On the values of fundamental atomic constantsrspa.royalsocietypublishing.org/content/royprsa/160/902/424.full.pdfI Cornu 1874 Fi 300,400 ±300 2 x 23 km. ... To make a measurement

On the Values of Fundamental Atomic ConstantsBy Sten von Friesen, D.Sc., Uppsala

(<Communicated by 0. W. Richardson, .— Received 27 January 1937)

The practice of giving limits of error for results of physical measurements probably originates from a desire to indicate the narrowest region within which one is sure to find the true value of the quantity in question.

If it were possible to find a truly objective way of fixing this region, it would then be permissible to judge the value of an experiment from the breadth of the “ region of error” . I t would also be possible directly to compare different determinations of a physical quantity.

The experimental errors, however, are of two principal kinds, accidental errors and systematic errors. Unfortunately, the former only can be treated in a quite objective way, that is, in this case, by mathematical methods. The systematic errors, on the other hand, can only be subject to an estimation where the experience and judgement of the experimenter himself must make the decision.

To avoid the difficulties of a decision of this kind many authors content themselves by giving some measure of their accidental errors and wholly neglect the systematic errors. They give, as a rule, the “probable error” as calculated by the method of least squares. In choosing such a course, they entirely abandon the thought of telling anything about the location of the true value. The probable error is a measure solely of the reproducibility of results obtained on a given occasion with one special instrument. It does not tell everything about the reliability of the method. The possibility of comparisons between results from different sources given by such a course of action is, therefore, purely imaginary.

To people who are not experimental physicists the inconveniences of such a practice are very severe. They lack those qualifications necessary for turning directly to the original publications to form an opinion of their own about the real accuracy. Such persons, as a rule, still look upon the limits of error as giving a region inside wdiich the true value is to be found. As a result of this misconception many curious situations have arisen. We have had, at different times, among other things, one deflexion and one spectroscopic value of the specific electronic charge, one oil-drop and one X-ray value of the charge of the electron, and attempts have even been made to convince us that velocity of light is some sine function of time.

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Values of Fundamental Atomic Constants 425

The course of action is dangerous even to the experimenter if the original papers do not give sufficient experimental details. In that case nothing but an intimate personal acquaintance with the author and his views can make a judgement of his work possible. One must, therefore, deeply regret those modern tendencies which suppress experimental details in order to reduce the bulk of scientific journals.

These questions were presented to the author of this paper in connexion with his experiments on e and h. I t became necessary to form an opinion about the true accuracy of the values usually given for some fundamental atomic constants, and in some cases, to choose other values in better agreement with the results of modern developments in this field. Therefore, a survey was undertaken of the experimental work concerning the constants c, e/m, e, and h. The present paper gives an account of the results of this survey. The values given with their limits of error arise from attempts having been made to indicate the narrowest regions within which one is sure to find the true values.

T h e V e l o c it y o f L ig h t iist V a c u u m

The velocity of light is, by far, the best known of our four constants. It has been the subject of a great number of determinations by eminent physicists. Table I contains the best of the determinations made during the

T a b l e I — V e l o c it y o f L ig h t

c Stated LightNo. Experim enter Year M ethod km./sec. error p a th References

I Cornu 1874 Fi 300,400 ±300 2 x 23 km. (1876)2 Michelson 1879 Fo 299,910 ± 50 2 x 0 -6 km. (1879)3 Newcomb 1882 Fo 299,860 ± 30 2 x3-7 km. (1885)4 Michelson 1882 Fo 299,853 ± 60 2 x 0 -6 km. (1885)5 Perro tin 1902 F i 299,901 ± 84 2 x 46 km. (1902)6 Rosa and

Dorsey1906 Indirect 299,781 ± 30 (1906)

7 Mercier 1923 99 299,782 ± 30 (1923)8 Michelson 1924 Fo 299,802 ± 30 2 x 35-4 km. (1924)9 Michelson 1926 Fo 299,796 ± 4 2 x 35-4 km. (1926)

10 M ittelstaedt 1928 Fi 299,778 ± 20 6-8 x 41-4 m. (1929)11 (Michelson)-

Pease and Pearson

1932 Fo 299,774 ± 11 8-10 x 1594 m. (1932)

last 60 years. Under the heading “ Method ” in the fourth column, information is given as to the general type of method used in the different cases.



