V
A new era opened in the history of chronometry
when Galileo discovered a natural periodic process that
could be conveniently adapted for the purposes of
accurate timekeeping. As a result of much mathe-
matical thinking on experiments with oscillating pen-
dulums, he came to the conclusion that each simple
pendulum has its own type of vibration depending on
its length. In his old age he contemplated applying
the pendulum to clockwork which could record me-
chanically the number of swings, but this step was first
taken successfully by Huygens in 1656. Strictly speak-
ing, the simple pendulum in which the bob describes
circular arcs is not quite isochronous. Huygens dis-
covered that theoretically perfect isochronism could
be achieved by compelling the bob to describe a cy-
cloidal arc. His first pendulum clock with cycloidal
“cheeks” was constructed in 1656. Great as was
Huygens' achievement, particularly from the point of
view of theory, the ultimate practical solution of the
problem came only after the invention of a new type
of escapement. Huygens' clock incorporated the verge
type, but about 1670 a much improved type, the an-
chor type, was invented that interfered less with the
pendulum's free motion.
The invention of a satisfactory mechanical clock had
a tremendous influence on the general concept of time.
For, unlike the water clocks, etc. that preceded it, the
mechanical clock if properly regulated can tick away
continually for years on end, and so must have greatly
influenced belief in the homogeneity and continuity
of time. This belief was implicit in the idea of time
put forward by Galileo in the dynamical part of Two
New Sciences (1638). For, although he was not the first
to represent time by a geometrical straight line, he
became the most influential pioneer of this idea
through his theory of motion.
Nevertheless, for the first explicit discussion of the
concept of geometrical time it seems that we must go
to the Lectiones geometricae (1669) of Isaac Barrow,
written about thirty years after the publication of
Galileo's book. Barrow, who occupied the chair of
mathematics in Cambridge in which he was succeeded
by Newton in 1669, was greatly impressed by the
kinematic method in geometry that had been devel-
oped with great effect by Galileo's pupil Torricelli.
Barrow realized that to understand this method it was
necessary to study time, and he was particularly con-
cerned with the relation of time and motion. “Time
does not imply motion, as far as its absolute and in-
trinsic nature is concerned; not any more than it im-
plies rest; whether things move or are still, whether
we sleep or wake, Time pursues the even tenour of
its way.” However, he argues, it is only by means of
motion that time is measurable. “Time may be used
as a measure of motion; just as we measure space from
some magnitude, and then use this space to estimate
other magnitudes commensurable with the first; i.e.,
we compare motions with one another by the use of
time as an intermediary.” Barrow regarded time as
essentially a mathematical concept which has many
analogies with a line “for time has length alone, is
similar in all its parts and can be looked upon as
constituted from a simple addition of successive in-
stants or as from a continuous flow of one instant; either
a straight or a circular line” (Geometrical Lectures,
London [1735], Lecture 1, p. 35). The reference here
to “a circular line” shows that Barrow was not com-
pletely emancipated from traditional ideas. Never-
theless, his statement goes further than any of Galileo's,
for Galileo only used straight line segments to denote
particular intervals of time. Barrow was very careful,
however, not to push his analogy between time and
a line too far. Time, in his view, was “the continuance
of anything in its own being.”
Barrow's views greatly influenced his illustrious suc-
cessor in the Lucasian chair, Isaac Newton. In particu-
lar, Barrow's idea that irrespective of whether things
move or are still time passes with a steady flow is
echoed in the famous definition at the beginning of
Newton's Principia (1687). “Absolute, true and mathe-
matical time,” wrote Newton, “of itself and from its
own nature, flows equably without relation to anything
external.” Newton admitted that, in practice, there
may be no such thing as a uniform motion by which
time may be accurately measured, but he thought it
necessary that, in principle, there should exist an ideal
rate-measurer of time. Consequently, he regarded the
moments of absolute time as forming a continuous
sequence like the points on a geometrical line and he
believed that the rate at which these moments succeed
each other is a variable which is independent of all
particular events and processes. His belief in absolute
time was supported by the argument for absolute mo-
tion that he based on his celebrated experiment with
a rotating bucket of water. He thought that it was not
necessary to refer to any other body when attaching
a physical meaning to saying that a particular body
rotates, and from this he concluded that time as well
as space must be absolute.
Newton's views made a great impression on the
philosopher John Locke in whose Essay concerning
Human Understanding (1690) we find the clearest
statement of the “classical” scientific conception of
time that was evolved in the seventeenth century:
... duration is but as it were the length of one straight
line extended in infinitum, not capable of multiplicity,
variation or figure, but is one common measure of all exist-
ence whatsoever, wherein all things, whilst they exist
equally partake. For this present moment is common to all
things that are now in being, and equally comprehends that
part of their existence as much as if they were all but one
single being; and we may truly say, they all exist in the
same moment of time
(Book II, Ch. 15, Para. 11).
Newton's conception of time has been frequently
criticized. If time can be considered in isolation “with-
out relation to anything external,” what meaning could
be attached to saying that its flow is not uniform and
hence what point is there in saying that it “flows
equably”? This objection does not apply to the idea
of time formulated by Newton's contemporary Leibniz
who rejected the idea that moments of absolute time
exist in their own right. Instead, he thought of them
as classes of events related by the concept of simul-
taneity and he defined time as the order of succession
of phenomena. Today this is generally accepted, and
we regard events as simultaneous not because they
occupy the same moment of time but simply because
they happen together. We derive time from events and
not vice versa. Nevertheless, Leibniz' definition of time
as “the order of succession of phenomena” is in-
complete insofar as it concentrates on the ordinal
aspect of time without explicit reference to its dura-
tional aspect and its continuity.
Newton recognized the practical difficulty of ob-
taining a satisfactory measure of time. He pointed out
that, although commonly considered equal, the natural
days are in fact unequal. We now know that in the
long run we cannot base our definition of time on the
observed motions of any of the heavenly bodies. For
the Moon's revolutions are not strictly uniform but are
subject to a small secular acceleration, minute irregu-
larities have been discovered in the diurnal rotation
of the Earth, and so on. Greater accuracy in the meas-
urement of time can, however, be obtained by means
of atomic and molecular clocks. Indeed, the greatest
accuracy so far achieved is with a frequency standard
in the radio range of the spectrum of the caesium atom
and is of the order of one part in 1011, which corre-
sponds to a clock error of only one second in 3000
years.
Implicit in these developments is the assumption that
all atoms of a given element behave in exactly the same
way, irrespective of place and epoch. The ultimate
scale of time is therefore based on our concept of
universal laws of nature. This was already recognized
last century, long before the advent of modern ultra-
precise time-keeping, in particular by Thomson and
Tait in their treatise Natural Philosophy (1890). In
discussing the law of inertia they argued that it could
be stated in the form: the times during which any
particular body not compelled by force to alter the
speeds of its motions passes through equal spaces are
equal; and in this form, they said, the law expresses
our convention for measuring time. It is easily seen
that this implies a unique time-scale except for the
arbitrary choice of time unit and time zero.
In practical life the precise standardization of time
measurement began with the foundation of the Royal
Observatory in 1675, and was further developed when
Greenwich time could be taken on each ship after John
Harrison had perfected the chronometer, about 1760.
The conventional nature of our choice of time zero
in civil time was clearly revealed when, in 1885, to
cope with the fact that solar time varies by four
minutes in a degree of longitude, it was found necessary
to divide the globe into a series of standard time-belts.
