Now C.G.S. units are one of the innumerable metric systems of systematic physical units thus placed at our disposal. This particular system is found to be inconvenient for use by practical men; which makes it desirable that they should be able on many occasions to avail themselves of other metric systems equally systematic and in closer relation to their work. This is the more to be recommended since the translation from any such system into the C.G.S. system, in which our best tables of physical units exist, or from the C.G.S. system into it, can by the proposed nomenclature be made so conspicuous as to be always certain and easy. The prefix hyper- and the affix -ein are designed to provide us with facilities for doing this.

Employing the word weights to designate the pieces of metal used with our balances, it may be stated to be the usual practice of engineers and physicists to measure forces by the gravitations of these weights, i.e., by the downward forces exerted by them at the station where the experimenter works. Now the gravitations or downward forces of all weights, and therefore of the metric series-the gram weight and its decimal multiples and submultiples-vary slightly from one station on the earth's surface to another; while the decimal series of systematic forces (determined by the condition that they are the force which will produce an acceleration of a metre per sec. per sec. in a mass of a kilogram, along with the decimal multiples and submultiples of this force) is a system of forces quite independent of the place of observation, and therefore each of them maintains the same value over the whole universe. Here, then, we have two decimal series of forcesone the fixed series required in dynamical calculations, the other the gravitations or downward forces of the metric weights, convenient in experiments but depending for the amounts of these forces upon the situation where the experiment is made. Now it so happens that the theoretic forces are close to-about two per cent. more than the laboratory forces; and hyper-, when prefixed to the name of a weight, is intended to signify the slight increase which has to be made in it to make its gravitation become equal to the adjoining theoretical force. Thus in the language of systematic measures the hektogram, kilogram, &c., are masses; but the hyper-hektogram, hyper-kilogram, and so on, are forces, viz., those forces of the systematic decimal series which are about two per cent. more than the gravitations of the hektogram, the kilogram, and the other metric weights. The prefix hyper may accordingly be paraphrased into 10g times the gravitation of the weight whose mass is a The coefficient 10g, which is indicated by hyper-, (in which g is gravity at the station where the experiment is made, expressed in metres per second per second), varies from 1·022 at the equator to 1017 at the pole, and is about 1019 in England; or, with more exactness, an observer at

1

The following is a convenient formula for the unit of absolute force :The hyper-hektogram = the gravitation or downward force in vacuo of

at latitude A, and at the height of h metres above the sea. Hence the hyper-hektogram to the nearest milligram

the extreme range, between the equator and the poles, being the gravitation of about half a gram (0·52 gram).

Manchester would have to put into one scale of his balance 101.902 gram weights (with small corrections for his height over the sea, and for the air displaced by the weights) in order to urge this scale downwards with precisely that force (the hyper-hektogram) which, if it acted on a mass of one kilogram, would generate in it an acceleration of one metre per second per second. This he would express by saying that the hyper-hektogram (that member of the series of decimal systematic forces which differs but little from the gravitation of a hektogram) is in reality the gravitation at Manchester of 101.902 gram weights, weighed in vacuo and at the level of the sea.

Another affix which will be found convenient is -ein, meaning 'unit of,' so that the forcein shall signify the unit of force, the massein the unit of mass, &c., which we happen at the time to be employing. Thus in the C.G.S. system

whence

The massein is one gram;

The lengthein is one centimetre ;

The timein is one second;

The forcein is the C.G.S. dyne, which is one hyper-milligram, and

The energein is the C.G.S. erg, which is the hundred-thousandth part of one hyper-grammetre.

The dyne is far too small a unit of force for convenient use in the laboratory of the mechanician or even of the physicist. It is the gravitation of a tiny fragment of note-paper not more than about one-eighth of an inch square. And the erg, the unit of energy in C.G.S. measure, is still more preposterously small. The grammetre is already a small measure of energy, the hyper-grammetre is only about two per cent. more; and the erg is the hundred-thousandth part of this small

measure.

Much better systems for practical use are the K.M.S. system and the M.M.S. system. The K.M.S. system, which is based on the kilogram metre and second, will be found the most convenient in the laboratory of the dynamical physicist. In this system

The massein is one kilogram;

The lengthein is one metre ; and

The timein is one second.