426 S. von Friesen

Fi means that a system of periodic screening off* of the light has been used This system is best known in connexion with the name of Fizeau. Fo denotes Foucault’s arrangement with rotating mirrors.

The most reliable of these eleven determinations might probably be the numbers 6, 9, 10, and 11.

Rosa and Dorsey (1906) obtained by a comparison of the capacity of condensers in the units of the electrostatic and the electromagnetic system. The electrostatic capacity was calculated from the dimensions of the condensers, which were carefully measured. The capacity in electromagnetic units was obtained by measurements at the charging and discharging of the same condensers, c emerges as the square root of the relation between the capacities in the two systems. These determinations were made with the utmost skill and are a true model for precision measurements. The true accuracy, certainly, is one of the very highest ever attained at a determination of c.

In 1926 Michelson made very exact measurements with a rotating mirror between two mountains in California, Mt. Wilson and San Antonio Peak. The distance was 25,385-53 m. Unfortunately, it was not possible to measure it directly. A broken base line had to be laid in the immediate neighbourhood of the foot of the mountains. By the aid of this base the distance was found by triangulation. The probable error of the straight-line distance was 1 part in 6,800,000, that is, + 5 mm. This corresponds to an error per metre of not more than 0-00015 mm. The officials from the U.S. Coast and Geodetic Survey, who made this determination, state that the actual error is surely less than 1 part in 300,000. It was their “ feeling” that the actual error lay somewhere between 1 part in 500,000 and 1 part in 1,000,000. 1 part in 500,000 means 2/ijm. To make a measurement of length with this grade of precision in the ideal surroundings of a laboratory requires great care. Considering the fact that the field measurements have been made under very difficult conditions one is inclined to think this a rather bold statement. Other errors must be added to the error of distance, e.g. errors in the determination of the speed of the revolving mirror. I t is obvious that the limits given ( + 4 km./sec.) do not undoubtedly cover the true value region.

Mittelstaedt (1929) substituted Kerr cells for the toothed wheel used by Fizeau. This arrangement permits the use of a very high screening frequency, and is of great advantage as it allows for the use of very short distances which are easily measured with great accuracy. The limits of error seem to be quite reasonable.

Pease and Pearson’s (1932) measurements took place in an evacuated



tube, 1 mile in length. The light was reflected several times at the ends of the tube. In this way the light was made to travel 8 or 10 miles. The experiment was a continuation of Michelson’s work. To a certain extent the same experimental arrangements were used. The true accuracy is probably somewhat less than that shown by the limits of error.

These four determinations and Mercier’s (1923) experiments on the velocity of electromagnetic waves on wires, from which c is calculated, give the velocity of light by four different methods. The agreement of the results is excellent. I t might be said, with a high degree of probability, that the value of the velocity of light is now known with an error less than 1 part in 10,000. Nevertheless, some persons have thought it possible to conclude from the experimental results that the velocity of light is a sine function ot time. Fig. 1, reproduced after de Bray, shows that the experimental


km//sec

300000

299900

299800

Year 1870 1880 1890 1900 1910 1920 1930 1940

F ig . 1—Variation w ith tim e of the velocity of light after E . J . Gheury de B ray (1934).

points really fit a sinus curve very well. If one turns, however, to fig. 2, where the limits of error are represented, it becomes quite obvious that the agreement is purely accidental. Moreover, the point of 1874 must be moved to a position not less than 410 km./sec. higher than shown by the diagram, de Bray used a value recalculated by Helmert which Cornu himself refused to accept. To state any variation in the velocity of light in virtue of the present material is entirely unjustifiable.

The result of our review is thatthe Velocity of Light in Vacuum = 299,780 ± 20 km.jsec.

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428 S. von Friesen

T h e S p e c if ic Ch a r g e o f t h e E l e c t r o n (e/m)

A great number of physicists has undertaken measurements of e/m by various methods. The first determinations were made by Schuster and J. J. Thomson. They found values of the right order of magnitude, about 107 e.m.u./g. Since then tne accuracy has steadily increased, although it is only lately that the reliability has reached a height to justify the use of the term “ precision measurements” . So recently as 1929 Birge thought it necessary to assume two different values of e/m, the deflexion value 1-769 x 107 e.m.u./g. and the spectroscopic value 1-761 x 107 e.m.u./g. The

/sec300000

299900

299800

Y ear 1870

F ig . 2—Determ inations of the velocity of light, with stated limits of error.

first one was to be used in cases concerning free electrons and the other in cases concerning atomic structure. This difference does not exist in reality. I t is due only to a considerable over-estimation of the accuracy attained at the time.

