Table XXV. compares the Random events with the Observed ones. Every case in which the calculated expectation is equal to or exceeds 0.05, is inserted in detail; the remaining group of petty cases are summed together and their totals entered in the bottom line. For fear of misapprehension or forgetfulness, one other example of the way in which the Randoms are calculated will be given here, taking for the purpose the first entry in Table XXIV. Thus, the number of all the different combinations of the 150 A with the 150 B individuals in the 150 couplets, is 150 x 150. Out of these, the number of double events in which pattern No. 1 would appear in the same combination, is 15 x 12 = 180. Therefore in 150 trials, the double event of pattern No. 1 would appear upon the average, on 180 divided by 150, or on 1.20 occasions. As a matter of fact, it appeared four times. These figures will be found in the first line of Table XXV.; the rest of its contents have been calculated in the same way. Leaving aside the Randoms that exceed 0 but are less than 1, there are nineteen cases in which the Random may be compared with the Observed values; in all but two of these the Observed are the highest, and in these two the Random exceed the Observed by only trifling amounts, namely, 5.18 Random against 5.00 Observed; 1.87 Random against 1.00 Observed. It is impossible, therefore, to doubt from the steady way in which the Observed values overtop the Randoms, that there is a greater average likeness in the finger marks of two brothers, than in those of two persons taken at hazard. Table XXVI. gives the results of applying the centesimal scale to the measurement of the average closeness of fraternal resemblance, in respect to finger prints, according to the method and under the reservations already explained in page 125. The average value thus assigned to it is a little more than 10 deg. The values obtained from the three fingers severally, from which that average was derived, are 9 deg., 10 deg., and 12 deg.; they agree together better than might have been expected. The value obtained from a set of fifty additional couplets of the middle fingers only, of fraternals, is wider, being 21 deg. Its inclusion with the rest raises the average of all to between 10 and 11.