Page images
PDF
EPUB

In conclusion your Committee submits the view that considering the very debatable nature of the subjects forming its report, the variety of opinions formed in different countries and expressed under different interests, the reception of the report has been remarkably favorable, and appears to have attained the desired object, namely a concentration of general opinion toward a concensus, in aid of the forthcoming Electrical Congress.

CARL HERING, Chairman.
A. E. KENNELLY.

ON THE NOTATION PROPOSED BY M. HOSPITALIER.

BY PROFESSOR ALEXANDER MACFARLANE.

I wish to make some observations on the "Table of Symbols of Physical Quantities and of Abbreviations" proposed by M. Hospitalier at the Frankfort Congress, and recently recommended for adoption by the Sub-Committee of the INSTITUTE On Programme for the Chicago Congress. My observations have reference to some features of the plan which it seems to me ought to be discussed and perhaps amended. The account of the sysem which I have before me is that published in the London Electrician for 15th of January, 1892.

The analysis upon which the system is based is thus stated: "The first and most indispensable point is to establish a clear and precise distinction between a physical quantity, its magni tude, and the unit which serves as a common measure in a given system to all magnitudes of the same kind. A physical formula always establishes a relation between physical quantities, each physical quantity being represented by a special symbol. The magnitude of a physical quantity is represented by the ratio between a physical quantity and the physical quantity of the same kind which is taken as unity. magnitudes of physical quantities are, therefore, essentially abstract numbers. Finally, the unit is a physical quantity of a particular size, which serves as a common measure, multiple or sub-multiple, to quantities of the same kind, which is designated by a special name, and which allows of abbreviations intended to simplify speech or writing. The symbols of physical quantities enter into physical formulæ, but units never do."

The

The above would be a sufficient analysis, if all physical quantities were of the non-directed or scalar kind. But it is not so; there are many electrical quantities of the vector kind, not to speak of more complex kinds. Thus in Clerk-Maxwell's "Electricity and Magnetism," vol. 1, page 10, we find, "When we wish to denote a vector quantity by a single symbol, and to call attention to the fact that it is a vector, so that we must consider its direction as well as its magnitude, we shall denote it by a German capital letter, as A B etc." In the writings of Fleming, Heaviside and other electricians, such vector quantities are denoted by simple black letters, such as A B, which are much easier to write and to read.

To avoid interference with such higher analysis or to provide for it, we require a more extended view of physical quantities. Physical quantities are either non-directed or directed. A nondirected quantity consists of magnitude only; a directed quantity consists of magnitude and axis. Magnitude is further analyzed into ratio and unit. In M. Hospitalier's scheme, symbols are provided for magnitudes only, none for physical quantities involving direction. Thus denotes the magnitude of a velocity, without regard to direction; F the magnitude of a force; the German M means the magnitude of the magnetic moment, not the magnetic moment itself; B the magnitude of the magnetic induction, not the magnetic induction itself. This defect may be removed by retaining the black letters M and A to denote the magnetic moment and magnetic induction, while corresponding italic letters M and A denote the respective magnitudes.

Another feature of the plan, which appears of doubtful utility to one who has studied the higher analysis, consists in denoting by the same symbol all physical quantities which have the same dimensions. For instance, W the symbol for work is also made the symbol for moment of a force, because the dimensions of both are LM T. But, though their dimensions are the same, these quantities are very different in nature; work is a nondirected quantity, while moment of a force is a directed quantity. In work the two lengths have a common direction, while in moment of a force they are transverse to one another. To give the same symbol to two quantities so different in their nature is not sanctioned by established notation, and it proceeds upon a principle which is novel and not in accord with the results of the higher analysis.

In the higher analysis it is important to have not only a symbol for an angle, but also a symbol for an axis. The Frankfort Congress recommended physical constants and angles to be represented by Greek letters. An axis is also best denoted by a Greek letter. Let B denote a directed physical quantity; then if the Italic B denotes its magnitude, and the Greek its axis, we get a compact systematic notation which is very easily remembered.