These are its fundamental units, whence are derived—

The velocitein of one metre per second, about an ordinary walking pace;
The densitein of one gram per litre, in which unit the maximum density of
water is 1,000, and the density of standard air is 1.276;

The forcein of one hyper-hektogram, a measure of convenient amount; and
The energein of one hyper-hektogrammetre, which is equally convenient.
The supply of this amount of energy per second is what electricians call a
'watt.'

To the engineer and to the electrician the M.M.S. system offers certain advantages over that just described; and either of them is immeasurably to be preferred

To each of these add one milligram for every 30 metres (100 British feet) that the station is above the sea, and add between 15 and 16 milligrams if the weights are used in air, and if they are brass weights.

The correction for latitude may be made with sufficient accuracy within the British Isles by allowing one centigram for every 1° 7' that the station is north of the latitude of 45°, i.e., one milligram for a difference in latitude of 6-7 minutes of arc; the error of this approximation amounting to only one milligram at Edinburgh, where it is more than at any other of the above stations-an erior which is usually of no account, since no determination of the kind can be made to within less than a fifthet of its entire amount.

in practical work to the C.G.S. system. In the M.M.S. system the fundamental units

The densiteinten grams per litre, in which unit the maximum density of water is 100;

The forcein one hyper-kilogram; and

The energein one hyper-kilogrammetre.

=

Inasmuch as the engineer, if he uses metric weights, determines all his forces in kilograms and measures energy in kilogrammetres, the M.M.S. system is the most convenient for him. He has only to increase each of these measures by 1-9 per cent. to have his determinations expressed in hyper-kilograms and hyper-kilogrammetres, i.e., in systematic measures adapted to any dynamical calculation he may have occasion to make. It is also deserving of note that this system is more conveniently related than the K.M.S. system to the C.G.S. system, in which our best tables have been computed. This arises from the circumstance that LM, a physical quantity which is constantly turning up in the dimensional equations of electricity and magnetism, is in the M.M.S. system an exact decimal multiple of what it is in the C.G.S. system. The relation here pointed out is of importance to the electrician.

The use of the prefix hyper- has the additional advantage of keeping steadily before the mind of the student the actual amounts of the measures of force and energy with which he is dealing, and thus helps him to make his conceptions correspond to the facts of nature. The amount of each measure is not brought into view by such names as dyne and erg unless supplemented by such names as hypermilligram and hyper-fifthet-grammetre, and is apt to be lost sight of in using the C.G.S. system.

The author was a member of the Committee of the British Association, which in 1873 recommended C.G.S. measures for general adoption by physicists. He put forward in competition with it the K.M.S. system, spoken of above, and also advocated the use of the prefix hyper- to be employed as described in this paper. It is correctly recorded in Everett's Units and Physical Constants' that he dissented from the choice made by the Committee, but the reason for his dissent is not correctly indicated. His main objection was that this choice needlessly led to such out of the way values for the dyne and erg-needlessly, because other choices might have been made, such as of either the K.M.S. or the M.M.S. system, which, while equally adapted to the sciences of electricity and magnetism, would have been free from this great inconvenience in dynamics. He regrets to have observed that the choice that was then made has retarded the use of systematic measures by practical men and even by students, and hopes that this may in some degree be remedied by the suggestions made in the present paper.

Another useful suffix is -et, meaning decimal submultiple. As applied to numerals it gives us such suitable names as sixthet, tenthet, seventeenthet for a unit in the sixth, tenth, and seventeenth places of decimals, which are otherwise expressed as 10-6, 10-10, 10-17. A convenient symbolical representation is VI, X, XVII, the symbol being very easily written and being what in Sir Isaac Pitman's system of shorthand spells thet, so that VI, X, XVII are to be read sixthet, tenthet, seventeenthet.

The suffix -et may also be appended to the names of measures, e.g., metrets are the decimal subdivisions of the metre. These in their order are to be spoken of as the decimetre; the centimetr; the millimetre; the IV'm, the fourthet-metre, or fourth metret; the Vm. fifthet-metre, or fifth metret; and so on. Thus the micron used by microscopists may be described either as

The sixth metret or as

The sixthet-metre,

this last being an abbreviated form of 'sixthet of a metre,' just as half-ounce and quarter-inch mean the same as half of an ounce and quarter of an inch. Similarly the measure in which wave-lengths of light are usually measured may be described indifferently as

The tenth metret or as
The tenthet-metre.

