Introducing the actual values of C and v, we have

The new unit of time will be about 1h 51m;

The new unit of length will be about 118 thousand earth quadrants;

The new unit of mass will be about 2·66 × 1014 times the earth's mass.

Modern Views on Electrical and Magnetic Dimensions.

257. Maxwell has pointed out (Elec. and Mag. § 622, 2nd edition) certain relations which must exist between the dimensions of various electrical and magnetic quantities in any consistent system, and has shown (§ 623) that the dimensions of any electrical or magnetic quantity can be definitely expressed

(1) In terms of mass, length, time, and quantity of electricity;

(2) In terms of mass, length, time, and quantity of

magnetism;

the dimensions thus obtained being the same for all systems.

Rücker (Phil. Mag., Feb. 1889) has pointed out, as an algebraic deduction from equations given by Maxwell, that the dimensions of all electrical and magnetic quantities can be definitely expressed

(1) In terms of mass, length, time, and specific inductive capacity ;

(2) In terms of mass, length, time, and magnetic permeability;

and maintains, in common with several of the leading exponents of Maxwell's views, that specific inductive capacity and magnetic permeability, which are usually regarded as mere numerical quantities, ought to be regarded as quantities of unknown dimensions. The numerical ratios usually understood by these terms must then be regarded not as absolute but merely as relative values, all of which are to be multiplied by the values for vacuum, which are at present unknown, and which depend, in some way not at present known, on the units of length, mass, and time employed.

The following are examples of the dimensions thus obtained, K denoting specific inductive capacity, and μ magnetic permeability.

258. In every case the ratio of the dimensions in terms of K to the dimensions in terms of μ is a power of K3μ3LT-1.

If electrical and magnetic actions are to be regarded as manifestations of the ordinary laws of dynamics applied

to motions which our present knowledge does not enable us to specify, then every electrical or magnetic quantity has definite dimensions in terms of mass, length, and time; hence the expression KμLT-1 must be of dimensions MoLoT, in other words Kμ must be the reciprocal of a velocity.

211

APPENDIX.

First Report of the Committee for the Selection and Nomenclature of Dynamical and Electrical Units, the Committee consisting of SIR W. THOMSON, F.R.S., PROFESSOR G. C. FOSTER, F.R.S. PROFESSOR J. C. MAXWELL, F.R.S., MR. G. J. STONEY, F.R.S.,* PROFESSOR FLEEMING JENKIN, F.R.S., DR. SIEMENS, F.R.S., MR. F. J. BRAMWELL, F.R.S., and PROFESSOR EVERETT (Reporter).

[1873.]

WE consider that the most urgent portion of the task intrusted to us is that which concerns the selection and nomenclature of units of force and energy; and under this head we are prepared to offer a definite recommendation.

A more extensive and difficult part of our duty is the selection and nomenclature of electrical and magnetic units. Under this head we are prepared with a definite recommendation as regards selection, but with only an interim recommendation as regards nomenclature.

Up to the present time it has been necessary for every person who wishes to specify a magnitude in what is called "absolute " measure, to mention the three fundamental units of mass, length, and time which he has chosen as the basis of his system. This necessity will be obviated if one definite selection of three fundamental units be made once for all, and accepted by the general consent of scientific men. We are strongly of opinion that such a selection ought at once to be made, and to be so made that there will be no subsequent necessity for amending it.

* Mr. Stoney objected to the selection of the centimetre as the unit of length.

We think that, in the selection of each kind of derived unit, all arbitrary multiplications and divisions by powers of ten, or other factors, must be rigorously avoided, and the whole system of fundamental units of force, work, electrostatic, and electromagnetic elements must be fixed at one common level—that level, namely, which is determined by direct derivation from the three fundamental units once for all selected.

The carrying out of this resolution involves the adoption of some units which are excessively large or excessively small in comparison with the magnitudes which occur in practice; but a remedy for this inconvenience is provided by a method of denoting decimal multiples and sub-multiples, which has already been extensively adopted, and which we desire to recommend for general use.

On the initial question of the particular units of mass, length, and time to be recommended as the basis of the whole system, a protracted discussion has been carried on, the principal point discussed being the claims of the gramme, the metre, and the second, as against the gramme, the centimetre, and the second,the former combination having an advantage as regards the simplicity of the name metre, while the latter combination has the advantage of making the unit of mass practically identical with the mass of unit-volume of water-in other words, of making the value of the density of water practically equal to unity. We are now all but unanimous in regarding this latter element of simplicity as the more important of the two; and in support of this view we desire to quote the authority of Sir W. Thomson, who has for a long time insisted very strongly upon the necessity of employing units which conform to this condition.

We accordingly recommend the general adoption of the Centimetre, the Gramme, and the Second as the three fundamental units; and until such time as special names shall be appropriated to the units of electrical and magnetic magnitude hence derived, we recommend that they be distinguished from "absolute" units otherwise derived, by the letters "C.G.S." prefixed, these being the initial letters of the names of the three fundamental units.

Special names, if short and suitable, would, in the opinion of a majority of us, be better than the provisional designations "C.G.S.