Table II gives a survey of the results of the most reliable measurements of e/m made during the last 10 years.

The determinations 1, 2, and 3 were made by a modification of a method first used by Wiechert. I t consists in a direct determination of the velocity v of electrons, accelerated by a known voltage V, by measuring the time they require to travel a measured distance. At the beginning and the end of the




distance they pass through plate condensers to which the same alternating voltage of known frequency has been applied. The accelerating voltage is varied until the electron beam passes straight through the condensers without any deflexion. This means that the A.C. voltage is zero at both passages. Thus, a whole number of half-periods must have elapsed during the time required by the electron to travel the measured distance, and v

TYIV^is found easily. The formula eV —----gives e/m.£

T a b l e II—M o d e r n D e t e r m in a t io n s o f t h e S p e c if ic E l e c t r o n ic

No. Experim enter Y ear

Ch a r g e

Method e/m0Statederror References

1 Perry and 1930 W iechert 1-761 ±0-001 (i93°)

2Chaffee

K irehner 1931 5? 1-7585 ±0-0012 (1932)3 >> 1931 1-7590 ±0-0015 (1932)4 D unnington 1933 Lawrence 1-7571 ±0-0015 (1933)5 H ouston (+ 1935 Zeeman effect 1-7570 ±0-0007 (1934*1935)

6

Camball and Kinsler)

H ouston 1927 R ydberg constants 1-7606 ±0-0010 (1927)

7 Shane and 1935H and H e+

R ydberg XH and 1-7579 ± 0-0003 (i935)Spedding * 2H

Dunnington (1933) used a method suggested by Lawrence. A filament emitted electrons which were accelerated by an alternating voltage of high frequency. The electrons describe circular paths under the influence of a magnetic field. A number of slits are arranged to define a circle of a certain fixed radius and those electrons which pass through the slits hit a collector. A cover round the collector has been electrically connected to the cathode. There is a value of the magnetic field at which no electrons are able to reach the collector. In this case, the time required by them to run through their circular path is equal to one whole period of the alternating voltage. They lose, therefore, their entire velocity and cannot enter the collector. Let 6 be the path of the electrons in angular measure, v the frequency and H0 that value of the magnetic field for which a minimum number of electrons

is registered at the collector, then e/m O.v

The methods hitherto mentioned give the specific charge of free electrons. The next two methods concern electrons inside an atom. They are usually referred to as the spectroscopic methods.



430 S. von Friesen

The first of the methods depends upon the measurement of Zeeman splitting at a known strength of the magnetic field. Apart from minor corrections owing to the exact theory of the Zeeman effect, one findse/m = 4ttcwhere Av means the change of frequency effected by the

application of the field H ,In the second spectroscopic method e/m is calculated from the Rydberg

constants of light and heavy hydrogen or, of hydrogen and ionized helium. The formula used by Shane and Spedding (1935) for 1H and 2H will exemplify this method:

c/m_ J ( aH — >11). A h

where F is Faraday’s constant, 1H and 2H the masses of the atoms, and RiH and R 2H the corresponding Rydberg constants.

In the first three determinations above there is a certain amount of uncertainty due to the possible occurrence of phase-displacements in the alternating voltages. Another cause of uncertainty lies in the unknown contact potentials which influence the accelerating voltage. Perry and Chaffee (1930) used concentrating coils to get a better intensity and definition of the electron beam. This arrangement must have an unfavourable effect on the accuracy. For this reason one seems justified in considering Kirchner’s (1932) measurements somewhat more reliable than those of Perry and Chaffee, in spite of Kirchner’s wider limits of error as given in his paper. With Dunnington’s (1933) arrangement there seems to be little risk of phase-displacements and, furthermore, it is quite independent of contact potentials. Such an experiment, therefore, ought to be capable of giving very good values. All these four determinations (1-4) have one thing in common, viz. that they seem to have been made with the greatest skill and care. They give a niean value for the specific charge of free electrons e/m = 1-759 x 107e.m.u./g.

