When Newton, in his doctrine of noxious, or flowing quantities, imagined length, space, solidity, and number itself, to be generated by a continual and gradual flow, as a line by the motion of a point, a surface by that of a line, and so on, it was objected that he introduced the ideas of time and motion, both of which were foreign to pure mathematics, and properly belonged to mechanics. To get rid of these intruders, the theory of limits, which the notion of fluxions immediately requires, was attached, not to flowing quantities, but to variable quantities. Let x be a variable quantity, is one of the moat common phrases of the systems which have superseded that of Newton. Now variation means change ; it is never pretended that a variable has two values at once. All the difference is, that by Newton the object of consideration is supposed to grow larger or smaller, while the moderns peas in thought from a larger quantity to a smaller, or rice rend, taking one first and the other afterwards. If so slight a difference as this be worth a contest, the distinction of pure and mixed science must be trivial enough : the fact is, that both systems consider successive values, and succession is time. If two computers were to quarrel which was the purer arithmetician, the one who stood still and counted the carriages as they passed by him, or the other who walked from one to another and counted them as they stood still, they would, to us, much resemble some of the disputants for and against the principle of noxious.
The actual measure of time depends upon our being able to secure successions of similar events which shall furnish epochs separated by equal intervals of time. We cannot do this by our thoughts, except approximately, and for short periods. The memory of a musician, aided by the sentiment or feeling of time which is part of a good ear for music, will do remarkably well for a short period : a person who could not well preserve the division of a second into eight parts at least would make a poor figure in an orchestra. As to the judgment of con siderable periods of time, it is materially influenced by the manner in which it has been spent : a time which seems to have been long through weariness has been long, and the contrary, on grounds already alluded to. Thus a year of mature age is really, to the thoughts, of a different length from one of childhood. Again, when we talk of a long period of time having passed quickly or slowly, we speak not of the time, but of our mode of remembering it. A person of rapid recapitulation always says that time has passed quickly, another of a contrary habit the contrary ; and this whether the rapidity be a consequence of quick ness of ideas, or of having little to recall.
In all the more correct machines which have been invented to measure time, there is but one principle : a vibration is kept up by the constant application of forces only just sufficient to counteract friction and other resistances, and machinery is applied to register the number of vibrations. The remarkable law noted under Isocnno NISM and Vninanosr makes it comparatively immaterial whether the vibrations are of precisely the same extent. But the imperfections of such instruments, or rather, our ignorance of the precise action of dis turbing causes, and particularly of changes of temperature, renders them comparatively useless for measuring long periods, so that if we could not have recourse to the motion of the heavenly bodies, there would be no permanent measure of time. And even in astronomi
cal phenomena there is no absolute recurrence at equal intervals, though nearly enough for common purposes. The value of such phe nomena for the most accurate measures consists in most of their irregularities being truly distributed about a uniform mean, so that the excesses of some periods are compensated by the defects of others, giving, in the long run, power of determining that mean with as much accuracy as our modes of measurement can appreciate. The determi nation of time for civil reckoning may be divided into two parts : first, the mode of making the different periods derived from the sun and moon agree with each other so as to afford an easy method of reckoning co-ordinately by both [PERIODS of REVOLUTION]; secondly, the mode of procuring true and convenient subdivisions of the natural unit consisting of a day and night. To the second of these we now turn our attention.
The actual revolution of the earth, as measured by the time elapsed between two transits of the same star over the meridian, is called a sidereal day. It is divided, as are all other days, into twenty-four hours of sixty minutes each, &c. The time so given is called sidereal time. If the sun were a fixed star, this sidereal time would be the common mode of reckoning. But the sun having its own slow motion in the ecliptic, in the same direction as the revolution of the earth, the interval between one meridian transit of that body and the next is [SvNonto] longer than the simple revolution of the earth, for just the same reason that the time in which the minute-hand of a watch moves from coincidence with the hour-hand to coincidence again is longer than the hour, or simple revolution of the minute-hand. If the sun moved uniformly, and in the equator, the real solar day, which means the interval between two meridian transits of the sun, would always be of the same length, and a little longer than the sidereal day. But the sun neither does move uniformly, nor in the equator ; and each of these circumstances causes a slight irregularity in the absolute length of the solar day, or, as it is called, the real solar day. This is the reason why the time shown by a sundial dove not agree with the watch. To remedy this inconvenience, a fictitious sun is supposed to move in the ecliptic, and uniformly, while another fictitious sun moves in the equator, also uniformly. Both the fictitious bodies have the average motion of the real sun, so that the years of the three are the same ; and the fictitious sun of the ecliptic is made to coincide with the real sun at the perigee and apogee, or nearest and farthest points from the earth ; while the fictitious body in the equator is made to coincide with the fictitious body of the ecliptic at the equinoxes (from which it arises that there is also a coincidence at the solstices). This fictitious sun of the equator is that to which clocks are adjusted ; the interval between two of its transits, which is always of the same length, is called a mean solar day, which is divided into twenty-four mean solar hours, &c. The difference between time as shown by the real sun and the fictitious sun in the equator, is called the equation of time.