“Qualis ab incepto” shall be the motto of this twelfth letter, the materials of which were undreamt of by me, when some three months ago I remitted the new and corrected edition of “the Letters” to England. The occasion which led me to the knowledge of the facts I have to mention, and their bearing, tally curiously with what has gone before.

For it is again winter, with its long, solitary evenings, against the tedium of which I had to seek a resource; and I bethought me, this time, of occupying myself with looking into the higher mathematics. Accordingly I sent to Herr Caspari, professor of mathematics in the gymnasium at Boppard, to solicit him to give me the instruction and assistance which I needed. And he obligingly came, in the evening of the 31st of December, to sit by my side and converse with me. And I went over preliminarily my schoolboy recollections of the elements of mathematics, and was pleased at finding the remembered difficulties vanish before the explanations of my well-informed tutor. And I learned, to my vast delight, that the inability under which asymptotes labour to touch hyperbolas is a purely arbitrary one, like the legislative prohibition not to marry with one’s deceased wife’s sister; but that, unlike the latter, it can be evaded; inasmuch as an asymptote, by changing its name and forfeiting its properties, may at any time unite itself with the object to which it had before been infinitely near. Again, I found my boyish distrust and disbelief in sines and cosines replaced by an intelligent and well-satisfied acquaintance with them. And I even obtained a glimpse of the higher analysis itself, pointing with its unerring finger to the exact height, else unmeasurable, at which my candle should stand in the centre of my round table, to shed upon it its maximum of illumination.

A liberal hour being over, and my dolphin-like recreation ended, my new friend entered into desultory chat, and asked me, among other things, if I had not written something on the divining-rod. I replied to his question by giving him the copy I had of “the Letters;” and promised, as a New-Year’s gift for the morrow, to present him with the implement itself. And I lent him Von Reichenbach’s book on Od, with which he was unacquainted. Then he told me that there were two or three experiments, possibly akin to trials with the divining-rod, with which he had been familiar for years, and which he had shown to many without receiving an explanation of them. He said that as far as he knew they were original and his own; and that he would willingly show them to me. He wanted only for that purpose a piece of silver, a gold ring, and a bit of silk. These were easily found. And he attached the silk to the ring, which he then held suspended by the silk over a silver spoon, at a distance of half an inch.

Shortly the ring shaped its first vague movements into regular oscillations in a direction to and fro, or towards and from, Herr Caspari. I will call such oscillations longitudinal. It was evident to me, that this phenomenon must be akin to the motion of the divining-rod.

Then, at Herr Caspari’s suggestion, I summoned the maid, who was directed to place her hand in Herr Caspari’s disengaged hand. On her doing so, the oscillations of the ring became transverse. How pregnant was this fact! An Od-current had been established between the two experimenters; and the apparent influence of the two metals on each other had been modified.

Herr Caspari told me that, as far as he knew, these experiments would only succeed when made with silver and gold, and a bit of silk. But he said that he had still another experiment to show me, which he did the following day. He said he had a little pea-like bit of something, which he had been told was schwefel-kies, that exhibited another motion: when held suspended by silk over either of the fingers, it rotated one way; when held suspended over the thumb, it rotated in the contrary direction.

Herr Caspari left me, after agreeing to assist me in the further examination of these phenomena; and the New Year coming in found me in busy thought how to elicit, through variations of Herr Caspari’s experiments, some important physical evidence as to the reality and agency of Von Reichenbach’s Od-force.

In ten days we have succeeded in disentangling the confused results which attended our first experiments; and as I see no likelihood of extending them at present in any new direction, I present them to the reader now, as complete as I can at present render them. I have used the term “divining-ring,” partly because I have a vague idea of having seen Herr Caspari’s first facts adverted to in some publication under that name; partly because it is really thus far deserved:—If you place a piece of silver on a table, and lay over the table and it an unfolded silk pocket-handkerchief, you can discover where the silver lies by trying with the suspended ring each part of the surface. The ring will only oscillate when held over the silver. But now I have to substitute another name for the sake of precision.

A fragment of any thing, of any shape, suspended either by silk or cotton thread, the other end of which is wound round the first joint either of the forefinger or of the thumb, I will call an Odometer. The length of the thread does not matter. It must be sufficient to allow the ring, or whatever it is, to reach to about half an inch from the table, against which you rest your arm or elbow to steady your hand. If there be nothing on the table, the ring or its equivalent soon becomes stationary. Then you test the powers of the odometer by placing upon the table under it what substances you please. These I would call Od-subjects.