It’is often said that spectroscopic determinations of e/m deserve particular credit as spectroscopic measurements can be made with a very high grade of accuracy. The actual position is such, however, that both with the Zeeman method and the Rydberg method the value of e/m depends upon small differences between spectroscopically measured magnitudes. Therefore, the accuracy obtainable is about the same with these methods as with the best methods working with free electrons.

Houston’s value from the Zeeman effect is the outcome of a long series of careful determinations where special care has been devoted to the




measurement of the magnetic field. He gives limits of error which probably must be slightly increased. As regards Houston’s other determination it seems advisable, even there, to widen the limits of error, among other reasons because of a certain degree of uncertainty as to which corrections must be used in consequence of fine structure in the spectral lines.

Shane and Spedding used the Rydberg constants of light and heavy hydrogen. These elements give lines with the same fine structure, which means that the errors are very much diminished. The errors given are probable errors. On account of a good agreement between results obtained with two different components of the lines the authors felt encouraged in the belief that the values are fairly free from systematic error. They felt justified in thinking that the probable errors describe closely the actual uncertainties in the results. However, the extreme values of e/m in their tables are T7566 and 1*7593. Therefore, it seems advisable to suppose that the real uncertainty is several times greater than the one given.

The above spectroscopic determinations give a value e/m =1*758 x 107 e.m.u./g., in very good agreement with the value for free electrons.

The determinations discussed above seem to permit the statement that the specific charge of the electron is now known with an accuracy of about one-tenth of a percent. They seem to indicate a value

e/m = (1*7585 ± 0*002) x 107 e.m.u./g.The figure 5 in the fourth decimal place is intended to tell that the best value seems to lie somewhere between 1*758 and T759, but it lacks any real physical significance.

T h e E l e c t r o n ic Ch a r g e (e)

The first precision determination of the electronic charge was undertaken by Millikan in 1913. He used the famous oil-drop method. The measurements were preceded by extensive investigations into the method. The result obtained was verified by a new determination in 1917 which gave exactly the same result e — 4*774 x 10-10 e.s.u. The limits of error were given (1917) as ± 0*005 x 10- 10 e.s.u. Millikan’s great renown and authority brought about the opinion that the question of the magnitude of e had practically got its definitive answer. A number of determinations by other people seemed to support this view.

In 1928 Backlin made precision measurements of the absolute wavelengths of some X-ray lines with a ruled grating. In this way he could find the factor of reduction between the conventional rock-salt scale of wave



432 S. von Friesen

lengths and the optical scale. The knowledge of this ratio enables a calculation of e. The result was considerably higher than Millikan’s and it was generally believed that some fundamental error was hidden in Backlin’s method. His value was e = (4-793 ± 0*015) x 10-10 e.s.u. Later on, the existence of a difference was confirmed by a number of new determinations by the same method. They were made by Backlin himself, Bearden in U.S.A. and others. The new experiments gave even higher values than Backlin’s first determination. The method was scrutinized in many quarters in order to find the reason of the discrepancy.

It was suggested that the ordinary grating equation loses its validity at those very great angles of incidence which must be used in X-ray work. The suggestion never met with very great approval and lately it has been experimentally disproved. Another attempt to explain the discrepancy pointed out the possibility of a difference in density between large crystal blocks and the crystals actually taking part in the production of spectra. The large crystals should have a mosaic structure, that is, they should be built from a number of small crystals, more or less inserted into each other. Against this assumption strong arguments could be adduced, but nevertheless, Millikan’s value of e was preferred generally. To arrive at a final decision it was necessary, either to repeat Millikan’s measurements and find a fault there or, to develop a new independent method of an accuracy high enough to make the choice possible between the competing values of e. Both paths have been trodden during the last few years and both have given a decision in favour of the X-ray value, showing that the higher value must be the most nearly cc?rrect one.

In 1935 the author of this paper published results of a precision measurement of electron wave-lengths which enabled the calculation of e with an accuracy of about + 0T %. The wave-length was measured for electrons of known velocity. The voltage accelerating the electrons was obtained from a high-voltage source by utilizing the Greinacher principle. A separate electron-valve device stabilized the voltage which remained constant within a few hundredths of a percent . The voltage was measured against a standard cell by means of a wire-wound potentiometer. The wave-lengths were obtained from spectra produced by diffraction with etched galena crystals. A beam of electrons defined by two narrow slits fell on the crystal, at grazing incidence, and penetrated small lumps of galena projecting from the surface. The lumps had retained their original orientation to the large crystal and acted as a transmission grating. They gave rise to very sharp spectral lines which could be photographed and measured with high accuracy.



