B.A. unit
of electrical resistance

A unit of electrical resistance, 1864 to about 1908, defined by the Committee on Electrical Standards of the British Association for the Advancement of Science, approximately 0.9866 ohms.

sources

engraving from BA report

1

The Committee considered that two distinct questions were before them, admitting of entirely independent solutions. They had first to determine what would be the most convenient unit of resistance, and second what would be the best form and material for the standard representing that unit. The meaning of this distinction will be apparent when it is observed that, if the first point were decided by a resolution in favour of a unit based on Professor Weber's or Sir Charles Bright and Mr. Latimer Clark's system, this decision would not affect the question of construction; while, on the other hand, if the second question were decided in favour of any particular arrangement of mercury or gold wire as the best form of standard, this choice would not affect the question of what the absolute magnitude of the unit was to be.

The Committee have arrived at a provisional conclusion as to the first question; and the arguments by which they have been guided in coming to this decision will form the chief subject of the present Report.

They have formed no opinion as to the second question, viz. the best form and material for the standard. In determining what would be the most convenient unit for all purposes, both practical and purely scientific, the Committee were of opinion that the unit chosen should combine, as far as was possible, the five following qualities.

1. The magnitude of the unit should be such as would lend itself to the more usual electrical measurements, without requiring the use of extravagantly high numbers of cyphers or of a long series of decimals.

2. The unit should bear a definite relation to units which may be adopted for the measurement of electrical quantity, currents, and electromotive force, or, in other words, it should form part of a complete system for electrical measurements.

3. The unit of resistance, in common with the other units of the system, should, so far as is possible, bear a definite relation to the unit of work, the great connecting link between all physical measurements.

4. The unit should be perfectly definite, and should not be liable to require correction or alteration from time to time.

5. The unit should be reproducible with exactitude, in order that, if the original standard were injured, it might be replaced, and also in order that observers who may be unable to obtain copies of the standard may be able to manufacture them without serious error.

The Committee were also of opinion that the unit should be based on the French metrical system, rather than on that now used in this country.

Fortunately no very long use can be pleaded in favour of any of the units of electrical resistance hitherto proposed, and the Committee were therefore at liberty to judge of each proposal by its inherent merits only; and they believe that, by the plan which they propose for adoption, a unit will be obtained combining to a great extent the five qualities enumerated as desirable, although they cannot yet say with certainty how far the fourth quality, that of absolute permanency, can be ensured.

The question of the most convenient magnitude was decided by reference to those units which have already found some acceptance. These, omitting for the moment Weber's metre/second, were found to range between one foot of copper wire weighing one hundred grains (a unit proposed by Professor Wheatstone in 1843) and one mile of copper wire of 1/16 inch diameter, and weighing consequently about 84½ grains per foot. the smaller units had generally been used by purely scientific observers, and the larger by engineers or practical electricians.

Intermediate between the two lay Dr. Werner Siemens's mercury unit, and the unit adopted by Professor W. Thomson as approximately equal to one hundred millions of absolute foot/seconds. The former is approximately equal to 371 feet, and the latter to 1217 feet, of pure copper wire 1/16-inch diameter at 15° C. Both of these units have been adopted in scientific experiments and in practical tests; and it was thought that the absolute magnitude of the unit to be adopted should not differ widely from these resistances.

The importance of the second quality required in the unit, that of forming part of a coherent system of electrical measurements, is felt not only by purely scientific investigators, but also by practical electricians, and was indeed ably pointed out in a paper read before this Association in Manchester by Sir Charles Bright and Mr. Latimer Clark.

First Report- Cambridge, October 3, 1862.
reprinted in
Fleeming Jenkin, editor.
Reports of the Committee on Electrical Standards Appointed by the British Association for the Advancement of Science.
London: E. & F. N. Spon, 1873.
Page 1.

2

Last year's Report announced the completion of the experiments determining the resistance in absolute measure of a certain coil of German silver wire. Taking this coil as the basis, Dr. Matthiessen, assisted by Mr. C. Hockin, prepared ten standards, each expressing the British-Association unit of electrical resistance; two of these standards are coils of platinum wire, two are of platinum-silver alloy, two are coils of wire drawn from a gold silver alloy, two are coils of wire drawn from a platinum-iridium alloy, and the remaining two are tubes of mercury.

The wires employed in the coils are from 0.5 millim. to 0.8 millim. diameter, and range from one to two metres in length. They are insulated with white silk, and are wound round a long hollow bobbin of brass. The wires are imbedded in solid paraffin, and enclosed in a thin brass case, which allows the coils to be plunged in a bath of water by which their temperature may be conveniently regulated and observed. Two short copper terminals project from the case and are forked at their ends, so that they may be connected with the Wheatstone's balance in the manner recommended by Professor W. Thomson, avoiding the error due to the possible resistance of connexions. The mercury standards consist of two glass tubes about three-quarters of a metre in length.

