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 forcein of one hyper-hektogram, a measure of convenient amount; and 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 67 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 error 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 are A massein of ten kilograms (the myriagram); A lengthein of one metre; and A timein of one second; whence we obtain, as derived units The velocitein = one metre per second; The densitein ten grams per litre, in which unit the maximum density of water is 100; 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. systein 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 centimetre; 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 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 624: 63. 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 64, 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. 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. 7. On Standards of Low Electrical Resistance. 8. On the Specific Conductivity of Copper. By J. TEIChmüller. WEDNESDAY, AUGUST 15. The following Papers were read :— 1. On the Displacements of the Rotational Axis of the Earth. By Professor W. FÖRSTER.-This Paper was ordered by the General Committee to be printed in extenso. See Reports, p. 476. 2. A Lecture-room Experiment to illustrate Babinet's Principle. By Professor A. CORNU, F.R.S.-This Paper was ordered by the General Committee to be printed in extenso. See Reports, p. 480. 3. A New Explanation of the Wave-movements of a Stretched String. By WM. BARLOW. The writer begins by setting out the commonly received explanation which attributes to the string when disturbed the properties of a cord slipping through a bent tube at a velocity such as to make the pressure on the tube arising from the centrifugal force just balance the pressure caused by the tension.1 He then argues that this course involves the fallacy that a wave-movement is supposed to take place spontaneously in the disturbed cord, whereas all that the argument offered proves is that if a wave is set up and travels at a certain rate in a given direction, it will have a constant form. He further shows that the conditions laid down do not suffice to determine the direction of the wave; that the direction is perfectly arbitrary. He then suggests another explanation of the wave-movements in question. This is based on the observed behaviour of a highly elastic cord, and he attributed the wave-movement to the successive orientation of segments of the stretched string caused by a difference of tension due to inertia, the spot at which the difference makes itself felt travelling along the string, now in one direction, now. in the opposite, as the string swings from side to side of its normal position. 5. On Lunar Curves of Mean Temperature at Greenwich, and the The great heat experienced in 1893 led the author to tabulate the mean temperatures of the day at Greenwich for that year, according to the age of the moon, to see how far a curve derived from them corresponded with the model curve for 618 lunations, which was exhibited by him on the last occasion when the British Association visited Oxford. Whilst closely following the curve alluded to, the maximum temperature showed itself two days earlier in the lunation; but the same abrupt fall in temperature occurred immediately after the first quarter, and continued below the average of the year from that period until the second day after last quarter. The difference between the maximum on the fourth day of the lunation and the minimum on the day of full moon was 6' Fahr. for twelve complete lunations. p. 416. 1 See Art. Wave,' Enc. Brit., 1894. Q Q |