quantities in terms of any unit which he likes to adopt. He may use the yard for linear measurement and the litre for cubic measurement, only there will then be a complicated relation between his different results. The system of derived units which we have been briefly considering, is that which gives the most simple and natural relation between quantitative expressions of different kinds, and therefore conduces to ease of comprehension and saving of laborious calculation.

Provisionally Independent Units.

Ultimately, as we can hardly doubt, all phenomena will be recognised as so many manifestations of energy; and, being expressed in terms of the unit of energy, will be referable to the primary units of space, time, and mass. To effect this reduction, however, in any particular case, we must not only be able to compare different quantities of the phenomenon, but to trace the whole series of steps by which it is connected with the primary notions. We can readily observe that the intensity of one source of light is greater than that of another; and, knowing that the intensity of light decreases as the square of the distance, we can easily determine their comparative brilliance. Hence we can express the intensity of light falling upon any surface, if we have a unit in which to make the expression. Light is undoubtedly one form of energy, and the unit ought therefore to be the unit of energy. But at present it is quite impossible to say how much energy there is in any particular amount of light. The question then arises,-Are we to defer the measurement of light until we can fully and accurately assign its relation to other forms of energy? If we answer Yes, it is equivalent to saying that the science of light must stand still perhaps for a generation;

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science but almost every other. The dony is to select, as the provisional unit light of convenient intensity, which can be hoa time to time in exactly the same inSa mad winchs defined by physical circumstances. se wheld. (12't may be experimentally investiCarved to Dis unit, for instance that obtained

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Weir by Bunsen and Roscoe ". In after berme a matter of inquiry what is the eved in such at of Hght; but it may be long od velation is exactly determined.

cendi y indereadent unit, then, means one which d physically defined in a safe and reproin order that particular quantities may se mere accurately than they can yet

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he primary units. In reality almost all cenas are made by such independent units. Cass is practically an independent one,

eat of heat ought to be simply the ready described. But a weight can e one millionth part, and temperature candth part of a degree Fahrenheit,

than the five-hundredth thousandth reaperature, whereas the mechanical obably not known to the thousandth ... provisional unit of heat, which isite to raise a unit weight of ..... through one degree Centigrade rou o° to 1°. This quantity of 4to expression in terms of by the natural constant, and called the mechanical

59), vol. exlix. p. 884, &c.

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equivalent of heat, we know that the assumed unit of heat is equal to the energy of 423'55 gramme-metres, or that energy which will raise the mass of 423'55 grammes through one metre against 9'80868 absolute units of force. Heat may also be expressed in terms of the quantity of ice at o° Cent., which it is capable of converting into water under an inappreciable pressure.

The science of electricity has lately become so much a matter of quantity, that it is necessary to have some means of accurate expression. When we know exactly the mechanical equivalent of electricity, we can express quantities of electricity in terms of energy, but in the meantime we need some easy available unit. The British Association accordingly have selected as the unit of electrical force that which can just overcome the resistance offered by a piece of pure silver wire 1 metre in length, and I millemetre in diameter. This unit must be regarded as merely a convenient provision for working purposes, to be employed for the easy expression of quantities not yet brought into precise relation with the ultimate standards of time, space, and mass.

There may

also be other provisionally independent units employed in electrical science, such as the voltametric unit of current strength, namely, that current which by decomposing water produces one cubic centimetre of detonating gas at 0° Cent. and 760 mm. of pressure in one minute. The unit of electrical quantity, again, is that quantity which when concentrated in a point and acting on an equal quantity also concentrated in a point at a unit of distance, exerts a repulsion equal to the unit of force. There must also be a unit of electro-magnetic force. All these electrical units must, however, be definitely related to each other, and to the fundamental units, and it is a matter for continual investigation to determine such relations more and more accurately.

plexity, and the powers of scientific ndingly augmented.

Za..bage proposed the formation of a f all the constant numbers of nature; an would be almost coextensive with f scientific literature. Almost all numbers vrks on Chemistry, Mineralogy, Physica, are natural constants, and it would b 5. give in any one work more than a * more important numbers,

et object will be to classify these constant y, according to their comparative gener rtance, under the following heads;

(1) Mathematical constants,

(2) Physical constants,

(3) Astronomical constants.

(4) Terrestrial numbers,
(5) Organic numbers,

(6) Social numbers.

Mathematical Constants.

At the head of the list of natural constants must come those which express the necessary relations of numbers to each other. The ordinary Multiplication Table is the most familiar and the most important of such series of constants, and is, theoretically speaking, infinite in extent. Next we must place the Arithmetical Triangle, the significance of which has already been pointed out (p. 206.) Tables of logarithms also contain vast series of natural constants, arising out of the relations of pure numbers, At the base of all logarithmic theory is the mysterious natural constant commonly denoted by E, e, or e, being equal to the infinite series

4

e British Association, Cambridge, as Peport, pp 484-499