INSTRUMENTAL MEASURING OF DIFFERENT HOMEOPATHIC DILUTIONS OF POTASSIUM IODIDE IN WATER

Igor Jerman, M.D., Sc.D., Full Professor of Theoretical Biology
Maja Berden, M.A. Biology
Metod Škarja, M.A. Physics
BION, Institute for Bioelectromagnetics and New Biology,
Celovška 264, 1000 LJUBLJANA, Slovenia

(Received October 10,1998; Accepted with revisions March 10, 1999)


ABSTRACT:

Although more than 200 years have elapsed since the beginning of homeopathy and in spite of numerous confirmatory scientific experiments, the so-called memory of water is still a highly disputable and controversial theme in scientific circles. To make a contribution to solving this riddle, our research group tried to examine memory properties of water by the method of differential corona discharge Kirlian electrophotography of water-drop pairs. The method is based on a modified form of Kirlian photography with a subsequent thorough computer picture analysis. The potassium iodide (KI) mother solution (0.1M) was diluted in the standard way (without potentisation) or with potentisation (succussion by hand - by striking the vial 60 times against a large book as used traditionally) to 10-3M, 10-6M, 10-10M, 10-16M, 10-17M and 10-24M KI solutions. In the electrophotography method a drop of KI solution was compared with a drop of control water. To get a dependable system of results we compared homeopathic dilutions with ordinary distilled water, sham-potentised distilled water and non-potentised (standard) solutions. The results were analyzed by the Chi-square Goodness-of-fit test and the Sign test. They showed repeatable and statistically significant effects of concentration of KI dilutions as well as potentisation on the corona discharge process (from p < 0.05 to p < 0.001). This indicates that there is some physical basis of molecular (ionic) information imprinted into water.

KEY WORDS: Corona discharge, Kirlian electrophotography, Potassium iodide, Ultra-high dilution, Homeopathy

 


INTRODUCTION

Although more than 200 years have elapsed since the beginning of homeopathy, the so-called (long-term) memory of water is still a highly disputable and controversial theme in scientific circles [ , , , , ] . On the basis of the known and accepted physical laws and properties of water, a vast majority of scientific community does not allow even a remote possibility that water might “remember” a substance once diluted in it. The reason for this is that the Brownian motion of water molecules and clusters would annihilate any memory structures in terms of picoseconds []. However, in spite of this presumably physical impossibility many healing practitioners as well as many scientists claim on empirical grounds that water can prove its memorising capacities [ , ]. In physical researches the most striking results indicating water memory were obtained from NMR, UV and X-ray spectroscopy of ultra-highly diluted water (ultra high dilution means a dilution of a substance in which there is high probability that not even one molecule is left; it is practically pure water), less significant results were gained from Raman spectroscopy [7, ,]. Many challenging results were obtained in physiological researches on various organisms such as wheat, tadpoles, chicken embryos, mice, humans, cell cultures etc. [ 8, , , , ] . There were also some extensive double-blind medical examinations of homeopathic treatment that showed statistically significant differences between placebo and homeopathic water effects [ 9] . If all these explorations and their results are to be taken seriously, then we are facing an interesting, if not bewildering, situation wherein a phenomenon was discovered, subsequently repeated by other research groups and verified several times [9, 13, 14, ], while at the same time it cannot be anticipated on the basis of the established physical or chemical science. However, the implications of this phenomenon, if eventually proven in a convincing manner, would not be confined only to physics and its basic research, for they would go beyond that and affect at least chemistry, biology and medicine. Thus, any honest and methodologically correct research, either theoretical or empirical, performed towards resolving the enigmatic phenomenon of water memory, should be taken with due attention.

Of course, certain scientists tried to build up models which would connect the staggering phenomenon to the known physical laws and properties of water []. A majority of such models tries to explain water memory through water globular and polymer structures that would remain stable for much longer time than anticipated by conventional physics. There is a model involving many possible, although rare, water isotopes like HDO (D stands for deuterium, H isotope with a mass number 2), DDO, HTO (T stands for tritium, radioactive H isotope with a mass number 3), DTO, TTO, H2O17 etc. [ ] . A very promising model is that by Del Giudice (University of Milano, Department of Nuclear Physics INFN, Italy), trying to explain water memory by means of quantum mechanics, more specifically with the electromagnetic superradiance phenomenon in a dense phase of water [ 3, ] (this model predicts, that the ground state of condensed mater is determined not only by short-range forces between the molecules and atoms, but also by long range interactions mediated via the endogenous electromagnetic field, which spontaneously emerges when the ground state is formed and is an irreducible part of it - the molecules and the field oscillate in phase). According to this model, and in harmony with quantum mechanics, water would have coherent domains where the electromagnetic field would remain trapped without irradiation. Thus Del Giudice provides a basis for a more universal understanding of water memory, including not only molecular solutions and their dilutions, but also the already examined and reported capacity of water to “remember” an electromagnetic field to which it was exposed for a certain period of time [ , , , , ] .

