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On Infinitesimal Doses.
To the Editors of the 'British Journal of Homoeopathy.'
Gentlemen,—Possibly the appeals lately made by Dr. Black and others for experimentation with what may be called reasonable doses of drugs homceopathically indicated may be helped forward by serious consideration of the following statement of facts which probably not one in a hundred of our practitioners has fairly looked in the face.
The first centesimal dilution of a drug contains ordinarily one hundredth of a drop of the mother tincture, or one hundredth of a grain of the crude substance. As all further dilutions are made by adding ninety-nine drops of Spirit, vini to one drop of the dilution below, the second dilution will contain one ten thousandth of the original drop or grain, the third one millionth and so on. And the simple rule results that in order to know what fraction of the mother tincture or crude drug we have in any dilution, it is necessary only to place double that number of ciphers after unity as the denominator of a fraction with unity for its numerator.
As an instance take the 3rd centesimal. After the figure I add six ciphers for the ^denominator, and write 1 for the numerator thus r,isW,'<nny> or one millionth.
It will therefore be seen that the fraction which will represent the quantity of the actual drug contained in the thirtieth dilution of any medicine will be one identical with that given for the 3rd, except that in place of six ciphers there will be sixty.
Dilution No. 3 as above shown contains one part of the drug, in one million parts of the Spirit, vini; and when we get to dilution No. 6 the quantity of spirits of wine to each drop of the drug will have mounted up not to the double of the million, be it observed, but to a billion of drops, that is, to a million millions, a proportion inconceivably large.
In truth as soon as dilution has gone beyond No. 3 or the millionth, the mind fails to grasp the figures which represent the proportion of the diluent.
I have said that sixty ciphers must find place in the denominator of the fraction which will represent the quantity of a drop in the 30th dilution, but some of our physicians are using the 200th dilution (or suppose themselves to be using it), and for the fraction representing the quantity of any drug which the 200th dilution would contain Foub Hundbed Ciphers would be necessary.
Has any serious thought been given to this?
Perhaps the following may help some to think.
The pharmacopoeia gives 76,800 as the number of minims in a gallon. Say that there are 10,000 drops in a gallon, for we can afford to cast in any number of odd thousands or millions without affecting appreciably the stupendous aggregates with which we have to deal. Sixty ciphers in the denominator represent the 30th dilution; strike off four of these and the remaining fifty-six with the unit preceding them will represent the number of gallons of spirits of crude wine with which a single drop or grain of any drug must be mixed in order to give the said 30th dilution.
Now, as this number of gallons is altogether beyond conception as a mere statement of figures, consider the following.
If a person were to drink a gallon of water every second for one year, the quantity drank would be 31,536,000 or say 32,000,000 gallons. If for a million of years a million of gallons were drank every second, the thirty-two would be followed by only eighteen ciphers. But all this quantity would be simply as nothing in comparison with the amount needed to mix with a single drop or grain of any drug in order to form the 30th dilution.
I have not the data for the calculation, but I question whether the whole bed of the Thames from its source to the sea contains the quantity of water that would be needed to mix with a single grain of any drug in order to turn the whole into the 200th dilution.
Think of one grain of common salt or one drop of aconite mixed with all the water in the Thames, and one drop (or a million gallons if you like) of this mixture given with any expectation of possible effect.
Recollect that if for millions of millions of years the patient were every second to swallow millions of millions of gallons, he could not succeed in getting into his stomach the millionth part of a drop or grain of any mother tincture or crude drug.
Can any mistake be shown in this? If not what answer has any sane man who deals in these dilutions (delusions had almost slipped from my pen)?
I am not suggesting that these dilutions cannot easily be made with very small quantities of the diluting fluid ; ninety-nine drops for each dilution, if only any one could be trusted to have made them. "What I desire to call attention to is the quality of the drug contained in the 30th (not to say the 200th) dilution, supposing them honestly prepared.
I trust that you and your readers will feel that this is a matter to be most seriously dealt with.
If those who are in the habit of prescribing one drop of a vast river with which at its source one grain of a drug was mixed have no other ground to rest on than thin fallible judgment as to what seemed to be results, the allopath who gives his scruples and drachms has far more justification when he asks you to rely on his experience as sufficient evidence that he beneficially affects the course of disease by his treatment. In his case it may be admitted that effects of some kind will be produced, and the only question will be whether they are curative. In the case of the high dilutionist, the first question will be as to the possibility of any fractional part being forthcoming of the evidence which ordinary intelligence must require before it can assent to what is so utterly inconceivable.—Fours, &c., N.
