Feb. 14, 1889] 



NATURE 



Z1Z 



he docs not think ; as he that has got the idea of exten- 

 sion from bodies by his sight or touch can apply it to 

 distances where no body is seen or felt." " Thus, a man 

 when he is asleep, or when his mind is entirely occupied 

 by one subject, has no notion of the passage of time." 

 " This consideration of duration, as set out by certain 

 periods and marked by certain measures or epochs, is 

 that, I think, which most properly we call time." 



According to Locke, then, duration is measured out, as 

 it were, into time by changes, and as these changes are, 

 so far as we know, due to motion, the ideas of time and 

 motion are closely connected. These views have been 

 further developed by Herbert Spencer (" First Principles," 

 163, 167, 171) : — "The relation of sequence is given in 

 every change of consciousness." " The abstract of all 

 sequences is time. The abstract of all co-existences is 

 space." " The conception of motion, as presented or 

 represented in the developed consciousness, involves the 

 conception of space, of time, of matter — a something 

 that moves ; a series of positions occupied in succes- 

 sion ; and a group of co-existent positions united in 

 thought with the successive ones." "These modes of 

 cohesion, under which manifestations are invariably 

 presented, and therefore invariably represented, we call, 

 when contemplated apart, space and time ; and when 

 contemplated along with the manifestations themselves, 

 matter and motion." 



The abstract idea of duration without beginning or end 

 is of the greatest value to the mathematician, but, so far 

 as we know, it has no representative in Nature. It 

 would, of course, be measured out by the equal spaces 

 passed over by a body moving under the action of no 

 forces, but no known body is in such a condition. As 

 possible instruments for the accurate measurement of 

 time, Thomson and Tait suggest a spring vibrating in 

 vacuo, and Clerk Maxwell the period of vibration of light- 

 waves of definite length. From this conception of dura- 

 tion or equable flow, Newton deduced his method of 

 fluxions, which, owing to his delay in publishing the 

 method, occasioned the lamentable controversy as to 

 priority with Leibnitz. Though the manuscript of New- 

 ton's first paper on fluxions has been found with the date 

 May 20, 1665, it was only communicated in a letter to 

 Collins in 1672, used in some papers on motion read 

 before the Royal Society in 1683, and printed in 1684. 

 The method was first definitely published to the world in 

 the " Principia," in 1687. According to Maclaurin : " In 

 the doctrine of fluxions, magnitudes are conceived to be 

 generated by motion, and the velocity of the generating 

 motion is the fluxion of the magnitude." Suppose a 

 movable point, starting from a fixed point, A, describes 

 a line A B, of length .r, Newton represented by x the 

 velocity with which the line is described. Again, the 

 velocity itself may not remain constant, but either in- 

 crease, as when a stone falls, or decrease, as when a shot 

 is fired. This change of velocity, now called acceleration, 

 was expressed by x. 



The conception of velocity is passing over a certain 

 space in a certain time, as a mile in a minute or 88 feet 

 in a second, and we may conceive both space and time 

 to become infinitesimally small, so that the ratio of the 

 one to the other becomes a fluxion. Acceleration is 

 measured by the number of units of velocity gained or 

 lost in the unit of time ; thus, the acceleration due to 

 gravity is a velocity of 32 feet per second gained or lost 

 in a second. 



The discussion of the connection between this concep- 

 tion of fluxions and the various methods of conceiving 

 space as made up of infinitesimal portions, which were 

 used more or less imperfectly by various mathemati- 

 cians, until they were generalized and systematized by 

 Leibnitz into the differential calculus (1675), would occupy 

 too much space. A fluxion or differential, as was clearly 

 pointed out by Newton, depends upon the philosophical 



conception of a limit, the foundation of so many of the 

 higher branches of mathematics. 



Important as are these theoretical questions deduced 

 from the idea of duration, the practical questions of time 

 and the means of measuring it with accuracy are far 

 more so. 



Since astronomers have been unable to find any truly 

 equable motion by which to measure equal intervals of 

 time, they make use of a fictitious sun, which apparently 

 moves round the earth in the same period as the real sun 

 does, alternately before and after it, but coinciding with 

 it four times in the year— on April 15, June 14, August 31, 

 and December 24. 



The interval between two apparent passages of the 

 fictitious sun over the meridian is a mean solar day, 

 which is divided into 24 hours, 1440 minutes, or 86,400 

 seconds. The length of the tropical year, or the interval 

 before the return of the sun to the same equinox, is 

 365*2422 mean solar days. 



In the observatory, astronomers use as their unit the 

 sidereal day, or the interval between two appearances of 

 the same star on the meridian ; owing to the apparent 

 motion of the sun, there are 366*2422 sidereal days in the 

 tropical year, or a mean solar day is equal to 1*0027379 

 sidereal days. About March 22 of each year, sidereal o 

 hour coincides with mean noon, and for each day from 

 that date the difference increases by 3 minutes 56 seconds. 

 For purposes of calculation, astronomers make use of 

 " the Julian period " of 7980 tropical years, of which 

 1889 is the 6602nd; and at mean noon on January i, 

 2,41 1,004 mean solar days of the period had elapsed. 



The oldest time-measurer, the sun-dial, dates from, at 

 all events, 700 B.C. In its most simple form it consists 

 of a style fixed parallel to the axis of the earth, and a 

 graduated circle upon which the shadow falls. The 

 clepsydra, or water-clock, in which time is measured 

 by the equable flow of water, was introduced into Rome 

 about 150 B.C.; and various methods of indicating the 

 quantity of water which had flowed out by bells, hands, 

 figures, &c., were subsequently added. A simple form of 

 the instrument is still used in physical laboratories for 

 measuring intervals of a few seconds. The replace- 

 ment of water by sand furnished the hour-glass used by 

 our ancestors for measuring out the eloquence of their 

 preachers, as their more feeble descendants now use the 

 three-minute glass for measuring the boiling of their eggs. 

 A transit-instrument affords a ready means of correct- 

 ing a clock ; and mean-time signals are now sent from 

 Greenwich to many places in England ; hence in practice 

 we individually measure only comparatively short intervals 

 of time, correcting our private clocks and watches by 

 public clocks regulated by time-signals. 



Of all measures, those of time are most frequently and 

 most accurately made. Public clocks are far more nume- 

 rous than public standards of length or mass, and in 1880 

 the value of the clocks and watches imported amounted 

 to ;^88o,ooo. Few persons carry a foot-rule costing say 

 \s., but many a watch costing more than £2. Even 

 among engineers but little attention is paid to lengths less 

 than 1/64 of an inch ; and few common balances indicate 

 a difference of i/ioo of the load. But, according to 

 Mr. Rigg (Cantor Lectures on Watch-making, 1881), a 

 watch that does not vary more than half a second per 

 diem, or 1/172800, is frequently met with, while an 

 accuracy of two or three minutes per week, 3/10000, is 

 attained even by cheap articles. It is no uncommon 

 occurrence to meet with a chronometer which does not 

 vary one-fifth of a second in twenty-four hours, or by 

 about I 432000 of the time measured out. 



Almost all modern instruments for measuring time 

 consist of three essential parts : (i) a motive-power, such 

 as a falling weight, an uncoiling spring, an electric current ; 

 (2) a regulator, to render the motion steady, such as a 

 pendulum, a balance-wheel, or a magnet ; (3) some means 



