numbers, since there is strong evidence to show that the differences must be due to experimental errors. The value of Nxe thus obtained is

Nxe=1.23 × 10-10,

e being the charge on an ion in a gas.

It has been pointed out that Nx E=1·22 10-10 where E is the charge on a hydrogen ion in a liquid electrolyte; and hence we see that the charges on ions in gases produced by various methods are equal to the charge on a hydrogen ion in a liquid electrolyte. This result depends only on the value of the product Nxe, and it is not necessary to rely on the determinations which have been made of these quantities separately in order to obtain a proof of the proposition.

The determinations which have been made of N and e vary over considerable ranges, and what are considered to be the most probable values of these quantities do not give the product Nxe=1·23 × 101o. If one of the quantities could be determined the other would follow, since the product is known accurately; but it is difficult to decide which has been found with the greater accuracy, as in both cases there are weak points in the assumptions which are made, and in addition there is considerable experimental error in the determination of the charge c. Nevertheless, it is not unsatisfactory to find that the product only differs by a factor of about 3 from the number 1.23 × 1010.

Lord Kelvin has recently passed in review the various methods which have been employed to determine N†, the number of molecules in a cubic centimetre of a gas at 0° C. and standard atmospheric pressure.

From the calculations he has made it seems more probable that 1020 is nearer to the true value of N than 8.9 × 1019, and it is not improbable that the true value is greater than 1020. This number is deduced from the coefficient of viscosity of argon and from its densities in the liquid and gaseous states. Using the formula NE=1·22 1010, it is seen that 1.22 10-10 is not improbably an upper limit to the values of the charge in electrostatic units.

The following are the values of e found experimentally by different observers ::

* Lord Kelvin, Phil. Mag. August & September 1902.

This number is about 5 per cent. greater than the value of N with which we have been dealing, which refers to 15° C. and standard atmospheric pressure.

With regard to the differences between his determinations, Prof. Thomson states in his recent paper: "The mean of these values gives 34 x 10-10 as the charge in electrostatic units of the gaseous ion. This is about half the value 6.5 × 10-10 I found in the earlier experiments. The difference is, as I have already explained, due to the expansions in the earlier experiments practically catching only the negative ions; this made the calculated value of n little more than half the true value, while it made the value of e twice as great as it ought to have been." The number n denotes the number of drops in the cloud formed by expanding the moist gas containing the ions. It appears from Mr. C. T. R. Wilson's experiments, that condensation of moisture takes place round negative ions for a slightly smaller expansion than is required to produce condensation round positive ions*. This may be the cause of the discrepancy between the experiments with radium radiation which give the value 34 10-10 and those which were first made by Prof. Thomson with Röntgen rays. The explanation does not, however, explain the difference between the value 34 10-10 and the value 6-8 10-10 which was obtained for the charge on the ions produced by the action of ultra-violet light. In the latter case no positive ions were present in the gas, and the number 6-8 10-10 was obtained from considerations of the presence of negative ions alone.

The mean of the values, omitting the value 6.5 × 10-10 for Röntgen rays, comes to 4.1 x 10-10.

Of the numbers in the table, that found by Dr. H. A. Wilson is probably the most reliable, and more weight ought to be given to his determination. By the method which he used he avoids the necessity of finding the number of drops in the cloud formed by the expansion of the conducting gas,

*C. T. R. Wilson, Phil. Trans. vol. cxciii. p. 289.

and a very uncertain quantity is thus eliminated from his calculations. Dr. Wilson concludes from his experiments that it may be considered established that e lies between 2× 10-10 and 4× 10-10 E.S. units." The lower limit is in fair agreement with the value 12 10-10 found for E by taking N=1020. We see, therefore, that the value 2 × 10-io does not differ by more than the factor 2 from the most probable values which can be obtained by both methods.

XXVIII. The Conductometer. By ROLLO APPLEYARD*. THIS is a direct-reading instrument, intended for the comparison of electrical conductivity† of copper and other wires, for a range within, say, 5 per cent. above and 5 per cent. below 100.

In

In comparing two wires, either may be regarded as the standard. Suppose that balance is obtained with two samples of equal length upon a straight bridge-wire, divided into 100 parts, the position of balance being L divisions: (A) assuming the two wires to be of the same mean diameter, but of different conductivities; (B) assuming the wires to be of equal conductivity, but of unequal diameters. case (A) it is found from the conditions of balance that a change of 1 per cent. conductivity between +5 per cent. and -5 per cent. corresponds on the average with 4 of the total length of the bridge-wire. If therefore the middle of the bridge-wire is marked" 100" and divisions are marked off from that point to right and left, each equal to 4 of the length of the bridge-wire, these approximately correspond to successive increments of 1 per cent. conductivity. Or again, if the standard wire is not 100 per cent., move the whole scale thus graduated so that the mark on it corresponding to the conductivity of the standard is in coincidence with the electrical middle of the bridge-wire. I have proved that this arrangement is still direct-reading, and that its indications may be trusted to within a considerable degree of accuracy.

