Of course the figures are not exact in every case, but they are never many feet wrong; and it may well be imagined that it is a difficult thing to deduce, even from the most refined observations, the position of the earth's pole to within a foot. The difficulty is exactly the same as that of measuring the length of an object 300 miles away to within an inch! Mr. Chandler winds up his second paper thus:-- "We thus find that the comparison of the simultaneous series at Pulkowa and Washington, 1863-1867, leads to the same conclusion as that already drawn from the simultaneous series at Berlin and Cambridge, 1884-1885. The direction of the polar motion may therefore be looked upon as established with a large degree of probability. "In the next paper I will present the results derived from PETERS, STRUVE, BRADLEY, and various other series of observations, after which the results of all will be brought to bear upon the determination of the best numerical values of the constants involved." [Sidenote: Bradley's observations.] [Sidenote: Latitude varied in twelve months then.] The results were not, however, presented in this order. In the next paper, which appeared on December 23, 1891, Mr. Chandler begins, with the work of Bradley, the very series of observations at Kew and Wansted which led to the discoveries of aberration and nutation, and which we considered in the third chapter. He first shows that, notwithstanding the obvious accuracy of the observations, there is some unexplained discordance. The very constant of aberration which Bradley discovered from them differs by half-a-second of arc from our best modern determinations. Attempts have been made to ascribe the discordance to changes in the instrument, but Mr. Chandler shows that such changes, setting aside the fact that Bradley would almost certainly have discovered them, will not fit in with the facts. The facts, when analysed with the skill to which we have become accustomed, are that there is a periodic swing in the results _with a period of about a year_, and not fourteen months, as before, "a result so curious," as he admits, that "if we found no further support, it might lead us to distrust the above reasoning, and throw us back to the possibility that, after all, BRADLEY'S observations may have been vitiated by some kind of annual instrumental error. But it will abundantly appear, when I have had the opportunity to print the deductions from all the other series of observations down to the present time, that the inference of an increase in the period of polar revolution is firmly established by their concurrent testimony." We shall presently return to this curious result, which might well have dismayed a less determined researcher than Mr. Chandler, but which only led him on to renewed exertions. The results obtained from Bradley's observations may be put in the form of a diagram thus:-- [Illustration: FIG. 7.]