356 



SCIENCE. 



[Vol. I., No. 13. 



time at all. So that our curve must sooner or 

 later become a straight line, and ultimatel^y 

 concave upwards. Drawing a straight line 

 which shall agree as nearly as possible with 

 our observations, we shall find from it, that the 

 speed of the trotting-horse is increasing at a 

 nearly uniform rate of 4^ seconds in ten j'ears ; 

 so that, on this supposition, it would cross the 

 two-minute line in 1907, and the one-minute 

 line in 2045. It is highly probable that the 

 curve will have become concave before the 

 latter period ; bat it does not seem too rash to 

 predict that a horse will be born before 1907 

 that can trot a mile in two minutes. 



II. — Total number of horses capable of trotting 

 in 2.30 or better. 



Table II. shows the enormous rate ' of in- 

 crease of this new breed of animals, amount- 

 ing to about twentj' per cent a j'ear. Treating 

 the observations b}' the logarithmic method, 

 we find, that, since 1864, the increase may, 

 with a reasonable degree of accuracy, be repre- 

 sented by the formula y=.00l&x*, where y 

 represents the number of horses, and x the 

 number of j-ears since 1850. Thus, for 1882, 

 we have 2/=.0016 x32^=1678. Applying this 

 formula, we find, that, if the present rate of 

 breeding is continued, the trotting-horses of 

 America in 1900, that can travel a mile in 2.30 

 or better, will number not far from 10,000. 



Wm. II. Pickering. 



THE ORIGIN OF CROSS-VALLEYS.^ 

 II. 



Retuening now to Virginia and Pennsj'lva- 

 nia, we have to consider not only why the 

 rivers there cross the mountains, but also why 

 they flow to the south-east instead of to the 

 north-west. Taking the last question first, we 

 are forced to suppose that the north-westerlj' 



1 Concluded from No. 12. 



slope, which must have existed at least up to 

 the end of the carboniferous, was then or soon 

 after reversed in the slow writhing of the sur- 

 face. This is demanded bj- the lay of the land, 

 and hy the now small area of what must have 

 been, in paleozoic time, a large crystalline land- 

 mass. The slope being changed early in the 

 growth of the folds, or before their beginning, 

 the streams tried to make their waj' to the 

 eastward ; and the Hudson, Delaware, Sus- 

 quehanna, Potomac, and James are the de- 

 scendants of those that succeeded.' Their 

 rectangular courses, alternately longitudinal 

 and transverse, bear witness to their defeats 

 and victories. Lakes must have been numer- 

 ous here once, though thej' are now all drained. 

 It is known that rivers often chose cross-faults 

 of small throw as points of attack in cutting 

 their waj^ through the growing ridges ; and it 

 is verj' probable that they made use of pre-es- 

 istent vallej's when they advanced over the 

 old sinking land. 



In considering the applicability of backward- 

 cutting lateral streams to the production of 

 our cross-vallej's, we should test the past by 

 the present, and examine such ridges as Kitta- 

 tinny or Bald liagle mountains in Pennsylvania, 

 or Clinch mountain in Tennessee, rising be- - 

 tween parallel longitudinal valleys, to see if 

 thej^ show embrj'onic cross-vallej's in the more 

 advanced stages of development. They do 

 not. The continuitj' of their crest-line is most 

 characteristic and remarkable : it veiy rarely 

 departs from its line of almost uniform height. 

 The excej)tions are, first, the finished water- 

 gaps, or transverse valleys, whose origin is in 

 discussion ; second, the occasional wind-gaps, 

 or notches, which sometimes cut the ridge a 

 third or half way to its base, and which are, 

 we believe, alwaj^s determined hy small trans- 

 verse faults ; third, the less conspicuous serra- 

 tions of small value. • It is difficult to assign 

 anj- reason v/hy lateral streams should not now, 

 as well as in former times, show us the later 

 stages of breaking down the ridge on which 

 thej' rise ; and yet these almost-formed cross- 

 valleys between adjoining longitudinal valleys 

 are practicallj' unknown in our Appalachian 

 topography. The reason of 'their absence can 

 hardly' be, that there are now enough completed 

 water-gaps for all practical purposes, and hence 

 the lateral streams stop making anj* more ; for 

 this would imply a consciousness of the end 

 that pla3-s no part in geological operations, 

 and we are therefore constrained to think that 

 Lowl's explanation cannot applj' to the Ap- 

 palachians in any general way. 



But it has a certain limited application in 



