December 30, 1897] 



NATURE 



211 



selection require very different mathematical treatment ; it is not 

 at all clear, that they have always been sufficiently distinguished 

 by writers on the theory of evolution. The above paper covers 

 only the ground of the first kind of selection, random selection, 

 but the memoir on epidemic selection is already completed, and 

 the theory of the other cases advanced. The importance of random 

 selection not only arises from the differentiation of species by 

 isolation of small groups from a general population, but also 

 from the fact that every measurement on a population is really a 

 measurement on a more or less extensive random selection or 

 sample. Hence the theory of random selection is also the theory 

 of the probable errors of the frequency constants for any race. 

 It enables us to determine the accuracy with which we have 

 measured the chief racial constants. 



Let the frequency-surface giving the distribution of a popula- 

 tion with regard to «-organs be 



Z=j{Xi X.2, Jf 3 . . . X,„ Cj, C^ C^ . . . Cq) 



where Cj <-, . . . Cg are the q constants which determine the charac- 

 ters of the population. Then the surfaces for the distribution of 

 the errors in c-^, c^. ■ . Cg'is given approximately by 



^ — 2„^-i(«ll ei- + 2ai2eie2+ . . .) 

 where 



AjK -— I . . . z ■ °p ^ dx^dxn . . . dx„ 



J J J dc^Cu 



Higher terms can be evaluated if needful ; we have then a skew 

 correlation of the system of errors. Approximately the diver- 

 gences of any random selection from the characters of the general 

 population form in themselves a normally correlated system, and 

 we can predict from a knowledge of the divergence in one 

 character the probable divergences in all the others. 



The general formulae are applied to the problems of 



(i. ) The random selection out of a population having n normally 

 correlated organs. 



If one character be changed, say the variability of one organ 

 be altered, it is shown how the probable changes in all the other 

 characters may be found ; for example, the changes in the 

 correlation of other organs. This is the death-blow to any 

 theory that either variability or correlation can be constant for 

 local races. 



(ii.) Skew Variation, for all the three types discussed in a 

 previous memoir. 



Criteria are obtained for determining when skewness is sig- 

 nificant ; when the mode really diverges from the mean, &c. 



In many cases in which the normal curve of errors is used, 

 the skewness is really significant, and thus many of the results 

 used are illegitimate. For example, personal equation is generally 

 sensibly skew, curves for size of organs during growth, and 

 nearly all cases of botanical distribution. 



These points are illustrated in the memoir by three numerical 

 examples : — 



(I.) Miillerian glands in the legs of swine; data from the 

 observations of two American naturalists. The skewness can be 

 determined with less than c per cent, of probable error. It is 

 therefore significant, and the use by the above-mentioned 

 biologists of the ordinary theory of errors is in this case to be 

 deprecated. 



(II.) Enteric fever. Skewness is known to i per cent, of 

 probable error. 



The effect of raising mean age, or altering the incidence, &c. 

 on the character of the disease follows at once from the tables 

 given. 



(III.) Stature during growth; a critical case, taken because 

 the distribution is almost normal. The skewness is, however, 

 probably significant, and the influence indicated of random 

 selection on stature during growth is in accordance with 

 experience. 



MODIFICATION OF THE GREAT LAKES BY 

 EARTH MO VEMENT} 



nrilE history of the Great Lakes practically begins with the 

 melting of the Pleistocene ice-sheet. They may have 

 existed before the invasion of the ice, but if so their drainage 

 system is unknown. The ice came from the north and north- 

 east, and, spreading over the whole Laurentian basin, invaded 



1 Abridged from a paper, by Prof. G. K. Gilbert, in t\\t National Geo- 

 graphic Magazine (September 1897). 



the drainage districts of the Mississippi, Ohio, Susquehanna 

 and Hudson. During its wandering there was a long period 

 when the waters were ponded between the ice front and the 

 uplands south of the Laurentian basin, forming a series of glacial 

 lakes whose outlets were southward through various low passes. 