These ten standards are equal to one another and to the British-Association
unit, at some temperature stated on the coil or tube, and lying between 14°.5
and 16°.5 C.

None of them, when correct, differ more than 0.03 per cent. from the value at 15°.5 C.

Fourth Report- Birmingham, September 6, 1865.
reprinted in
Fleeming Jenkin, editor.
Reports of the Committee on Electrical Standards Appointed by the British Association for the Advancement of Science.
London: E. & F. N. Spon, 1873.
Page 132.

3

The original Committee was dissolved in 1870. In 1881 it was reconstituted in response to a number of experiments showing varying values for the B.A. standards.

It appeared to the Committee that in order to perform the task entrusted to them, they had two principal questions to consider: First, to select or prepare a well-defined standard of accurately known absolute value for each kind of magnitude; and, secondly, to take measures for making certified copies of each of the adopted standards accessible to the public.

The standard magnitudes which the Committee have had under consideration as yet are-

1. The Standard of Resistance.

2. The Standard of Capacity.

3. The Standard of Electromotive Force.

As to the first of these, the standard of Resistance, the Committee were of opinion that, in view of the discrepant results obtained by experimenters who have re-examined the absolute resistance of the B.A. unit, it might be well to reconsider the question whether the “ohm” should be defined by reference to a particular coil of wire preserved as a concrete standard, or whether the term “ohm" should be understood to mean a resistance of 109 C. G. S. units. They were also of opinion that it was desirable to continue the experimental investigation of the absolute resistance of the existing standards.

The repetition of the determination with the original apparatus, by Lord Rayleigh and Professor Schuster in the Cavendish Labomtory, has gone far to supply this requirement. Experiments by another method have also been carried on by Professor G. C. Foster in the Physical Laboratory of University College, London. Some account of these experiments is given in Appendix I. to this Report, but the results hitherto obtained can only be regarded as preliminary. With regard to the issue of authorised copies of the ohm for general use, the Committee did not see their way to making arrangements for actual construction of standard coils.

A further question arising out of the mutual relations of the fundamental units was that of the magnitude of the practical units to which distinctive names should be attached. The present usage with respect to this matter is that a resistance of 109 C. G. S. units is called an Ohm; an electromotive force of 108 C. G. S. units is called a Volt; and the current produced by a Volt acting through an Ohm, that is to say, a current of 108 ÷ 109 or 0.1 C. G. S. unit is called a Weber. In the opinion of the Committee it was considered highly desirable, from a scientific point of view, that the relations among these standards should be simplified by defining them as follows:-

Ohm = 109 C. G. s. units of resistance.

Volt = 108 C. G. S. units of electromotive force.

Weber = 1 C. G. S. unit of current.

It was felt, however, that any recommendation involving a change in the value attached to terms which are rapidly coming into extensive use among practical electricians, might give rise to serious inconvenience. Therefore, although with regard to the scientific aspect of this proposal the Committee were decidedly in favour of the change, they felt that a public recommendation could not well be made until the practical inconveniences likely to follow had been very carefully investigated.

Eighth Report- York, 1881.
Reports of the Committee on Electrical Standards Appointed by the British Association for the Advancement of Science.
Cambridge: Cambridge Univ. Press, 1913.
Pages 293 & 296.

4

I wish to call the attention of readers of Nature who are interested in the experiments which have recently been made for the determination of the B.A. unit of resistance, to a paper by F. Kohlrausch, read before the Academy of Sciences at Göttingen, September 6, 1882, “On the Measurement by Electrical means of the mean Area of the windings of a Coil.” Prof. Kohlrausch has applied his method to redetermine the mean area of the coils of the earth inductor used by him in his experiments on the value of the B.A. unit in 1874. He finds the area of this coil to be 387,200 sq. cm.; the value used in 1874, calculated from the geometrical measurements of Weber in 1853, was 392,800 sq. cm. In consequence the value of the B.A. unit as determined from his experiments requires alteration, and, making the necessary corrections, Prof. Kohlrausch obtains 1 B.A. unit = .990 7 × 109 cm/sec., agreeing much more nearly with the values found by Rowland, Rayleigh and Schuster, and myself.

R. T. Glazebrook.
Nature vol. 26, page 597 (19 October 1882)
doi:10.1038/026597d0

5

The Paris Congress adopted as a standard, to be called the “legal ohm,” the resistance at 0° C. of a column of mercury 106 centimetres long, and one square millimetre in section. The standard resistances at present in use being B. A. units, it became necessary to assume a relation between the B. A. unit and the legal ohm, in order to construct coils whose resistance should be one legal ohm. This relation has been determined by various observers with slightly different results, and a meeting of the Committee was held on June 28 to consider the question. At this meeting the following resolution, proposed by Professor W. G. Adams, seconded by Lord Rayleigh, was carried:- “That, for the purpose of issuing practical standards of electrical resistance, the number of B. A. units adopted as the resistance of a column of mercury 100 [sic] cm. in length, 1 sq. mm. in section, at 0° C., be .9540.”