To obtain uniform results with the Odometer, it is important to attach the sustaining thread always to the same finger of the same hand,—best to the forefinger of the right hand. It is evident that this rule is not to prevent the experimenter, when he has succeeded in thus obtaining a series of consistent results, from trying what will come of substituting his other digits for that first employed.

I have armed the odometer with gold, silver, lead, zinc, iron, copper; with coal, bone, horn, dry wood, charcoal, cinder, glass, soap, wax, sealing-wax, shell-lac, sulphur, earthenware. As Od-subjects I have likewise tried most of the substances above enumerated. All do not go equally well, or perform exactly the same feats, with each odometer. For example, an odometer of dry wood remains stationary over gold; while it oscillates with great vivacity over glass. The respective habitudes of different odometers to different Od-subjects is one of the simplest points of investigation which the facts I am narrating suggest.

A gold ring with a plain stone in it was the first odometer which I employed, and it is one of the most largely available. And gold forms in general the most successful Od-subject. Sulphur likewise displays very lively motions in the odometer. But the material which I finally employed to verify the following phenomena was shell-lac, a portion a full inch long, broader towards the lower end, then cut to be lancet-shaped. The odometer moves more sluggishly with some than with others, and in the same hand on different days; and doubtless is capable of manifesting a greater variety of effects than I have yet elicited from it. I can only pledge myself to the certainty of my being always now able to obtain with the shell-lac odometer all the results mentioned in the XXVII. experiments which first follow. Over rock-crystal, however, the shell-lac odometer acts very feebly; but a glass odometer moves with brilliant vivacity. I would besides advise the reader to try a gold-ring odometer, in preference, for experiments X., XI., XII., XIII.

Then here are the results:—

I. Odometer (we will suppose armed with shell-lac) held over three sovereigns heaped loosely together to form the Od-subject; the odometer suspended from the right forefinger of a competent person of the male sex. Result—Longitudinal oscillations.

II. Let the experimenter, continuing experiment I., take with his unengaged hand the hand of a person of the opposite sex. Result—Transverse oscillations of the odometer.

III. Then, the experiment being continued, let a person of the sex of the experimenter take and hold the unengaged hand of the second party. Result—Longitudinal oscillations of the odometer.

IV. Repeat experiment I., and, the longitudinal oscillations being established, touch the forefinger which is engaged in the odometer with the forefinger of your other hand. Result—The oscillations become transverse.

V. Repeat experiment I., and, the longitudinal oscillations being established, bring the thumb of the same hand into contact with the finger implicated in the odometer. Result—The oscillations become transverse.

VI. Then, continuing experiment V., let a person of the same sex take and hold your unengaged hand. Result—The oscillations become again longitudinal.

VII. Experiment I. being repeated, take and hold in your disengaged hand two or three sovereigns. Result—The oscillations become transverse.

VIII. Continuing experiment VII., let a person of the same sex take and hold your hand which holds the sovereigns. Result—The oscillations become longitudinal.

IX. If the odometer be attached to the thumb instead of to the forefinger, it oscillates longitudinally; but on approaching the thumb so as to touch the forefinger, the oscillations become of course transverse.

X. Repeat experiment I., but let the Od-subject be a double row of five sovereigns, each disposed longitudinally from you, and hold the odometer over the middle of the double row of sovereigns. Result—Longitudinal oscillations, but the excursions are inordinately long. Still, on touching the forefinger with the thumb, the oscillations become either transverse, or the odometer moves in an ellipse, of which the long axis corresponds with the axis of the double line of sovereigns.

XI. Dispose ten sovereigns longitudinally from you in two parallel rows, an inch and a half apart, and hold the odometer over the middle of the interval. Result—Longitudinal oscillations.

XII. Modify experiment XI. by holding the odometer not midway, but nearer one of the rows of sovereigns. Result—Oblique oscillations.

XIII. Dispose ten sovereigns heaped in a short longitudinal group, and hold the odometer over the table half an inch to one side of the middle of the heap. Result—Transverse oscillations.

From the latter experiments and their modifications, it became evident that the magnitude and shape of the Od-subject have each a direct influence on the result. A greater force of attraction evidently exists towards the greater mass.

XIV. Odometer held over the northward pole of a magnetic needle contained in a compass-box under glass. Result—Rotatory motion in the direction of the hands of a watch.

XV. Odometer held over the southward pole. Result—Rotatory motion in the direction contrary to the motion of the hands of a watch.

XVI. Repeat experiments XIV. and XV., with the difference of touching the forefinger implicated in the odometer with the thumb of the same hand. Results—The rotatory motions observed in the two experiments referred to become exactly reversed.