Either of these is to be preferred to the designation tenth-metre, which the author suggested many years ago,' and which has since been in some degree used. Either tenth-metret or tenthet-metre is correct, but the author himself prefers the latter form.

In the same way gramets are the decimal subdivisions of the gram. As an example of their use, it is possible by the kinetic theory of gases to arrive at an estimate of the mass of a single chemical atom of each element. That of hydrogen proves to be about the XXVg-the twenty-fifth gramet, or twentyfifthet of a gram, i.e., the twenty-fifth of that descending decimal series of which the decigram, the centigram, and milligram are the first three terms.

For multiples it is convenient to introduce the syllable -o-: thus, in the case of numbers, the name uno-eighteen will mean 1018, the number which as ordinarily written would be 1 with eighteen ciphers after it. (This is about the number of molecules in each cubic millimetre of air at the bottom of our atmosphere.) The above number may be symbolised by XVIII, and so on in other cases. Again, this affix may be appended to such words as metre, gram, &c. Thus the velocity of light in vacuo is to be written 3mVIII/sec., and is to be read three metroeights per second.' In like manner a tonne weight (the metric ton) is the gramosix, and so on.2

Other useful affixes are -el and -ane: -el to be applied to British measures of length, -ane to metric. An accordance between British and metric measures of length may be brought about in either of two ways-either by slightly shortening the British inch, foot, and yard, or else by in an equal degree lengthening the metre. In the one case the British foot is shortened down to be exactly 30 centimetres, in the other case the metre is lengthened out to be exactly 40 inches. The syllable -el may be used to indicate the change required in the yard, foot, and inch. Accordingly the words inchel, footel, and yardel will mean the inch, foot, and yard shortened in the ratio of 63: 62, or, which is the same thing, in the ratio of 1016 to 100. On the other hand, the syllable -ane may be used to signify an equal change in the opposite direction of metric measures, so that the metrane, decimetrane, centimetrane, and millimetrane are to be understood as the metric measures lengthened in the same ratio, i.e., as 62: 634. With this convention as to the meaning of the affixes we may write

(Light in vacuo advances almost exactly one footel in each ninthet of a second of time.)

Phil. Mag. for August 1868, p. 138.

2 It would, no doubt, be more in consonance with the genius of the English language to call these the eighteenth uno, the eighth metro, the sixth gramo, and so on; but this consideration seems more than balanced by the great advantage possessed by the names as given in the text, of distinguishing in the broadest possible way between multiples and submultiples.

=

• The numbers we should otherwise have to use are: inch 25.4 mm., 30.48 cm., yard 9.144 dm.

foot

The use of these equivalents makes it easy for persons who are accustomed to the British yard, foot, and inch to think also in metric measures. They also furnish a link between British and metric measures which yields a ready means of effecting a closely approximate conversion of either into the other. For example, if we want to convert 27 yards into metres we write

The correction of 1 in every 62.5 (which is the same as 1 in every 61, or as 02 in every 14) requires the addition of rather less than

as the approximate equivalent. The accurate value differs from this by less than half an inch, and, moreover, by continuing the process two steps further the accurate value may always be got out. The calculation is of a kind which, when one is accustomed to it, can be made in the head rapidly and with ease.

DEPARTMENT III.

1. Report of the Electrical Standards Committee.-See Reports, p. 117.

2. Determination of the International Ohm in Absolute Measure.
By Professor VIRIAMU JONES, F.R.S.-See Reports, p. 123.

3. Comparison with the B.A. Units of some Coils of Low Resistance. By R. T. GLAZEBROOK, F.R.S.-See Reports, p. 128.

4. Comparison of the Standards of the Board of Trade with the B.A. Unit. By J. RENNIE.-See Reports, p. 130.

5. Comparison of some Standards belonging to the Indian Government. By E. O. WALKER.-See Reports, p. 131.

6. On the Specific Resistances of Copper and Silver.
By Rev. T. C. FITZPATRICK.-See Reports, p. 131.

7. On Standards of Low Electrical Resistance.
By Professor VIRIAMU JONES, F.R.S.

8. On the Specific Conductivity of Copper. By J. TEICHMÜLLER.