set forth by Digby and others, the use of the Powder of Sympathy is free from all taint of witchcraft or magic, but, in another form, it was wholly dependent upon incantations and other magical performances. This idea of sympathetic action was even carried so far as to lead to attempts to destroy or injure those whom the operator disliked. In some cases this was done by moulding an image in wax which, when formed under proper occult influences, was supposed to have the power of transferring to the victim any injuries inflicted on the image. Into such images pins and knives were thrust in the hope that the living original would suffer the same pains and mutilations that would be inflicted if the knives or pins were thrust into him, and sometimes the waxen form was held before the fire and allowed to melt away slowly in the hope that the prototype would also waste away, and ultimately die. Shakespeare alludes to this in the play of King John. In Act v., Scene 4, line 24, Melun says:

"A quant.i.ty of life Which bleeds away, even as a form of wax, Resolveth from his figure 'gainst the fire?"

And Hollinshed tells us that "it was alleged against Dame Eleanor Cobham and her confederates that they had devised an image of wax, representing the king, which, by their sorcerie, by little and little consumed, intending thereby, in conclusion, to waste and destroy the king's person."

In these cases, however, the operator always depended upon certain occult or demoniacal influences, or, in other words, upon the art of magic, and therefore examples of this kind do not come within the scope of the present volume. In the case of the Powder of Sympathy the results were supposed to be due entirely to natural causes.

FOOTNOTES:

[3] Touching the Cure of Wounds by the Powder of Sympathy. With Instructions how to make the said Powder. Rendered faithfully out of French into English by R. White, Gent. London, 1658.

[4] Canto III. Stanza 23.

A SMALL BUDGET OF PARADOXES, ILLUSIONS, AND MARVELS

THE FOURTH DIMENSION AND THE POSSIBILITY OF A NEW SENSE AND NEW SENSE-ORGAN

This subject has now found its way not only into semi-scientific works but into our general literature and magazines. Even our novel-writers have used suggestions from this hypothesis as part of the machinery of their plots so that it properly finds a place amongst the subjects discussed in this volume.

Various attempts have been made to explain what is meant by "the fourth dimension," but it would seem that thus far the explanations which have been offered are, to most minds, vague and incomprehensible, this latter condition arising from the fact that the ordinary mind is utterly unable to conceive of any such thing as a dimension which cannot be defined in terms of the three with which we are already familiar. And I confess at the start that I labor under the superlative difficulty of not being able to form any conception of a fourth dimension, and for this incapacity my only consolation is, that in this respect I am not alone.

I have conversed upon the subject with many able mathematicians and physicists, and in every case I found that they were in the same predicament as myself, and where I have met men who professed to think it easy to form a conception of a fourth dimension, I have found their ideas, not only in regard to the new hypothesis, but to its correlations with generally accepted physical facts, to be nebulous and inaccurate.

It does not follow, however, that because myself and some others cannot form such a clear conception of a fourth dimension as we can of the third, that, therefore, the theory is erroneous and the alleged conditions non-existent. Some minds of great power and acuteness have been incapable of mastering certain branches of science. Thus Diderot, who was a.s.sociated with d'Alembert, the famous mathematician, in the production of "L'Encyclopedie," and who was not only a man of acknowledged ability, but who, at one time, taught mathematics and wrote upon several mathematical subjects, seems to have been unable to master the elements of algebra. The following anecdote regarding his deficiency in this respect is given by Thiebault and indorsed by Professor De Morgan: At the invitation of the Empress, Catherine II, Diderot paid a visit to the Russian court. He was a brilliant conversationalist and being quite free with his opinions, he gave the younger members of the court circle a good deal of lively atheism. The Empress herself was very much amused, but some of her councillors suggested that it might be desirable to check these expositions of strange doctrines. As Catherine did not like to put a direct muzzle on her guest's tongue, the following plot was contrived. Diderot was informed that a learned mathematician was in possession of an algebraical demonstration of the existence of G.o.d and would give it to him before all the court if he desired to hear it. Diderot gladly consented, and although the name of the mathematician is not given, it is well known to have been Euler. He advanced toward Diderot, and said in French, gravely, and in a tone of perfect conviction: "_Monsieur, (a + b^n) / n = x, therefore, G.o.d exists; reply!_" Diderot, to whom algebra was Hebrew, was embarra.s.sed and disconcerted, while peals of laughter rose on all sides. He asked permission to return to France at once, which was granted.