Taking this number, then

1 legal ohm = 1.0112 B. A. units.

1 B. A. unit = .9889 legal ohms.

Eleventh Report- Montreal, 1884.
Reports of the Committee on Electrical Standards Appointed by the British Association for the Advancement of Science.
Cambridge: Cambridge Univ. Press, 1913.
Pages 325-324.

6

The question of the best value to adopt for the dimensions of a mercury column having a resistance of 1 ohm has been raised by some members of the Committee during the year. There is no doubt that the column of 106 centimetres adopted by the Paris Conference in 1884 is too short.

After a discussion of the results of the most recent observations, the following resolutions were adopted by the Committee:-

1. The Committee recommend for adoption as a standard of resistance sufficiently near to the absolute ohm for practical purposes the resistance of a column of mercury 106.3 cm. in length 1 square mm. in section at a temperature of 0° C.

2. That for the purpose of issuing practical standards of resistance the number .9866 be adopted as the ratio of the B. A. unit to the ohm.

Seventeenth Report- Leeds, 1890.
Reports of the Committee on Electrical Standards Appointed by the British Association for the Advancement of Science.
Cambridge: Cambridge Univ. Press, 1913.
Page 366.

7

In November, 1890, the Association was invited by the President of the Board of Trade to nominate two members to represent the Association on a Committee “On Standards for the Measurement of Electricity for use in Trade.” A meeting of the Electrical Standards Committee was held on December 2, and it was agreed to suggest to the Council of the Association the names of Professor Carey Foster and Mr R. T. Glazebrook as representatives. These gentlemen were appointed by the Board of Trade together with Mr Courtenay Boyle, C.B., Major Cardew, Mr E. Graves, Mr W. H. Preece, Sir Wm. Thomson, Lord Rayleigh, Dr Jno. Hopkinson, and Professor Ayrton.

This Committee after various meetings drew up a report, a copy of which is printed as Appendix 1. to this Report.

APPENDIX I.

Report of the Electrical Standards Committee Appointed by the Board of Trade.

6. After a careful consideration of the questions submitted to us, and the evidence given by the various witnesses, we have agreed to the following resolutions:-

Resolutions.

1. That it is desirable that new denominations of standards for the measurement of electricity should be made and approved by Her Majesty in Council as Board of Trade standards.

2. That the magnitudes of these standards should be determined on the electro-magnetic system of measurement with reference to the centimetre as unit of length, the gramme as unit of mass, and the second as unit of time, and that by the terms centimetre and gramme are meant the standards of those denominations deposited with the Board of Trade.

3. That the standard of electrical resistance should be denominated the ohm, and should have the value 1,000,000,000 in terms of the centimetre and second.

4. That the resistance offered to an unvarying electric current by a column of mercury of a constant cross sectional area of one square millimetre, and of a length of 106.3 centimetres at the temperature of melting ice, may be adopted as one ohm.

5. That the value of the standard of resistance constructed by a committee of the British Association for the Advancement of Science in the years 1863 and 1864, and known as the British Association unit, may be taken as .9866 of the ohm.

6. That a material standard, constructed in solid metal, and verified by comparison with the British Association unit, should be adopted as the standard ohm.

7. That for the purpose of replacing the standard, if lost, destroyed, or damaged, and for ordinary use, a limited number of copies should be constructed, which should be periodically compared with the standard ohm and with the British Association unit.

8. That resistances constructed in solid metal should be adopted as Board of Trade standards for multiples and submultiples of the ohm.

7. We have adopted the system of electrical units originally defined by the British Association for the Advancement of Science; and we have found in its recent researches, as well as in the deliberations of the International Congress on Electrical Units, held in Paris, valuable guidance for determining the exact magnitude of the several units of electrical measurement, as well as for the verification of the material standards.

8. We have stated the relation between the proposed standard ohm and the unit of resistance originally determined by the British Association, and have also stated its relation to the mercurial standard adopted by the International Conference.

9. We find that considerations of practical importance make it undesirable to adopt a mercurial standard; we have, therefore, preferred to adopt a material standard constructed in solid metal.

10. It appears to us to be necessary that in transactions between buyer and seller a legal character should henceforth be assigned to the units of electrical measurement now suggested, and with this view, that the issue of an Order in Council should be recommended, under the Weights and Measures Act, in the form annexed to this report.

Eighteenth Report- Cardiff, 1891.
Reports of the Committee on Electrical Standards Appointed by the British Association for the Advancement of Science.
Cambridge: Cambridge Univ. Press, 1913.
Pages 423-428.

8

For an excellent history of the development of the electric and magnetic units up to 1913, see U. S. Bureau of Standards Circular 60.

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