THE RELATIONSHIPS TO WHICH THEY CORRESPOND See also the Chapter on Notation, pp. 50—53. B. Brother b. Sister. F. Father. f. Mother. G. Grandfather, viz. Father's father. GB. Great-uncle, viz. Father's father's brother. GF. gF. Great-grandfather, viz. Father's father's father. Great-grandfather, viz. Mother's father's father. GF. Great-grandfather, viz. Father's mother's father. gF. Great-grandfather, viz. Mother's mother's father. Gf. Great-grandmother, viz. Father's father's mother. gf. Great-grandmother, viz. Mother's father's mother. Gf. Great-grandmother, viz. Father's mother's mother. gf. Great-grandmother, viz. Mother's mother's mother. GG. Great-great-grandfather, 8 forms, see p. 53. GN. First cousin once removed ascending, male, 8 forms. APPENDIX 8 THE deviations from an average are given in the following table. of M. Quetelet as far as 80 grades; they are intended to be reckoned on either side of the average, and therefore extend over a total range of 160 grades. The eightieth is a deviation so extreme, that the chances of its being exceeded (upwards or downwards, whichever of the two events we please to select) is only 5,000,000 - 4,999,992 or less than one in a million. That is to say, when firing at a target (see Diagram, p. 28) less than one out of a million shots, taking the average of many millions, will hit it at a greater height than 80 of Quetelet's grades above the mean of all the shots; and an equally small number will hit it lower than the 80th grade below the same mean. 10,000,000 = 10,000,000' Column M gives the chance of a shot falling into any given grade (80 x 2 or) 160 in total number. Column N represents the chances from another point of view; it is derived directly from M, and shows the probability of a shot lying between any specified grade and the mean; each figure in N consisting of the sum of all the figures in M up to the grade in question, and inclusive. Thus, as we see by Column M, the chance against a shot falling into the Ist grade (superior or inferior, whichever we please to select) is 025225 to 1, and .025124 to I against its falling into the 2d, and .024924 to I against its falling into the 3d; then the chance against its falling between the mean and the third grade, inclusive, is clearly the sum of these 3 numbers, or .075273, which is the entry in Column N, opposite the grade 3. These columns may be used for two purposes. The one is to calculate a table like that in . p. 34, where I have simply lumped II of Quetelet's grades into I, so that my classes A and a correspond to his grade 11 in column N, my classes B and b to the difference between his grades 22 and 11, my C and c to that between his grades 33 and 22, and so on. The other is as a test, whether or no a group of events are due to the same general causes; because, if they are, their classification will afford numbers that correspond with those in the table; otherwise, they will not. This test has been employed in pp. 30, 31, and 33. The method of conducting the comparison is easily to be understood by the following example, the figures of which I take from Quetelet. It seems that 487 observations of the Right Ascension of the Polar Star were made at Greenwich between 1836 and 1839, and are recorded in the publications of the Observatory, after having been corrected for precession, nutation, &c., and subject only to errors of observation. If they are grouped into classes separated by grades of 0.5 sec. the numbers in each of these classes will be as shown in Column III. page 380. We raise them in the proportion of 1,000 to 487 in order to make the ratios decimal, and therefore comparable with the figures in Quetelet's table, and then insert them in Column IV. These tell us that it has been found by a pretty large experience, that the chance of an observation falling within the class of 0.5 sec. from the mean, is 150 to 1,000; of its falling within the class of 1.0 sec. is 126 to 1,000; and so on, for the rest. This information is analogous to that given in Column M of Quetelet's table, and we shall now proceed to calculate from IV. the Column V. which is analogous to Quetelet's N. The method of doing so is, however, different. N was formed by adding the entries in M from the average outwards; we must set to work in the |