A combination of de Broglie’s law with the expression for the Rydberg

constant gave e. The most common form of de Broglie’s law A = — canmv

be transformed in the following manner:

A 111i eF \_ v _ h _V \ 2m0c2J em0F )’


v is the velocity of the electron, A the electron wave-length, and V the voltage accelerating the electrons. The square root following A expresses the influence of velocity on mass. A' has been introduced to facilitate the calculations.

According to Bohr: 27T2e4m0 = ck3

For the charge of the electron we get:

F*.A'* where

The constants R and c are known with very high accuracy, and e/w0 which is less well known ( ~0T %) enters in the power 1/4 and thus does not cause an uncertainty exceeding 1/40 %. The determination gave a value for the electronic charge e = (4-796 + 0-005) x 10-10 e.s.u.

The limits of error are meant to take into account all known sources of error.

In the same year Kellstrom redetermined the viscosity of air, rj. This enters into the calculations of the oil-drop value of e in the power 3/2. Millikan used a value by Harrington o = 18,227 x 10-8. The value had been chosen as being apparently the best of a number of values which varied greatly among themselves.

Therefore, the thought was near at hand that the error in e was due to the use of Harrington’s tj. Kellstrom’s results show that the value 7}23o = 18,227 x 10~8 is most probably about 0-67 % too low. He got a value r}23° = 18,349 x 10-8 which has been confirmed by Bond who obtained exactly the same result from a different method. This means that Millikan’s value of the electronic charge must be increased by about 1 % to (e = 4-818 ± 0-011) x 10-10 e.s.u. The error ± 0-011 x 10~10 e.s.u. comprises that part only of the total error which comes from uncertainty in rj. The appropriate limits of error are even greater.

Finally, Backlin and Flemberg in 1936 used the oil-drop method for a new determination. A great improvement was gained by the use of diffusion pump oil of very low vapour pressure. This implies the advantage



434 S. von Friesen

that the loss of mass due to evaporation from the droplets has been made imperceptibly small, so that a very great number of observations of the velocity of fall and rise could be made for each individual droplet. Backlin and Flemberg (1936) give as the preliminary result of their experiment the value e = 4*800 x 10~10 e.s.u. I t has been computed with Kellstrom’s r/. The agreement with the X-ray and electron wave values is very satisfactory.

For many years Millikan’s value 4*774 has been one of the most familiar numbers to all students of physics but now it is quite obvious that it cannot be maintained any longer.

Table III gives a survey of the values of e obtained by the different methods.

The most satisfactory agreement of the more recent determinations by the X-ray method shows that we know fairly well the ratio between the wave-lengths as measured on the optical and on the conventional X-ray

scale. The factor of reduction is y- °pt* = 1 *0020. The value has been verified^ X -ray s

by direct comparisons between optical lines and high-order X-ray lines in concave grating spectrographs. There might be, however, some small uncertainty in the calculation of e from this ratio. Du Mond and Bollman (1936) have redetermined, on the one hand, the density of calcite and, on the other, the dimensions of the calcite unit rhombohedron. By using Bearden’s wave-length measurements they recalculated e with their new data and got the value e = 4*799 x 10-10 e.s.u.

It has been said against the electron-wave method that the etching of the crystals perhaps could have changed the grating constant of the small crystal lumps exposed by the etching but experimental observations by Du Mond and Bollman and others give no support to such an assumption. They found the same density for very small crystals as for large blocks.

Summing up what has been said above, one finds that the modern determinations give values of the electronic charge which group themselvesabout the value .. ,fte = (4*800 + 0*005) x 10-10 e.s.u.,which ought to give, with its limits of error, rather reliable directions for the search after the true value.

P l a n c k ’s Co n st a n t (h)

Planck’s constant can be measured in many different ways but, nevertheless, it is less well known than any other of the four constants discussed in this paper. The experiments never give h alone; it is alwrays combined



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436 S. von Friesen

with one of the constants e, e/m and m. The combination h/en with 3/34/3, or 5/3, occurs most frequently. The uncertainty of this other constant is added to the experimental errors.