XVII. Hold the odometer over the centre of the needle. Result—Oscillations at right angles, or transverse, to the axis of the needle.

XVIII. Hold the odometer over, and half an inch to one side of, the centre of the needle. Result—Oscillations parallel to the axis of the needle.

XIX. Repeat experiment XIV. Then, during its continuance, place a pile of three sovereigns on the compass-box, in front of the northward pole of the needle, and about an inch from it. Result—Direction of original rotatory motion reversed.

Then follow experiments with results exactly parallel to the preceding, having the greatest physiological interest.

XX. Hold the odometer over the tip of the forefinger of your disengaged hand. Result—Rotatory motion in the direction of the hands of a watch.

XXI. Hold the odometer over the thumb of your disengaged hand. Result—Rotatory motion against that of the hands of a watch.

XXII. Hold up the forefinger and thumb of the disengaged hand, their points being at two and a half inches apart. Hold the odometer in the centre of a line which would join the points of the finger and thumb. Result—Oscillations transverse to the line indicated.

XXIII. Modify the preceding experiment by holding the odometer half an inch to one side of, and over, the middle of the line indicated. Result—Oscillations parallel to the said line.

XXIV. Modify experiment XXIII. by approximating the ends of the forefinger and thumb of the disengaged hand, so that they touch. Result—The odometer no longer moves.

XXV. Forefinger and thumb of the disengaged hand held upwards and apart, sustaining a short file longwise between them. Odometer then held over the last joint of the finger. Result—Odometer stationary. Odometer then held over the last joint of the thumb. Result—Odometer stationary.

XXVI. Odometer held over the northward pole of the magnetic needle, and its consequent rotatory motion in the direction of that of the hands of a watch established. Then advance the finger or the thumb of the other hand towards the odometer. (The odometer should be held in these experiments half an inch above, and a little wide of, or before, the apex of the needle.) The finger, or the thumb, is then to be brought as near to the odometer as is consistent with not touching it in its rotation. Result—Direction of the rotation reversed. Then join the finger and thumb, and hold the two thus brought into contact in the same proximity to the odometer. Result—The rotation returns to the former direction; that is, to the direction of the motion of the hands of a watch.

XXVII. Odometer held over the radial (or thumb) edge of the wrist. Result—The same as when held over thumb. Odometer held over the little-finger edge of the wrist. Result—The same as when held over either of the fingers. This difference in result extends a third the length of the fore-arm, over the middle of which the odometer becomes stationary.

XXVIII. A portion of rock-crystal five inches long, about two wide and deep, placed on the table with its long axis transverse to the operator. Glass odometer held over the middle of the upper plain surface. Result—Oscillations parallel to the axis of the crystal. Position of the crystal shifted, so as to make its axis point from the operator. Result—Oscillations as before parallel to the axis of the crystal, but longitudinal to the operator. Then the thumb applied to the forefinger. Result—Transverse oscillations.

XXIX. Glass odometer held suspended over one apex of the crystal. Result—Rotatory motion in the direction of the hands of a watch. Odometer held over the opposite end. Result—Rotation in the direction contrary to that of the hands of a watch.

XXX. The last experiment repeated. The forefinger of the operator’s unengaged hand brought near to the odometer in each of its two varieties. Result—The previous rotatory motion reversed. Then the point of the thumb brought into contact with the odometer finger. Result—The original rotatory motion re-established.

I will add in reference to the first and simplest experiments, that the interposition of several folds of silk between the Od-subject and the odometer renders the motions of the latter less brisk.

The development which I have thus given to the few, isolated, and long-hoarded experiments of Herr Caspari, was not so simple an affair as it may seem to be. For several days I was in doubt as to the genuineness of the results, so capricious and contradictory were they. It was only when I had discovered, first, the reversing effect of touching the odometer finger with the thumb of the same hand, and, secondly, that approaching the thumb towards the odometer finger, or even allowing the other fingers of the odometer hand to close upon the ball of the thumb, has the same effect with bringing the point of the thumb into contact with the odometer finger, that I succeeded in obtaining unvarying results. The interest of these experiments is unquestionably very considerable. They open a new vein of research, and establish a new bond of connexion between physical and physiological science, which cannot fail to promote the advancement of both. They contribute a mass of objective and physical evidence to give support and substantiality to the subjective results of Von Reichenbach’s experiments. They tend to prove the existence of some universal force, such as that to which he has given theoretical form and consistence under the designation of Od. And such a universal force, what other can we deem it to be than the long-vilipended influence of Mesmer, rendered bright and transparent and palatable by passing through the filter of science?