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These are not identical in value, because the outline of the Scheme is a curved and not a straight line, but the difference between them is small, 'and is approximately the same in all Schemes. It will shortly be seen that Q'=1.015 x Q approximately ; therefore a series of Deviations measured in terms of the large unit Q' are numerically smaller than if they had been measured in terms of the small unit. (for the same reason that the numerals in 2, 3, &c., feet are smaller than those in the corresponding values of 24, 36, &c., inches), and they must be multiplied by 1.015 when it is desired to change them into a series having the smaller value of Q for their unit.

All the 18 Schemes of Deviation that can be derived from Table 2 have been treated on these principles, and the results are given in Table 3. Their general accordance with one another, and still more with the mean of all of them, is obvious.

Normal Curve of Distribution.-The values in the bottom line of Table 3, which is headed " Normal Values when Q = 1," and which correspond with minute precision to those in the line immediately above them, are not derived from observations at all, but from the wellknown Tables of the " Probability Integral " in a way that mathematicians will easily understand by comparing the Tables 4 to 8 inclusive. I need hardly remind the reader that the Law of Error upon which these Normal Values are based, was excogitated for the use of astronomers and others who are concerned with extreme