April 5, 1877] NATURE 493 It has,T believe, become more generally known than formerly, that although the characteristics of height, weight, strength, and fleetness are different things, and though different species of plants and animals exhibit every kind of diversity, yet the differences in height, weight, and every other characteristic, are universally distributed in fair conformity with a single law. The phenomena with which it deals are like those per¬ spectives spoken of by Shakespeare which, when viewed awry, show nothing but confusion. Our ordinary way of looking at individual differences is awry ; thus we naturally buttyrongly judge of differences in stature by differences in heights, measured from the ground, whereas on changing our point of view to that whence the law of deviation regards them, by taking the average height -of the race, and not the ground, as the point of reference, all confusion disappears, and unifor- .roity prevails. It was to Quetelet that we were first indebted for a knowledge of the fact that the amount and frequency of deviation from the average among members of the same race, in respect to each and every characteristic, tends to conform to the mathematical law of deviation. The diagram contains extracts from some of the tables, American soldiers, France Belgium, Quetelet Heights. 25,878 observations. (Hargenvilliers). 20 years' observations. Metres. Observed Calcu¬ lated. [ Observed Calcu¬ lated. Observed Calcul^ed 1*90 I 3 I90 7 5 1 « l ' , 87 14 13 - I » \ ' 84 25 28 25 3 2 3 8t 45 52 7 - 7 . 7 79 99 84 16 14 «4 76 112 117 32 32 34 28 73 138 I42 55 55 48 53 70 148 150 88 87 102 107 68 137 137 114 ns 138 136 65 93 109 144 140 I29 150 62 IOQ 75 140 «45 162 150 6O 49 45 Il6 132 106 136 57 14 24 105 IEO 107 54 8 IX - 73 1 53 51 I 4 44 1 28 48 45 X - 286 24 II 1- «47 1 14 7 42 - 4 1 J 3 39 2 I 36 I IOOO IOOO IOOO IOOO IOOO IOOO Degrees of Dynanometer. Lifting power of Belgian Men, Observed. Calculated. 200 I I 190 I80 9 IO 170 ' l6o 23 ■ 23 150 I40 33 32 130 120 22 23 IIO IOO 12 IO 90 I I ICO IOO by which he corroborates his assertion. Three of the series in them refer to the heights of Americans, French, and Bel¬ gians respectively, and the fourth to strength, to that of Belgians, In each series there are two parallel columns, one entitled “ observed,” and the other “ calculated,” and the close conformity between each of the pairs is very striking. These Tables serve another purpose ; they enable those who have not had experience of such statistics to appre¬ ciate the beautiful balance of the processes of heredity in ensuring the repetition of such finely graduated propor¬ tions as those they record. The outline of my problem of this evening is, that since the characteristics of all plants and animals tend to con¬ form to the law of deviation, let us suppose a typical case, in which tie conformity shall be exact, and which shall admit of discussion as a mathematical problem, and find what the laws of heredity must then be to enable succes¬ sive generations to maintain statistical identity. I shall have to speak so much about the law ot devia¬ tion, that it is absolutely'necessary to tax your attention for a“ few minutes to explain the principle on which it is based, what it is that it professes to show, and what the two numbers are which enable long series to be calculated like those in the tables just referred to. The simplest way of explaining the law is to begin by showing it in action. For this purpose I will use an apparatus that I employed three years ago in this very theatre, to illustrate other points connected with the law of deviation. An extension of its performance will prove of great service to us to¬ night, but I will begin by working the instrument as I did on the previous occasion. The portion of it that then existed and to which I desire now to confine your atten¬ tion, is shown in the lower part of Fig. 1, wheie I wish you to notice the stream issuing from either of the divisions just above the dots, its dispersion among a a 2