2. "It would seem in fact that in coarse and rude observations the errors proceed from a _very few_ principal causes, and in consequence our hypothesis [as to the Exponential Law of Error] will probably represent the facts only imperfectly, and the frequency of the errors will only approximate roughly and vaguely to the law which follows from it. But when astronomers, not content with the degree of accuracy they had reached, prosecuted their researches into the remaining sources of error, they found that not three or four, but a _great number_ of minor sources of error of nearly co-ordinate importance began to reveal themselves, having been till then masked and overshadowed by the graver errors which had been now approximately removed.... There were errors of graduation, and many others in the contraction of instruments; other errors of their adjustments; errors (technically so called) of _observation_; errors from the changes of temperature, of weather, from slight irregular motions and vibrations; in short, the thousand minute disturbing influences with which modern astronomers are familiar." (Extracted from a paper by Mr Crofton in the Vol. of the _Philosophical Transactions_ for 1870, p. 177.) 3. _Typical Laws of Heredity_; read before the Royal Institution, Feb. 9, 1877. See also _Journal of the Anthrop. Inst._ Nov. 1885. CHAPTER IV. _ON THE MODES OF ESTABLISHING AND DETERMINING THE EXISTENCE AND NUMERICAL PROPORTIONS OF THE CHARACTERISTIC PROPERTIES OF OUR SERIES OR GROUPS._ 1. At the point which we have now reached, we are supposed to be in possession of series or groups of a certain kind, lying at the bottom, as one may say, and forming the foundation on which the Science of Probability is to be erected. We have described with sufficient particularity the characteristics of such a series, and have indicated the process by which it is, as a rule, actually brought about in nature. The next enquiries which have to be successively made are, how in any particular case we are to establish their existence and determine their special character and properties? and secondly,[1] when we have obtained them, in what mode are they to be employed for logical purposes?