In the plan of M. Hospitalier centimetre per second is abbreviated by cm/s, dyne per square centimetre by dyne/cm,2 and centimetre per second per second by em/s. Here we have a contradiction. If dyne/cm2 expresses dyne per square centimetre, then by the same rule cm/s2 expresses centimetre per second squared. The unit centimetre per second per second is properly abbreviated by (cm/s) /s; the idea cannot be unambiguously expressed without the use of a bracket. For example, 980 (cm/s)/s expresses the acceleration of gravity, while 490 cm/s expresses the connection between the fall and the square of the time elapsed.

The importance of the use of a bracket in expressing a derived unit in terms of the fundamental units, is well shown in the case of the unit of specific resistance. In some English works such as Ayrton's Practical Electricity, specific resistance is expressed in terms of "ohm per cubic centimetre." In a recent paper, printed in the Electrical Engineer, for December 28th, 1892, M. Hospitalier criticises this usage as follows: "For the same reason, only the units of the quantities which de fine that quantity should enter into the definition of a unit of measure for a given quantity. Thus for example, the English persist in expressing specific resistance in ohm per cm3 on the assumption that the specific resistance of a substance is the resistence of a cube of 1 cm. cross section between opposite faces. Specific resistance cannot be measured in ohms per cm, it is the product of a length and a resistance, and should be measured in

centimetre-ohms."

I drew attention to this matter in a paper read before the American Association for the Advancement of Science at the Washington meeting in 1891. Specific resistance is not properly expressed in ohms per cm3 because per denotes proportionality, and the resistance is not proportional to the volume. The true unit can be expressed with the help of a bracket, thus: ohm per (cm per cm3), that is, the resistance is proportional to the length divided by the cross-section. This is the direct definition of the quantity, and much more logical than the definition by means of dimensions. In M. Hospitalier's table no names are suggested for the C.G.s magnetic and electro-magnetic units. It is to be hoped that the principle of defining them by means of their dimensions will not be adopted. Given words for the c.G.s. units of intensity of pole, current, electromotive force, and resistance, then the others can be defined by compound words which express not the dimensions, but the relations of the units to one another. Let P denote the word chosen for c.G.s unit of intensity of pole; X the word for c.G.s. unit of current; Y the word for the C.G.S. unit of electromotive force; Z the word for the c.G.s. unit of resistance. Then,

the unit of magnetic moment is P-centimetre.

[merged small][ocr errors][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][ocr errors]

intensity of magnetization, P per cubic centimetre.
intensity of field, dyne per P.

magnetic flux, dyne per P-square centimetre.
quantity of electricity, X-second.

capacity, second per Y.

specific resistance, Z per (centimetre per square

Γ.

conductivity, X per 1.

resistance, I per X (=Z.)

centimetre.)

specific conductivity, centimetre per square centi

metre per Z.

Etc.

[blocks in formation]

Etc.

COMMENTS ON THE REPORT OF THE COMMITTEE ON THE PROVISIONAL PROGRAMME

FOR THE CONGRESS.

BY DR. JOHN SAHULKA, AUSTRIAN DELEGATE TO THE CONGRESS.

[TRANSLATION.]

I. NEW UNits.

1. In the calculation of magnetic circuits the field strengths which occur in practice would have to be expressed in very small decimals, and magnetic resistances in very large numbers. In order to have convenient numbers, it would therefore be necessary to use the units micro-gauss and mega-oersted. This makes it desirable to retain the absolute c. G. s. system of units. The practical units volt, ampere and ohm, were introduced only because the absolute c. G. s. units would have given inconvenient figures for the quantities occuring in practice. In magnetic circuits no reason exists for giving up the absolute system of units.

2. The introduction of a unit (the mho) for the electrical conductivity of a circuit is not a necessity, as all calculations can be made with the units ohm, ampere and volt.

II. NAMES FOR NEW UNITS.

1. Should the absolute c. G. s. system of units for magnetic circuits be retained, which from recently expressed opinions seems probable, the introduction of new names would not be necessary.

2 The name "mho" for the unit of electrical conductivity was probably used by some one because it was introduced by Sir Wm. Thomson; should the new unit be introduced, it would be easy to find an appropriate name (thomson). In order to be consistent, one would then have to introduce a practical unit for magnetic conductivity (reluctivity ), and give it a name which is the reverse of the name oersted.

3. The name henry for the practical unit of self and mutual induction is preferred to the term quadrant, because induction coefficients are not lengths.

1 Inductivity, or magnetic permeability, is doubtless what was meant. Tr.

« PreviousContinue »