So far, no model has been able to explain all the observed phenomena of water memory, which indicates that to establish a reliable basis of empirical findings, research work should include much more experiments. For some three years our research group has been developing new methods of detecting subtle changes in water exposed to different electromagnetic fields [ , , ] . One of the methods, based on the Kirlian corona discharge photography [ , , , , , , ] , is called differential Kirlian electrophotography. It is based on a high-frequency high-voltage electrical field, demonstrating otherwise almost non-detectable differences in the investigated objects. By this method an image of electric discharge (known also as corona discharge) around the objects being examined is obtained. In our research we began to use water drops, which enabled us to avoid some of the most common problems associated with the direct electrophotography of objects and, in particular, organisms or their parts (such as shape, skin temperature and resistance, perspiration activity, ion composition etc.). Some other problems, especially the lack of control over possible unknown and uncontrollable parameters, were presumably avoided through simultaneous electrophotographing of pairs of water drops (solution vs. control water). Stability of parameters, regarding the operation of the device (voltage, frequency, pulse repetition rate, exposure time), was achieved through its careful design. With all these advantages we managed to obtain a method well capable of exploring subtle and stable changes in water, supposedly structural and dynamic at the same time. This advanced system of electrophotography was greatly enriched by an extensive computer analysis of scanned corona discharge pictures.

Our previous research showed that even extremely weak electromagnetic (EM) fields can be “imprinted” into water and then reproduced in a statistically significant way (not the fields themselves, but some information about their imprinting). Encouraged by the results of the experiments involving EM fields, we tried to find out whether our method can differentiate between different homeopathic (potentised) dilutions of potassium iodide (KI) and non-potentised solutions of the same concentration.

Potentisation [pronounced as p t3 nt« iseio n] is a term used by homeopaths. It is a process of stepwise dilution of a substance e.g. in water or a water-alcohol mixture and input of exogenic energy by agitation (succussing or vortexing) between the dilution steps. Denotation D means dilutions are diluted in steps of 1:10 (they can be also diluted in steps 1:100 in which case they are denoted as C) [definitions from ref.16, where succussing means vigorous shaking and vortexing means shaking the vials with conventional laboratory Vortex shaker]. Through the preparation process, information is believed to be transferred to the solvent. It is assumed that this information is more marked, the more often the process of agitation and dilution has taken place. To get a dependable system of results we compared homeopathic dilutions with ordinary distilled water, sham-potentised distilled water (the distilled water went through exactly the same procedure of potentisation, but there was no substance present in water) and non-potentised (standard) solutions.

If the method reveals some statistically significant differences between differently prepared solutions of the same concentration, this would support scientific evidence, already accumulated, about water memory and would put some additional weight in favour of homeopathy. And besides, it would be possible to deduce at least some rough properties of dilution and the potentising process from the computer analysis of corona discharge pictures.


MATERIALS AND METHODS

Experimental Design

A series of experiments was performed, in which potassium iodide (KI) solutions of different concentrations (prepared in twice distilled water; water was prepared in the Laboratory for Analytical Chemistry, Faculty of Chemistry and Chemical Technology, University of Ljubljana) were compared with pure twice distilled water (control, named K0). KI solution was used because it gave most significant results in our research of the influence of ionic composition of water on the corona discharge around water drops [see 34]. pH of twice distilled water was around 6 (presumably because of CO2) and any solid precipitates from glass were present only in traces. However, KI solutions were prepared with the same water as the control, so any trace impurities were present in both compared waters.


