Experiment 2. The same element with the same filling. w=7·411 S. M. U., w" 7.279 S. M. U., e'=20.094, 'millim. mgr.

e"=20'007, E=19.150 × 1010

sec.2

Experiment 3. Daniell's element-freshly amalgamated zinc, sulphuric acid of sp. gr. 1.035, concentrated solution of sulphate of copper, copper.

w=6.949 S. M. U., w" 7.081 S. M. U., 11.952,

e"=11741, E=11.286 × 1010

Mean values.

w1=7015

(millim♬ mgr.).

sec.2

e=11.847.

Result.

1 S. M. U. =0.9526 x 1010 (millim.).

Experiment 4. The same element with the same filling. w1'=6·831 S. M. U., w1"=7·125 S. M. U., e'=11·887,

e"=11739, E=11317 x 1010(

Mean values.

(millim. mgr.

w1=6·978 e=11.814.

Result.

sec.2

1 S. M. U. =0·9579 × 1010 (millim

sec.

Experiment 5. Daniell's element-freshly amalgamated zinc, concentrated solution of sulphate of zinc, concentrated solution of sulphate of copper, copper.

w=16-598 S. M. U., w" 16.039 S. M. U., e=11.453,

e"=11-450,

=

E=10.954 x 1010

Mean values.

w=16-319 e=11.451.

Result.

1 x

S. M. U.=0-9565 × 1020 (millim.).

sec.

Phil. Mag. S. 5. Vol. 5. No. 30. March 1878.

The determinations executed according to this third method, of the absolute electromagnetic value of Siemens's mercury unit, have given the following results:

=0·9550 × 10° sec.

For facility of review, I place the final results for the absolute value of the S. M. U. together. We have found the absolute electromagnetic value of:

1 S. M. U. =0·9545 × 101(millim.)

from 18 series of experiments, in which the variable currents generated by magneto-induction were employed;

1 8. M. U, =0·9554 × 1010 (millim.)

sec.

from 24 series of experiments, in which the variable currents called forth by sudden voltaic induction were employed; and

1 S. M. U. =0·9550 × 1010 (millim.)

from 5 series of experiments, in which the heat-production of stationary galvanic currents was used.

The general mean,

1 S. M. U. = 0.9550 1010 (millim.),

is only per cent. greater than the result found by Messrs. Maxwell, Jenkin, and Stewart. After these results I hold that the questions of the true absolute value of the S. M. U., and whether the British resistance-unit does or does not represent the value asserted, are settled. The true value of S. M. U. millim. lies between 0-9536 ×

/millim.) and 0.9550 x 1010;

sec.

and the British unit represents, neglecting very minute differences possibly still present, the value asserted, 1010

(millim.).

When an observer finds the same result in three different

ways, and employing three quite different natural laws-when, further, this result but very slightly differs from that of another group of observers who worked according to a fourth, essentially different method, certainly it can be pretty safely maintained that the result so found is correct.

In instituting this last series of experiments, besides ascertaining the absolute value of the S. M. U., I pursued also, have already intimated, another aim, which, in conclusion, I will briefly explain.

M. Favre has repeatedly determined with the aid of the mercury calorimeter the quantities of heat developed by the most various electromotive forces in their circuits during the time in which they consume equal quantities of zinc—namely, the quantity which is chemically equivalent to the unit of mass of hydrogen. As the result of his experiments, he found that the ratio of those quantities of heat gives quite another value than does the ratio of the corresponding electromotive forces when measured galvanometrically. Thus, according to M. Favre, the quantities of heat which the elements of Daniell and Grove produce in their circuits during the time within which they consume 1 equivalent of zinc are 23993 and 46447 units. The ratio of these numbers is 1: 1.93, while the electromotive forces of the Daniell and Grove elements stand (according to all galvanometric measurements hitherto executed) in the ratio of from 1: 1.68 to 1: 1.70. This result of M. Favre's directly contradicts certain galvanic laws which are universally regarded as resting on a secure foundation, as will be evident from the following consideration:

If E denotes the hydroelectromotive force of a circuit, w the sum of all the resistances of the circuit, and Q the sum of all the quantities of heat which the constant current i calls forth in the circuit during the time z, then, according to Joule's law (which we have demonstrated under section III. to be correct),

JQ=&wz;

or, if, according to Ohm's law, we put iw=E,

JQ=iEz.

If a denotes the electrochemical equivalent of zinc, the quantity m of zinc which is consumed within the element during the time z becomes, according to Faraday's law of electrolysis,

m=aiz.

Therefore the total heat Q produced in the entire circuit by the

electromotive force E during the time that within the element the quantity m of zinc is consuming is

Em = Ja

Hence, if the galvanic laws of Joule, Ohm, and Faraday are universally true, the quantities of heat Q and Q2 which two different electromotive forces E1 and E2 develop in their circuits during the time they consume equal quantities of zinc must be in exactly the same proportion as the electromotive forces E1 and E2. Consequently M. Favre's measurements and the three laws mentioned are irreconcilable with each other.

M. Favre's results are refuted by the above-stated determinations. The relative values of the electromotive forces, measured by a galvanometric method, have been found to be:For Bunsen's element, in the mean,

e1=19.927.

For Daniell's element with sulphuric acid, in the mean,

e2=11.830.

For Daniell's element with sulphate of zinc,

eg=11.451.

And the absolute values of these electromotive forces, determined simultaneously by the heat generated in the entire circuit, have given :

For Bunsen's element, in the mean,

From these we get for the ratio of the galvanometrically measured electromotive forces and the electromotive forces measured by their heat-evolution the values

numbers which rigorously correspond to the deductions from the laws of Ohm, Joule, and Faraday. The cause of Favre's result being so seriously faulty lies probably, in great part, in the circumstance that, in all his calorimetric investigations, he made use of the mercury calorimeter, with the use of which a whole series of uncertainties are necessarily connected, and which it should be a maxim not to employ. For all galvanocalorimetric investigations in which the duration of the heatevolution can be chosen entirely at discretion, and so the heat produced can be made as great as we please, the simple water calorimeter, managed with nicety, is by far the most reliable, and, for many reasons, even preferable to Bunsen's ice calorimeter. The numerous measurements instituted by M. Favre many years since, respecting heat-production by galvanic currents and electromotive forces, were very probably all vitiated by an error of the same order as were the values given by him for the heat developed by Daniell's and Grove's elements. Should a secure basis be obtained in this department, nothing remains but to repeat with more accurate methods all the more important of his measurements.

The unit of length employed in these investigations is the millimetre of the cathetometer of the Physical Laboratory at Zurich; the time-unit is the second of mean time; the Siemens resistance-unit is the No. 1914, which I obtained from M. W. Siemens at the commencement of the investigation, and which was most carefully compared with all the other resistances employed.

Zurich, August 1877.

XXVII. Rain-Clouds and Atmospheric Electricity. By W. E. AYRTON and JOHN PERRY, Professors in the Imperial College of Engineering, Tokio, Japan.

GIVI

To the Editors of the Philosophical Magazine and Journal. The Imperial College of Engineering, GENTLEMEN, Tokio, Japan, December 8, 1877. IVING all due weight to the theories of thermoelectric currents produced by rotation of the earth under the sun, and of currents which might be produced by moving electrified shells of air, we have always thought that these sources of electric disturbance on the earth were far too inconsiderable to give rise to the phenomena of earth-currents and of atmospheric electricity, and also totally inadequate to account for currents of sufficient intensity to produce terrestrial magnetism. We think that there cannot be any