[We think our anonymous correspondent can hardly be fully acquainted with homoeopathic literature if he thinks that the mere numerical aspect of dilution has not been repeatedly presented. But we give place to his remarks, as it may be useful from time to time to bring the facts before the busy practitioner. We are under the impression that the above statement considerably underrates the bulk of the total mass required to dilute, to ensure the attenuation within the 30th. We have likewise a novelty in our
VOL. XXXII, NO. CXXVII. JANUARY, 1874. M
correspondent's letter in that he writes out at length the denominator of the fraction corresponding to the 200th dilution, but we have not space to reproduce it, as it occupies 43-J inches at the rate of 9"17 ciphers to the inch.
We fear our correspondent is rather sanguine as to the effect that the mere statement uf these facts must have on rational beings having any influence on high dilutionists, for we find no longer ago than August, 1872, Dr. H. Hartlaub writing thus: "In homoeopathy it is not with small doses that we have to do, but with immaterial doses; these are the peculiarity of homoeopathy, and it is these which place a boundary between what belongs to homoeopathy and what is foreign to it." And again: "The homoeopathic preparation of medicines has for its object not the dilution nor the decomposition of the matter, but the removal of it altogether." And again: "To constitute true homoeopathy we reckon not only the simile strictly according to the proving on the healthy, as well as single medicines without any foreign admixture, but also the immaterial dose, which is that without which the total mass has neither spirit nor life. With this spirit and life of the medicine stands or falls the spirit and life of the whole of homoeopathy" (Allgem. Horn. Zeitung, August, 1872). Against ideas like this what avail all the wealth of facts and reasoning offered to us by physics, chemistry and physiology? We can only protest against and repudiate the pretentious presumption of such dreamers to put forward their silly speculations as the creed of the homoeopathic school. It is almost sufficient to quote one paragraph from Hahnemann to dispose of these pretensions. In the Organon, 5th edit., p. 288, we find the following words addressed to those who doubt the possibility of the action of the ordinary homoeopathic dilutions: "They may learn from the mathematician that a substance when divided into ever so many parts still contains in the smallest imaginable part some of the substance, and the smallest imaginable part cannot cease to be some portion of this substance and thus cannot possibly become nothing" [i.e. immaterial].
But as the old vague notions of spiritual essences as the cause of the properties or qualities of things, and the possibility of a separation of those spiritual essences from the matter to which they were supposed to be attached by a not insoluble bond, may still lie at the root of that credulity and want of true philosophical method which is conspicuous in dealing with the ." potency" question by all so-called high dilutionists, it may be well to say a few words on the subject in its old form and in the newer one of a "force" supposed to be capable of being set free. Hahnemann unfortunately for a time fell into the chemical blunder of supposing that Causticum was the "principle of causticity" which was detached from an alkali and held in combination for the time by an indifferent substance. But this was speedily recognised as an error. Nevertheless a similar idea of the possible detachment of the specific virtue of medicine from the material substance still apparently haunts some minds, and against that it is impossible to argue if those who believe it hold the doctrine that the properties of matter reside in superadded immaterial essences. From these, however, we can only demand rigid proof of the action of each dilution by ordinary experiment. What can we know about immaterial essences and the effect of dilution upon them? Can you dilute an immaterial substance? And if you could, what good or harm could it do? But to those who talk of " medicinal force " capable of transference and transformation we can hold a different language, and tell them beforehand that the whole idea lies in mere confusion and misapprehension of the meaning of the word force. It is only common force—in all probability, merely motion either molar or molecular of the particles of matter—-which is capable of transference and transformation, while the specific properties which distinguish one kind of matter, whether simple or compound, from another, are inherent in the matter itself and incapable of being either detached from it or being manifested by any other kind of matter. All the specific powers of medicine with which it is our business to deal belong to these inherent intransferable properties, and consequently can only be manifested while some portion of the actual material is present. However little of this specific action of a substance be required it is necessary that matter must be divisible to the extent of the dilution that may be in question. But there are very strong reasons for holding the finite divisibility of matter, and of late Sir W. Thomson has given good grounds for supposing that the size of the ultimate atom may be ascertained approximately and that far below our higher dilutions.