Description of terms:

Mother solution 0.1M KI solution

10xM solutions standard solutions; x = -3, -6, -10, -16, -17, -24

DX dilutions homeopathic dilutions prepared with dilution of mother solution in steps of 1:10 (parts per volume); each of different successive dilutions was succussed by hand - by strongly striking the vial 60-times against a flat surface of the top of a large book with a hard cover to create mechanical shocks; X stands for consecutive numbers, which tell us in how many steps the dilution was diluted, e.g. D2 was diluted and succussed twice; in our case X = 2, 5, 9, 15, 16 and 23, so the dilutions are named D2, D5, D9, D15, D16 and D23

K0 control water is pure twice distilled water

KX sham-potentised pure water prepared with exactly the same procedure as DX dilutions from the control water (equally succussed and "diluted"); X stands for consecutive numbers, which tell us in how many steps the control water was "diluted" and succussed; X = 9, 16 or 23 and thus K9, K16 and K23

The KI mother solution (0.1M) was diluted in the standard way (without potentisation) to 10-3M, 10-6M, 10-10M, 10-16M, 10-17M and 10-24M KI dilutions. At the same time it was diluted to the same concentrations with potentisation, namely D2 (10-3M KI dilution), D5 (10-6M), D9
(10-10M), D15 (10-16M), D16 (10-17M) and D23 (10-24M) dilution of KI (for D23 the mother solution (0.1M) was diluted and succussed 23-times which brings us to the dilution concentration of 10-24M). Tests were performed from day 2 to day 14 after the preparation. The dilutions were kept in reagent bottles (transparent borosilicate glass) in plastic cups in the dark (to prevent any possible influence of light rays on the water "structure"). Higher potentised dilutions (D9, D16, D23) were also compared with the sham-potentised pure waters (named K9, K16 and K23). In these experiments D9 was compared with K9, D16 to K16 and D23 to K23. The sham-potentised pure waters K16 and K23 were additionally compared with the control water (K0).

 

Corona Discharge Imaging System

The effects of different dilutions on corona discharge were compared through our 32 parameters of corona images [ ] . The images of the corona discharge around the drops were obtained by means of a conventional Kirlian device adjusted to our needs [ 25, 26, 34] , with a high-voltage (12.5 kV) high-frequency (45 kHz) electric field procured by means of a Tesla coil, the repetition rate 800 Hz and exposure time being 20 s (Figure 1). The schematic experimental setup is shown in Figure 2.

 Fig. 1. Oscilloscopic picture of discharge waveform of device.

 

instr1.gif (14631 bytes)

Fig. 2. Diagram of experimental arrangement for electrophotography. The presented dimensions do not correspond to the real ones.


The images were obtained on specially prepared black and white photographic paper (Ilfospeed RC IS2.1M - brillant, Ilford, Great Britain). Before imaging, the paper was exposed to artificial light (the exposure time was 17 minutes at the illumination of 420 lux), until the color of the paper changed from white to light blue-violet. Paper prepared in this way is no longer sensitive to light, but it becomes sensitive to substances produced and transported in the corona discharge process. The main contribution to the brightness of the image present the ions and water radicals extracted at the drop surface (H+ ion, HO and HOO radicals) and transported in the corona discharge area, where they interact with the emulsion. After that two drops of water (one from solution and one from the control) were put on a photographic paper directly and were simultaneously exposed to the corona discharge procedure (Fig.2). After about a two hours in the darkness an image with clearly visible streamers was developed. Special care was taken for the drops to be of the same shape and size. Many tests were performed for each solution (at least 3, up to 12 for higher dilutions) and for each test 5 pairs of drops (solution vs. control) were electrophotographed. At every subsequent discharge the position of both drops was interchanged to avoid any possible position-dependent influence on the discharge.

 

Computer Analysis of Pictures and Data

The simultaneously photographed pair of pictures was scanned with a color scanner (Genius, Color Page - I, KYE Systems Corporation) and analyzed with appropriate computer software that was partly bought (i-Photo deLuxe from U-Lead Systems, Inc., Taipei, Taiwan and MS Excel from the Microsoft Corporation) and mainly developed by our research group. Each scanned picture was first transformed into a grid of 104 x 104 pixels, the value of each pixel corresponded to the luminosity of the original picture in the range 0 (pure black) – 255 (pure white), the range being determined by the i-Photo deLuxe program (Fig.3). Then the grid was subject to further analysis, where general, angular (streamer) and radial characteristics of the corona discharge image were determined (thoroughly described in [ 25, 34]). The characteristics of the corona discharge image were first established for the whole picture (general analysis) and then determined in a ring extending from the border of the drop 5 mm radially (15 pixels in

 

instr2.jpg (58000 bytes)

Fig. 3. Grid of 104 x 104 values corresponding to the luminosity of each pixel in the original picture. A streamer analysis is performed in a ring (0 – 15 pixels from the drop border, i.e. between the first and the third circle) and also in the three rings indicated (0 – 8, 9 –16, 17 – 24 pixels) to follow the radial changes of streamer parameters. In each ring the angular dependence of luminosity is obtained by the angular fragmentation of the corona into 3° angular segments and by the determination of the average luminosity of these segments.

