Annular eclipses and lunar eclipses are of comparatively little consequence, but any recorded eclipse may become of value in connection with chronology. We date our letters in a particular year of the twentieth century, and commonly suppose that the years are reckoned from the birth of Christ; but this is an error, for the eclipses which were observed of old and by the chroniclers have been associated with events of his life, when examined by the astronomers are found quite inconsistent with astronomic theory. They are, however, reconciled with it if we assume that our system of dates has its origin four years after the birth of Christ, or, in other words, that Christ was born in the year 4 B. C. A mistake was doubtless made at the time the Christian era was introduced into chronology. At many other points the chance record of an eclipse in the early annals of civilization furnishes a similar means of controlling and correcting the dates assigned by the historian to events long past. CHAPTER VIII INSTRUMENTS AND THE PRINCIPLES INVOLVED IN THEIR USE 74. TWO FAMILIAR INSTRUMENTS.--In previous chapters we have seen that a clock and a divided circle (protractor) are needed for the observations which an astronomer makes, and it is worth while to note here that the geography of the sky and the science of celestial motions depend fundamentally upon these two instruments. The protractor is a simple instrument, a humble member of the family of divided circles, but untold labor and ingenuity have been expended on this family to make possible the construction of a circle so accurately divided that with it angles may be measured to the tenth of a second instead of to the tenth of a degree--i. e., 3,600 times as accurate as the protractor furnishes.