Even such a mind as that of Buckle, who was generally acknowledged to be a keen-sighted thinker, could not form any idea of a geometrical line--that is, of a line without breadth or thickness, a conception which has been grasped clearly and accurately by thousands of school-boys. He therefore a.s.serts, positively, that there are no lines without breadth, and comes to the following extraordinary conclusions:

"Since, however, the breadth of the faintest line is so slight as to be incapable of measurement, except by an instrument under the microscope, it follows that the a.s.sumption that there can be lines without breadth is so nearly true that our senses, when una.s.sisted by art, can not detect the error. Formerly, and until the invention of the micrometer, in the seventeenth century, it was impossible to detect it at all. Hence, the conclusions of the geometrician approximate so closely to truth that we are justified in accepting them as true. The flaw is too minute to be perceived. But that there is a flaw appears to me certain. It appears certain that, whenever something is kept back in the premises, something must be wanting in the conclusion. In all such cases, the field of inquiry has not been entirely covered; and part of the preliminary facts being suppressed, it must, I think, be admitted that complete truth be unattainable, and that no problem in geometry has been exhaustively solved."[5]

The fallacy which underlies Mr. Buckle's contention is thus clearly exposed by the author of "The Natural History of h.e.l.l."

"If it be conceded that lines have breadth, then all we have to do is to a.s.sign some definite breadth to each line--say the one-thousandth of an inch--and allow for it. But the lines of the geometer have no breadth. All the micrometers of which Mr. Buckle speaks depend, either directly or indirectly, upon lines for their graduations, and the positions of these lines are indicated by rulings or scratches. Now, in even the finest of these rulings, as, for example, those of n.o.bert or Fasoldt, where the ruling or scratching, together with its accompanying s.p.a.ce, amounts to no more than the one hundred and fifty thousandth part of an inch, the scratch has a perceptible breadth. But this broad scratch is not the line recognized by the microscopist, to say nothing of the geometer.

The true line is a line which lies in the very center of this scratch and it is certain that this central line has absolutely no breadth at all."[6]

It must be very evident that if Mr. Buckle's contention that geometrical lines have breadth were true, then some of the fundamental axioms of geometry must be false. It could no longer hold true that "the whole is equal to all its parts taken together," for if we divide a square or a circle into two parts by means of a line which has breadth, the two parts cannot be equal to the whole as it formerly was. As a matter of fact, Mr. Buckle's lines are saw-cuts, not geometrical lines.

Geometrical points, lines, and surfaces, have no material existence and can have none. An ideal conception and a material existence are two very different things.

A very interesting book[7] has been written on the movements and feelings of the inhabitants of a world of two dimensions. Nevertheless, if we know anything at all, we know that such a world could not have any actual existence and when we attempt to form any mental conception of it and its inhabitants, we are compelled to adopt, to a certain extent, the idea of the third dimension.

But at the same time we must remember that since the ordinary mechanic and the school-boy who has studied geometry, find no difficulty in conceiving of points without magnitude, lines without breadth, and surfaces without thickness--conceptions which seem to have been impossible to Buckle, a man of acknowledged ability--it may be possible that minds const.i.tuted slightly differently from that of myself and some others, might, perhaps, be able to form a conception of a fourth dimension.

Leaving out of consideration the speculations of those who have woven this idea into romances and day-dreams we find that the hypothesis of a fourth dimension has been presented by two very different cla.s.ses of thinkers, and the discussion has been carried on from two very different standpoints.

The first suggestion of this hypothesis seems to have come from Kant and Gauss and to have had a purely metaphysical origin, for, although attempts have been made to trace the idea back to the famous phantoms of Plato, it is evident that the ideas then advanced had nothing in common with the modern theory of the existence of a fourth dimension. The first hint seems to have been a purely mathematical one and did not attract any very general attention. It was, however, seized upon by a certain branch of the transcendentalists, closely allied to the spiritualists, and was exploited by them as a possible explanation of some curious and mysterious phenomena and feats exhibited by certain Indian and European devotees. This may have been done merely for the purpose of mystifying and confounding their adversaries by bringing forward a striking ill.u.s.tration of Hamlet's famous dictum--

"There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy."

A very fair statement of this view is thus given by Edward Carpenter:[8]

"There is another idea which modern science has been familiarizing us with, and which is bringing us towards the same conception--that, namely, of the fourth dimension. The supposition that the actual world has four s.p.a.ce-dimensions instead of three makes many things conceivable which otherwise would be incredible. It makes it conceivable that apparently separate objects, e. g., distinct people, are really physically united; that things apparently sundered by enormous distances of s.p.a.ce are really quite together; that a person or other object might pa.s.s in and out of a closed room without disturbance of walls, doors or windows, etc., and if this fourth dimension were to become a factor of our consciousness it is obvious that we should have means of knowledge which, to the ordinary sense, would appear simply miraculous. There is much, apparently, to suggest that the consciousness attained to by the Indian gnanis in their degree, and by hypnotic subjects in theirs, is of this fourth dimensional order.