Fig.3), which covers the brightest part of the image. Here the characteristics of streamers i.e. more or less prominent radial like formations (where the most intense corona discharge is taking place) were determined (streamer analysis). To follow the radial dependence of parameters (radial analysis), the same procedure was repeated in three rings, the first one extending from the drop border 8 pixels radially (ring I), the second from 9 to 16 pixels (ring II), and the third from 17 to 24 pixels (ring III) (see Fig.3).

Parameters related to the whole picture were five. The “high intensity of brightness” represented the number of the brightest pixels for each picture with the luminosity in the chosen range. Other four parameters expressed the total luminescence of four rings (the sum total of the luminosity of all the pixels included).

On the basis of the streamer analysis five parameters were calculated for each ring: 1. streamer luminosity (the sum of luminosity of separate streamers above half of their maximum values), 2. streamer contrast (the average difference in luminosity between the streamer summit and the average value of two adjacent depressions), 3. streamer width (the average full width of the streamer at half of its maximum), 4. homogeneity of streamer widths (the inverse value of the standard deviation of the average streamer width) and 5. streamer relative eccentricity (the average absolute angular deviation of the streamer summit from its center, halfway between its two depressions). For the explanation of parameters, see also Figure 4.

Seven parameters were related to the radial analysis, i.e. three for the average lengths of the streamers, three for standard deviations of lengths, and a slope of average radial dependence of streamer luminosity. The length of the streamer was defined as the length where the streamer luminosity exceeds a predefined threshold value. We chose three threshold values (three lengths for each streamer were thus determined) giving the lengths in the ranges of approximately one, two and three quarters of the radial extent of the corona (Fig.5). The slope was calculated between 5 and 25 pixels from the drop border.

Fig. 4. The angular dependence of luminosity of corona discharge, obtained after the determination of the average luminosity of 3° angular segments. The range of luminosity values is determined by the computer program (i-Photo deLuxe) from 0 to 255 (0 - pure black, 255 - pure white).

Fig. 5. The radial dependence of luminosity of one streamer. Three threshold values of luminosity for the determination of the lengths of the streamer are indicated with dashed lines. The length of the streamer for threshold value is indicated with solid line.

In every pair of pictures the values of parameters were first determined for each picture separately. Later the values were compared for each parameter. If the value of a parameter of the picture of a solution drop in the individual pair was higher than that of the control one (solution : control > 100%), it was marked as positive (positive polarity), in the opposite case as negative (negative polarity; solution : control < 100%); in the case of equality (solution = control) it was marked as zero. Results in the form of positive and negative points for particular parameters for a given pair (solution vs. control) were analyzed by means of the Chi-square Goodness-of-fit test and the Sign test [ , ; where Chi-square Goodness-of-fit test is defined as a statistical test used for analysis of categorical data and the Sign test is defined as a nonparametric test that can be used to compare two paired samples] . This rather simple analysis of the results was necessary since the absolute values of the parameters varied from pair to pair because of high non-linearity of the electrical discharge process. This was also the main reason for our choosing the simultaneous photographing of two drops and of the following computer analysis of those pairs.

 

RESULTS

The results manifested the influence of both the solution concentration and the potentisation on the properties of water. The parameters of the whole picture and the brightest part of the corona (0-15 pixels) comparing the solutions of the same concentration prepared with or without potentisation (e.g. homeopathic or standard solutions) are presented in histograms (Figure 6 - 10). The statistical (Chi-square) significance of the same parameters is presented in Tables 1 and 2 (the Sign test yielded similar results). The parameters of the I., the II. and the III. ring yielded similar results.