Table IV contains those determinations of h, which are of interest to us in this connexion. The Table gives for each determination on the one hand the value published by the experimenter, on the other a value recalculated with more modern values of constants entering the calculations. In some cases incomplete information only is given as to values originally used. For this reason an additional error of a unit or two in the fourth place might have entered some of the recalculated values. When regarding the errors it must be remembered that Feder and Schaitberger do not consider the error of e when stating limits of error.

With the method based on the photoelectric effect, h is determined from the maximum energies which photoelectrons are able to attain at illumination with light of a number of known frequencies. I t is difficult to measure this maximum energy accurately and for that reason the value of h obtained is less accurate than those given by the methods II, IV, and V of our Table. Lukirsky’s and Prilezaev’s work, in particular, has been subject to severe criticism.

With the X-ray method, associated values of wave-length and voltage are observed near the point where the emission of the continuous X-ray spectrum begins. One of the magnitudes wave-length and voltage is kept constant and the other is varied in small steps. The intensity of the radiation is measured and one extrapolates to zero intensity. It is difficult to know how to make this extrapolation, and it constitutes, therefore, the most serious source of error in this method. I t seems necessary to assume an error of at least two-tenths of a percent, if the uncertainty of the value of e is taken into account.

Gnan measured the wave-length of electrons, the velocity of which had been measured according to Kirchner’s method of deflexion by alternating electric fields. He found him. He measured the wave-length on the crystal scale and, therefore, it is necessary to reduce his value to the absolute scale. The method is of great interest, but it has not been able as yet to give a very reliable value of h.

The other electron diffraction method (von Friesen) is experimentally exactly the same as that described above for the determination of e, the only difference being the elimination of e between the equations instead of h. The author’s opinion is that the limits of error may reasonably be taken to cover the true value of Planck’s constant.

The last value of Table IV has been derived from the formula for the



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438 S. von Friesen

Rydberg constant by use of those values of c, e, and e/m which have been chosen above. The accuracy of this value is of about the same magnitude as for the other values.

An inspection of Table V, which gives a survey of the results from different methods, shows that the agreement is quite satisfactory. This fact disproves the statement that the use of Millikan’s value of e should

T a b l e V— M e a n V a l u e s o f h

Method h Limits of errorPhotoelectric effect 6-60 ±0-03X-rays 6-607 ±0-015Electron diffraction I 6-61 ±0-02Electron diffraction I I 6-612 ±0-012Rydberg constant 6-619 ±0-013

alone be able to reconcile the results from the different methods. The limits of error in this Table include the error of the electronic charge. We shall choose as a reasonable value for Planck’s constant

h = (6-610 + 0-015) x 10“27 erg. sec.,and there is reason to believe that the true value will be found inside its limits.

M a ss o f H y d r o g e n A tom (Mh )

The most reliable method of obtaining ilfH is based upon the determination of Avogadro’s number N0. This number may be calculated from the

F .cformula N0 = -2 - . Its reciprocal equals the mass of an atom of unit atomic

weight. If we know, therefore, N0 and the atomic weight of the atom we know also the mass of the hydrogen atom. The formula for N0 contains F, e, and c. Birge has chosen for the Faraday a value 9648-9 e.m.u./g. equiv. In order to reduce this value from the chemical to the physical scale, we must apply a factor 1-00022 obtained from the determination of the relativeabundance of the isotopes of oxygen. We get the value F = 9651-1 which used with the values e = 4-800 x 10~10 e.s.u. and c = 2-9978 x 1010 cm./sec. gives N0= (6-028 ± 0-008) x 1023.

Aston’s new value for the atomic weight of HI is 1-00812 and so we find Mu = (1-673 ± 0-003) x 10~24 g.

The value is higher than Birge’s by about two-thirds of a percent. The difference is due chiefly to the use of the higher value for e. e/ilfH on the other hand is changed by about one-hundredth of a percent only from 9574-5 (Birge) to 9573-4 e.m.u./g. The ratio M-^jm becomes 1837. In both




N0 and Mn the dominating source of error is the uncertainty of the value of e.