"As a solid is related to its own surface, so, it would appear, is the cosmic consciousness related to the ordinary consciousness. The phases of the personal consciousness are but different facets of the other consciousness; and experiences which seem remote from each other in the individual are perhaps all equally near in the universal. s.p.a.ce itself, as we know it, may be practically annihilated in the consciousness of a larger s.p.a.ce, of which it is but the superficies; and a person living in London may not unlikely find that he has a back door opening quite simply and unceremoniously out in Bombay."

On the other hand, the mathematicians, looking at it as a purely speculative idea, have endeavored to arrive at definite conclusions in regard to what would be the condition of things if the universe really exists in a fourth, or even in some higher dimension. Professor W. W. R.

Ball tells us that

"the conception of a world of more than three dimensions is facilitated by the fact that there is no difficulty in imagining a world confined to only two dimensions--which we may take for simplicity to be plane--though equally well it might be a spherical or other surface. We may picture the inhabitants of flatland as moving either on the surface of a plane or between two parallel and adjacent planes. They could move in any direction along the plane, but they could not move perpendicularly to it, and would have no consciousness that such a motion was possible. We may suppose them to have no thickness, in which case they would be mere geometrical abstractions; or we may think of them as having a small but uniform thickness, in which case they would be realities."

"If an inhabitant of flatland was able to move in three dimensions, he would be credited with supernatural powers by those who were unable so to move; for he could appear or disappear at will; could (so far as they could tell) create matter or destroy it, and would be free from so many constraints to which the other inhabitants were subject that his actions would be inexplicable to them."

"Our conscious life is in three dimensions, and naturally the idea occurs whether there may not be a fourth dimension. No inhabitant of flatland could realize what life in three dimensions would mean, though, if he evolved an a.n.a.lytical geometry applicable to the world in which he lived, he might be able to extend it so as to obtain results true of that world in three dimensions which would be to him unknown and inconceivable. Similarly we cannot realize what life in four dimensions is like, though we can use a.n.a.lytical geometry to obtain results true of that world, or even of worlds of higher dimensions. Moreover, the a.n.a.logy of our position to the inhabitants of flatland enables us to form some idea of how inhabitants of s.p.a.ce of four dimensions would regard us."

"If a finite solid was pa.s.sed slowly through flatland, the inhabitants would be conscious only of that part of it which was in their plane. Thus they would see the shape of the object gradually change and ultimately vanish. In the same way, if a body of four dimensions was pa.s.sed through our s.p.a.ce, we should be conscious of it only as a solid body (namely, the section of the body by our s.p.a.ce) whose form and appearance gradually changed and perhaps ultimately vanished. It has been suggested that the birth, growth, life, and death of animals, may be explained thus as the pa.s.sage of finite four-dimensional bodies through our three-dimensional s.p.a.ce."

Attempts have been made to construct drawings and models showing a four-dimensional body. The success of such attempts has not been very encouraging.

Investigators of this cla.s.s look upon the actuality of a fourth dimension as an unsolved question, but they hold that, provided we could see our way clear to adopt it, it would open up wondrous possibilities in the way of explaining abstruse and hitherto inexplicable physical conditions and phenomena.

There is obviously no limit to such speculations, provided we a.s.sume the existence of such conditions as are needed for our purpose. Too often, however, those who indulge in such day-dreams begin by a.s.suming the impossible, and end by imagining the absurd.

We have so little positive knowledge in regard to the ultimate const.i.tution of matter and even in regard to the actual character of the objects around us, which are revealed to us through our senses, that the field in which our imagination may revel is boundless. Perhaps some day the humanity of the present will merge itself into a new race, endowed with new senses, whose revelations are to us, for the present, at least, utterly inconceivable.

The possibility of such a development may be rendered more clear if we imagine the existence of a race devoid of the sense of hearing, and without the organs necessary to that sense. They certainly could form no idea of sound, far less could they enjoy music or oratory, such as afford us so much delight. And, if one or more of our race should visit these people, how very strange to them would appear those curious appendages, called ears, which project from the sides of our heads, and how inexplicable to them would be the movements and expressions of intelligence which we show when we talk or sing? It is certain that no development of the physical or mathematical sciences could give them any idea whatever of the sensations which sound, in its various modifications, imparts to us, and neither can any progress in that direction enable us to acquire any idea of the revelations which a new sense might open up to us. Nevertheless, it seems to me that the development of new senses and new sense organs is not only more likely to be possible, but that it is actually more probable, than any revelation in regard to a fourth dimension.