The standard 10-3M and homeopathic D2 dilutions did not differ greatly from the 0.1M mother solution (Fig.6). Significant differences from the mother solution appeared in the 10-6 M and D5 dilutions (Fig.7). At this stage, differences between standard and homeopathic dilutions occurred as well. While the influence of dissolved KI as a substance lessened in higher dilutions prepared in a standard way, the situation with homeopathic dilutions was more complex. The differences from the control (pure twice distilled water), produced by the D5 homeopathic dilution, were more distinctive than those produced by the standard 10-6 M solution. Differences of the D9 dilution from the control were smaller than for the standard 10-10 M solution (Fig.8). D15 showed no differences from the control whatsoever (this dilution showed almost the same electrophotographic characteristics as the control water). D16 showed again more marked results than standard 10-17 M solution (Fig.9). The same was true of the D23 and 10-24 M solutions (Fig.10). Tests were performed from day 2 to day 14 after the preparation and in that time the solution properties did not weaken, but sometimes they manifested themselves only after a few days from preparation.

 


Legend to Figures 6 - 10

The black columns represent the values of parameters for the mother solution (0.1M KI). The gray columns represent the values of parameters for standard solutions. The white columns represent the values of parameters for homeopathic solutions.

Legend to parameters:

a streamer contrast

b streamer width

c homogeneity of streamer widths

d streamer relative eccentricity

e high intensity of brightness

f total luminescence

g streamer luminosity

h average length of short streamers

I average length of medium streamers

j average length of long streamers

k slope of average radial dependence of streamer luminosity

l standard deviation of short streamer length

m standard deviation of medium streamer length

n standard deviation of long streamer length

 

The analysis of Kirlian electrophotographic parameters showed that some of them distinguished between higher dilutions (from 10-6 M KI up) prepared in two different ways (with or without potentisation): streamer contrast, streamer width, homogeneity of streamer widths, streamer relative eccentricity (a-d in Figures and Tables). They were designated “homeopathic” parameters. In homeopathic dilutions their values coincided with the values of the mother solution, while in the standard solutions they were in general opposite and non-significant. Other parameters designated “concentration” parameters, differentiated among different concentrations regardless of the type of preparation (0.1M, 10-3 M, 10-6 M and higher dilutions): high intensity of brightness, total luminescence, streamer luminosity, lengths of streamers and partly the standard deviations of streamer lengths (e-j and l-n in Figures and Tables).

When the homeopathic dilutions D9, D16 and D23 were compared with the equally succussed and "diluted" (sham-potentised) pure water (K9, K16, K23), the results of comparison between D9 and K9 were approximately the same as when D9 was compared with the control water (K0). At D16 the values of “homeopathic” parameters varied with regard to whether D16 was compared with K16 or K0. The experiments comparing sham-potentised and control water showed some differences between K16 and K0 and no significant difference between K23 and K0. Still, the results of the comparison between D23 and K0 were much more marked than those of D23 compared with K23.

There was a highly interesting inversion of polarity of the “homeopathic” parameters values in standard 10-10 M KI and homeopathic D9 solutions (significant only in the homeopathic solution). In 10-24 M KI and D23 solutions the differences in values of “homeopathic” parameters were reduced. The only difference between homeopathic and standard solution was that the results related to D23 were more pronounced than those obtained with the standard
10-24M solution.

 

Table 1.

Statistical (Chi-square) significance of parameters for standard (not potentised) solutions.

homeopathic parameters

concentration parameters

a

b

c

d

e

f

g

h

I

j

k

l

m

n

0.1 M

-

0.07

-

-

>0.001

-

-

-

>0.001

>0.001

>0.001

-

-

0.02

10-3 M

0.03

0.001

-

-

0.01

0.01

-

0.001

0.01

-

0.06

0.07

-

-

10-6 M

-

-

-

-

0.02

0.02

0.02

0.02

0.02

-

-

0.07

-

-

10-10 M

-

-

-

-

0.005

0.07

0.09

0.02

0.02

0.02

-

-

0.02

-

10-17 M

-

-

-

-

0.02

-

-

-

0.02

0.02

-

-

-

-

10-24 M

-

-

-

-

0.002

-

0.08

-

0.02

0.002

-

0.02

-

-

 

Table 2.