T h e V a l u e o f S o m m e r f e l d ’s F i n e S t r u c t u r e Co n s t a n t

2 i7TC^Sommerfeld’s fine structure constant — is a pure number. AccordingitCto a hypothesis by Eddington its inverse value is exactly equal to 137. With the constant values chosen above we get 136-9, which, within the limits of error, agrees with the hypothetic value.

R e s u l t s o f t h e S u r v e y

Velocity of light =Specific charge of the electron = Electronic charge =Planck’s constant =Avogadro’s number =Mass of hydrogen atom =

(2-9978 ± 0-0002) x 1010 cm./sec. (1-7585 + 0-002) x 107 e.m.u./g. (4-800 ± 0-005) x 10~10 e.s.u. (6-610 ± 0-015) x 10~27 erg. sec. (6-028 ± 0-008) x 1023 (1-673 ± 0-003) x 10- 24 g.

The ± terms are estimates of reasonable limits of error (not probable errors).

R e f e r e n c e s

Backlin 1928 Uppsala Univ.— 1935 Z. Phys. 93, 450.

Backlin and Flem berg 1936 Nature, Lond., 137, 635. Bearden 1931 Phys. Rev. 37, 1210.— 1935 Phys. Rev. 48, 385.

Birge 1929 Rev. Mod. Phys. 1.Cornu 1876 A nn . Obs. Paris, 13.de Bray, E . J . Gheury 1934 Nature, Lond., 133, 948. Duane and others 1921 J . Opt. Soc. Amer. 5, 213.D u Mond and Bollm an 1936 Phys. Rev. 50, 524. Dunnington 1933 Phys. Rev. 43, 404.Feder 1929 A nn . Phys., Lpz., 1, 497.Gnan 1934 A nn . Phys., Lpz., 20, 361.H ouston 1927 Phys. Rev. 30, 608.

— 1934 Phys. Rev. 46, 533.— 1935 Zeeman Verhandelingen, The Hague, 71.

M ittelstaedt 1929 A nn. Phys., Lpz., 2, 285.K irchner 1932 A nn. Phys., Lpz., 12, 503. K irkpatrick and Ross 1934 Phys. Rev. 45, 454. Lukirsky and Prilezaev 1928 Z. Phys. 49, 236. Mercier 1923 J .Phys. Radium, 5, 168.



440 S. von Friesen

Michelson 1879 Amer. J . S 18, 390.— 1885 Astr. Pap., Wash., p. 235.— 1924 Astrophys. J . 60, 256.— 1926 Astrophys. J . 65, 1.

Millikan 1913 Phys. Rev. 2, 109.— 1916 Phys. Rev. 7, 355.— 1917 Phil. Mag. 34, 1.— 1930 Phys. Rev. 35, 1231.

Newcomb 1885 Astr. Pap., Wash., p. 112.Olpin 1930 Phys. Rev. 36, 251.Pease and Pearson 1932 Astrophys. J . 82, 26. Perrotin 1902 C.R. Acad. Sci., Paris, 135, 681.Perry and Chaffee 1930 Phys. Rev. 36, 904.Rosa and Dorsey 1906 Bull. U.S. Bur. Stand. 3, 433. Shane and Spedding 1935 Phys. Rev. 47, 33. von Friesen 1935 Uppsala Univ. Arsskr.Schaitberger 1935 A nn. Phys., Lpz., 24, 84.

The Transport Numbers of the Ions in Solutions of Silver Dodecyl Sulphate

B y 0 . R h y s H o w e l l a n d H a r r y W a r n e

The College of Technology, Manchester

(Communicated by Eric K. Rideal, — Received 1 February 1937)

The electrical conductivities of a number of metallic long-chain alkyl sulphates have been measured at different temperatures (Lottermoser and Piischell 1933; Howell and Robinson 1936).

The curve for each salt at each temperature consists of three distinct ranges.*

Over the first range the conductivity falls as a linear function of the square root of the concentration. The behaviour is typical of that of a simple electrolyte and conforms to the Debye-Huckel theory of ionic interaction, the Onsager slope is only a little greater than for a simple salt. It is therefore generally agreed that over this first range the electrolyte is completely

* Compare the curve for silver dodecyl sulphate, fig. 2.



On the values of fundamental atomic constantsrspa.royalsocietypublishing.org/content/royprsa/160/902/424.full.pdfI Cornu 1874 Fi 300,400 ±300 2 x 23 km. ... To make a measurement

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