 A great stream from the Erie basin crossed the divide at Fort 

 Wayne to the Wabash river. A river of the magnitude of the 

 Niagara afterwards flowed from the Michigan basin across the 

 divide at Chicago to the Illinois river ; and still later the chief 

 outlet was from the Ontario basin across the divide at Rome to 

 the Mohawk valley. 



The positions of the glacial lakes are also m.arked by shore- 

 lines, consisting of terraces, cliffs, and ridges, the strands and 

 spits formed by their waves. Several of these shore-lines have 

 been traced for hundreds of miles, and wherever they are 

 thoroughly studied it is found that they no longer lie level, but 

 have gentle slopes towards the south and south-west. Formed 

 at the edges of water surfaces, they must originally have been 

 level, and their present lack of horizontality is due to unequal 

 uplift of the land. The region has been tilted towards the south- 

 south-west. The different shore-lines are not strictly parallel, 

 and their gradients vary from place to place, ranging from a few 

 inches to three or four feet to the mile. 



Early History of the Lakes. 



The epoch of glacial lakes, or lakes partly bounded by ice, 

 ended with the disappearance of the ice-field, and there remained 

 only lakes of the modern type, wholly surrounded by land. 

 These were formed one at a time, and the first to appear was in 

 the Erie basin. It was much smaller than the modern lake, 

 because the basin was then comparatively low at the northeast. 

 Instead of reaching from the site of Buffalo to the site of Toledo, 

 it extended only to a point opposite the present city of Erie, 

 and it was but one-sixth as large as the modern lake. Since 

 that time the land has gradually risen at the north, canting the 

 basin towards the south, and the lake has gradually encroached 

 upon the lowlands of its valley. 



The next great lake to be released from the domination of the 

 ice was probably Ontario, though the order of precedence is 

 here not equally clear. Before the Ontario valley held a land- 

 bound lake it was occupied by a gulf of the ocean. Owing to 

 the different attitude of the land, the water surface of this gulf 

 was not parallel to the present lake surface, but inclined at an 

 angle. In the extreme north-east, in the vicinity of the 

 Thousand Islands, the marine shores are nearly 200 feet above 

 the present water level, but they descend southward and west- 

 ward, passing beneath the lake level near Oswego, and towards 

 the western end of the lake must be submerged several hundred 

 feet. This condition was of short duration, and the rising land 

 soon divided the waters, establishing Lake Ontario as an in- 

 dependent water body. The same peculiarity of land attitude 

 which made the original Erie a small lake served to limit the 

 extent of Ontario, but the restriction was less in amount because 

 of the steeper slopes of the Ontario basin. Here again the 

 southward tilting of the land had the effect of lifting the point of 

 outlet and enlarging the expanse of the lake. 



There is some reason to think that the upper lakes, Huron, 

 Michigan and Superior, were at first open to the sea, so as to 

 constitute a gulf, but the evidence is not so full as could be 

 desired. When the normal lacustrine condition was established 

 they were at first a single lake instead of three, and the outlet, 

 instead of being southward from Lake Huron, was north-eastward 

 from Georgian bay, the outlet river following the valleys of the 

 Mattawa and Ottawa to the St. Lawrence. The triple lake is 

 known to us chiefly through the labours of Mr. F. B. Taylor, 

 who has made extensive studies of its shore-line. This line, 

 called the Nipissing shore-line, is not wholly submerged, like 

 the old shores of lakes Erie and Ontario, but lies chiefly above 

 the present water surfaces. It has been recognised at many 

 points about Lake Superior and the northern parts of lakes 

 Huron and Michigan, and measurements of its height show that 

 its plane has a remarkably uniform dip, at 7 inches per mile, 

 in a souih-south-west direction, or, more exactly, S. 27° W. 

 The southward tilting of the land, involving the uplift of the 

 point of outlet, increased the capacity of the basin and the 

 volume of the lake, gradually carrying the coast-line southward 

 in Lake Huron and Lake Michigan until finally it reached the 

 low pass at Port Huron, and the water overflowed vid the St. 

 Clair and Detroit channels to Lake Erie. The outlet by way of 

 the Ottawa was then abandoned, and a continuance of the 



NO. 1470. VOL. 57] 