Statistical (Chi-square) significance of parameters for homeopathic (potentised) solutions.

homeopathic parameters

concentration parameters

a

b

c

d

e

f

g

h

I

j

k

l

m

n

D2

>0.001

>0.001

0.09

0.06

-

-

0.01

-

-

-

0.07

-

-

-

D5

0.002

0.095

0.07

0.03

>0.001

0.01

>0.001

0.01

0.01

0.01

-

0.01

0.001

-

D9

-

0.04

-

0.01

0.04

-

-

-

-

0.04

-

0.03

-

-

D15

-

-

-

-

-

-

0.06

-

-

-

-

-

-

0.07

D16

0.01

-

0.03

-

0.06

-

0.003

-

-

-

-

-

0.04

0.03

D23

-

-

0.04

-

0.003

0.003

0.001

0.03

>0.001

0.001

-

-

-

-

 

Legend to Tables 1 and 2:

numbers in bold type p<=0.05

numbers in regular type 0.05 < p < 0.1

- 0.1 < p

 

DISCUSSION

The results of our research show differences between solutions prepared with or without potentisation, at least in some parameters (“homeopathic” parameters). At the same time, a group of other parameters (“concentration” parameters) roughly discriminates between various magnitudes of dilutions regardless of the solution type. The “homeopathic” parameters are associated with circumferential characteristics of the streamers. On the other hand, the “concentration” parameters are connected with the picture brightness and with the radial characteristics of streamers (see Fig.6 - 10). These effects are rather persistent, showing themselves even in the outer part of corona (the III. ring in the analysis).

In general, the results of homeopathic parameters for homeopathic solutions are of the same polarity (positive or negative) as the results of mother solution (0.1M), while the results of standard solutions are of opposite polarity (but not statistically significant). The concentration parameters are of the opposite polarity if compared with the mother solution in both types of solutions, ranging from 10-6 M KI up. In contrast to these findings we have an interesting case of standard 10-10M and the parallel homeopathic D9 solution. Here the polarity of homeopathic parameters values is opposite to the general case in both types of solutions. At the same time the polarity of concentration parameters is not changed. This exception can remind us of the experiment with wheat seedlings exposed to different homeopathic solutions of silver nitrate, where the D24 and D26 dilutions were highly effective in significantly enhancing their development, while the D25 dilution was repeatedly found ineffective [ 13] . This implies that there may be some special dilutions, homeopathic as well as standard ones, where some special non-linear effects may demonstrate themselves.

It is somewhat astonishing that even very high standard dilutions (e.g. 10-17 M and 10-24 M) significantly differentiated from distilled water by the method of differential Kirlian electrophotography. This means that even high dilutions with no potentisation have a reproducible effect or impact on water. On the other hand, succussion has also some special effects of its own, but it is difficult to estimate its importance in comparison with the dilution. These effects can also be seen from the fact that when homeopathic dilutions D16 and D23 were compared with sham-potentised pure water (K16 and K23), the effects were smaller than when dilutions were compared with the control (K0).

Our results therefore reveal two different effects: that of dilution and that of succussion (the vigorous shaking of the solution during the potentisation process [16]); they are both combined in homeopathic solutions. The effect of diluted substances, generally directed in opposite to that of normally effective solutions (for instance poisons), is already known as the hormesis effect (according to Neafsey hormesis is a term which has been applied to a variety of stimulatory responses to low doses of otherwise toxic substances which improve health and enhance longevity) [ ] . Our results consistently prove that strongly diluted substances have an effect opposite to that of the mother solution and usually to that of the weak solution (10-3 M) as well. This indicates a possibility that the hormesis effect is not based only on some general physiological properties of organisms but on the as yet unknown physical properties of the solutions themselves. But there is also a certain difference between the hormesis effect and our investigations, since the former usually disappears at higher dilutions (around 10-5), while Kirlian electrophotography still reveals some significant effects even at dilutions as high as
10-24 M (see Fig.10).

In conclusion, our results demonstrate repeatable and statistically significant effects of highly diluted standard and homeopathic dilutions of KI on corona discharge Kirlian electrophotography. This, together with countless results obtained by other research groups, related to biological effects of homeopathic dilutions, indicates that there is some physical basis enabling organisms to utilize information imprinted into water.

 

ACKNOWLEDGMENTs

This work was supported by the Slovenian Ministry of Science and Technology, grant MS - 11/96. We would like to thank Mojca Piskernik and Lidija Berden, who edited the language. Our special thanks go to dr. C.W.Smith, dr. P.C. Endler and dr. J. Schulte for reading our manuscript and for their valuable comments.

 

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The running titles:

JERMAN, BERDEN, ŠKARJA

INSTRUMENTAL MEASURING OF HOMEOPATHIC DILUTIONS