In case (B), suppose the two wires have diameters d and (d+y) respectively. Then an expression for L in terms of y and d can be found. If in this expression y is given some definite value, say 1 mil, and if d is then given successive values corresponding to the whole range of diameters of wires in common use, a table or curve can be constructed showing at once the amount by which the slider must be

*Communicated by the Physical Society: read December 11, 1903.

See "The Electrical Conductivity of Copper," Electrical Review, June 19, July 3 & 10, and August 14, 1903.

moved, i. e. the deviation to be applied, to compensate for 1 mil, or for any fraction of 1 mil difference of diameters of the two wires, for any value of d within the range. Provided that y and d are in the same unit, the expression for L is perfectly general.

1

1

400

A

These partial operations (A) and (B), when combined, represent the complete corrections to be applied within the required limits of accuracy. I have proved that the errors involved by carrying out this method for a range from 95 to 105 per cent. conductivity never exceed 0.1 per cent. In the conductometer, the two partial operations are carried out by setting two scales with reference to the electrical middle of the bridge-wire. The first scale, marked "100" at the middle, is divided into say 10 divisions, each of the length of the bridge-wire, every such division representing 1 per cent. conductivity. This scale is set to correspond with the conductivity of the standard wire, as above explained. Or the standard wire may be replaced by a resistance-coil of the same material, corresponding to the resistance of a wire of length equal to that of the test-wire of diameter d, and of say 100 per cent. conductivity, in which case the "100" mark of this scale is placed in coincidence with the middle of the bridge-wire, and is there clamped so long as that kind of wire is being tested. A second scale is divided into graduations each equal to 1 of the total length of bridgewire. The middle point of this scale is marked "0." sliding contact for the bridge-wire can be set and clamped to this scale, at a point along it corresponding to the deviation, as above explained. This setting is to right or left of the "0," according to whether the test-wire is of greater or of less diameter than the standard wire. The deviation can be calculated from the mass, as well as from the diameter of the wire; the appropriate scale-setting is then given simply by 'fifty times the difference of the masses, divided by the sum of the masses," for any equal lengths whatever of test-wire and standard wire, the masses being expressed in any single unit of mass whatever. For routine testing, where large quantities of copper have to be dealt with, the average time of a test for a long series of tests has by this instrument been reduced to 18 seconds, with the diameter method. The theory and the mechanical details of the instrument are fully described in the Proceedings of the Institution of Civil Engineers,' vol. cliv. Session 1902-1903, part iv. It is clear that the principle above described for compensating for differences of diameter can be applied to potentiometer work generally. If conductivity is assumed constant, the instrument can be used as a very sensitive micrometer.

66

XXIX. On a Method of Mechanically Reinforcing Sounds. By T. C. PORTER, M.A.*

IT

[Plate XVI.]

T is now about ten years since a friend, Mr. A. J. JexBlake, first drew my attention to the fact that if a small tuning-fork be struck and then held in the flame of a bunsenburner the loudness of its note is very materially increased; at that time the explanation, though simple, did not occur to me, and although I mentioned the fact to two or three physicists, they did not suggest the cause.

That the phenomenon is not a case of ordinary resonance is proved by the fact that no increase in the loudness of the note is observed if the fork is held over the burner, either with or without the gas turned on; nor when the length of the tube of the burner is altered so that it would naturally respond, when filled with the mixture of gas and air, to the pitch of the fork employed. There is, in this case, some resonance, but it is very much fainter than the reinforcement we are considering.

Further, if the fork be held in the luminous flame from the same burner, caused by stopping up its holes, the sound is slightly louder, so that it is the action of the rarefactions and condensations of the sound-waves in the burning mixture of gas and air which gives rise to the increased loudness. The following experiment shows this admirably. A piece of wire gauze is supported about three-quarters of an inch above the bunsen, and the issuing mixture of gases ignited above the gauze, and the supply of gas and air so adjusted that the flame is all blue, and nearly quiet; if the fork be then held in the flame there is a very marked increase of loudness, whilst if it be held, as it easily can with a little care, between the gauze and the top of the burner, there is scarcely any augmentation of the sound.

If the various parts of a bunsen flame be explored with a sounding fork it will be found that there is the greatest effect in the hottest part of the flame, i. e. in that part where the most rapid chemical action is proceeding, and if experiments are made to compare the effects of the luminous and nonluminous flames of the same bunsen-burner, it appears that the latter is the more energetic, though the reinforcement caused by the former is very considerable. The effect of the sound-pulses is probably therefore to change the continuous flame of the burner into one which is more or less

* Communicated by the Physical Society: read December 11, 1903.