If l be the true length of suspension, and C the length of the chord of the arc of displacement of the bob after being struck, then
| C² = 2hl, and v = ( | W | + 1) √ | g | . C. |
| w | l |
Also if T be the time of a complete small oscillation of the pendulum,
| 2π | = √ | g | , |
| T | l |
so that
| v = ( | W | + 1) | 2πC | . |
| w | T |
CHRONOLOGY (Gr. χρονολογία, computation of time, χρόνος), the science which treats of time, its object being to arrange and exhibit the various events which have occurred in the history of the world in the order of their succession, and to ascertain the intervals of time between them. The term “chronology” is also used of the order in time itself, as adopted, and of the system by which the order is fixed.
The preservation of any record, however rude, of the lapse of time implies some knowledge of the celestial motions, by which alone time can be accurately measured, and some advancement in the arts of civilized life, which could be attained only by the accumulated experience of many generations (see [Time]). Before the invention of letters the memory of past transactions could not be preserved beyond a few years with any tolerable degree of accuracy. Events which greatly affected the physical condition of the human race, or were of a nature to make a deep impression on the minds of the rude inhabitants of the earth, might be vaguely transmitted through several ages by traditional narrative; but intervals of time, expressed by abstract numbers, and these constantly varying besides, would soon escape the memory. The invention of the art of writing afforded the means of substituting precise and permanent records for vague and evanescent tradition; but in the infancy of the world, mankind had learned neither to estimate accurately the duration of time, nor to refer passing events to any fixed epoch.
For these reasons the attempt at an accurate chronology of the early ages of the world is only of recent origin. After political relations began to be established, the necessity of preserving a register of passing seasons and years would soon be felt, and the practice of recording important transactions must have grown up as a necessary consequence of social life. But of these deliberate early records a very small portion only has escaped the ravages of time and barbarism.