Febecaky 1, 1892. 



KNOWLEDGE 



33 



V 



(--'V. 



^A "k TZON A 



I of the Canon District. The shaded areas are covered with basalt. 

 The residue of lava overflows from the !X.E. 



region is sandstone, in all its varieties. Sometimes it is 

 quartzite, sometimes common sandstone in massive beds. 

 Shales, however, abound in the Permian and Trias. These 

 pass into the marly beds of the Cretaceous and Eocene. 

 Thus vre see that, while the strata are remarkably uniform 

 in their horizontal range, they vary very much in vertical 

 range, producing layers that differ very much in hardness, 

 compactness, and solubility. Obviously the results of the 

 attack of erosion on all these different rocks will be very 

 different. These important facts have had a great in- 

 fluence in determining the architectm-al features of the 

 cUfls and their profiles. 



The upper tributaries of the Colorado Eiver have then- 

 sources in lofty regions at a distance which are abimdantly 

 watered. But the main stream and its lower tributaries 

 flow through regions which are exceedingly dry, so that 

 nearly all the water flowing through the Grand Canon 

 comes from the highlands far away — the Uinta and the 

 Rocky Movmtains {see atlas). Though numbers of water- 

 ways open into the Canons, very few of them carry living 

 streams, the rest o'nly convey spasmodic floods for a few 

 days or hom-s when snows melt or showers and storms 

 prevail. The rainfall is very slight. For the region 

 draining laterally into the Glen and Marble Canons it 

 may be estimated at foiu- inches per annum ; but when 

 rainstorms do come theu' consequences are very striking. 

 The riUs and washes are thick with mud and sand, and 

 their waters loaded to their utmost capacity. There is 

 nothing to hold the earthy matters together, so that the 

 instant a rill is formed it is a rill of mud. Eills and 

 streams gather together with marvellous rapidity, plunging 

 furiously along. Although the rainfall on the middle and 

 lower levels — about 5000 feet above sea-level — is on the 

 whole quite small, the transporting power of such water 

 as runs into the river is very great ; a cubic yard of running 

 water in the plateau country probably carries several times 

 ■more sediment than the same quantity of water in rivers, 

 such as the Mississippi, that rim into the Atlantic. There are 

 two causes for this remarkable difference ; First, the com- 

 minuted d^hria of the plateaus due to " weathering " is not > 

 held together by vegetation , but lies loosely on the rocks ! 

 and slopes of loose stones (called Uduses) ; secondly, 

 because the slopes are always very great, and we have 

 already pointed out that the transporting power of streams j 



is enormously increased by an increase in the declivity, 

 as well as corroding power, it follows that much more 

 solid matter is brought down. Soil and vegetation exist 

 only in moist regions where a good deal of rain falls 

 throughout the year, and they retard the work of erosion 

 ■ by forming a covering that protects the rocks below. They 

 also tend to store up water and so equalize the flow of 

 rivers and streams throughout the year, thus preventing 

 the rapid floods we have alluded to above. The direct 

 effect of increased rainfall is to increase erosion, but its 

 indirect effect, through soil and vegetation, is to retard it. 

 With regard to the slopes or gradients of the Eiver 

 Colorado, they vary considerably. The length of the part 

 we are now considering is about 21S mOes, and the average 

 fall 7-56 feet per mile. But it varies from 3 or 4 to 21 

 feet per mile. The river is still sinking its chasm in the 

 strata, though a great part of the river bed is over bare 

 rock, and wherever this is so corrosion is proceeding 

 rapidly. Its great cutting power is due to the large quan- 

 tity of sand which it carries and the high velocity due to 

 -steep gradients. It only remains to notice a very curious 

 I phenomenon in the Red "Wall Limestone, viz. the 

 'numerous niches or panels (see Fig. lU.). Of these there 

 are literally himdreds along the extent of the limestone 

 front, and, as far as is known, they are seen in no other 

 member of this series of strata. Captain Button says 

 he is unable to explain the cause of this persistent 

 phenomenon, and is very much perplexed by it. We can 

 only suggest that they may have been dissolved out by 

 the action of percolating water. It used to be thought 

 that the Caiious might originally have been due to gi'eat 

 cracks which the river has deepened and widened, but on 

 reviewing carefully the mass of evidence brought forward 

 in Captam Button's able monograph we find absolutely no 

 trace of e^idence for this idea. "Faults ' and cracks 

 could never have made such a great network of valleys. 



Ecttrrs. 



[The Editor does not hold himself responsible for the opinions or 

 statements of correspondents.] 



A LAW IX LOGARITHMS— AX ERROR OF VEGA'S. 

 To the Editor of Knowledge. 



Dear Sib, — It is of course widely known that the 

 logarithms of numbers cannot be ahrai/s calculated from 

 tables by means of proportional parts, and that the degree 

 of accuracy extends merely to a certain number of places. 

 But it is not, 1 think, nearly so well known that the 

 accuracy increases with the s(iu<ires of the numbers. Thus 

 suppose we are given -OOOiSIOTTo for the logarithm of 

 1001, and we calculate the logarithm of 1000-3 therefrom, 

 by means of proportional parts, the restilt will be 

 •0002170387 . . . ; the arithmetical mean between the 

 logarithm of 1000 and the logarithm of 1001. But the 

 real logarithm of 10005 is 0002170920 . . . ; and the 

 logarithm calculated by proportional parts is too small 

 by -OOOOOOOol ... If in the same way we calculate the 

 logarithm of 100005 from that of 10001 !^ we shall find the 

 result is too small by "00000000051 ; and so on, the error 

 decreasing by two zeros for every increase of one figure in 

 the number. The same law holds good with all inter- 

 mediate numbers, and 0000000054 (8 zeros) is the error 

 in the logarithm of 31G25 if calculated by taking the 

 arithmetical mean of the logarithms of 3162 and 3163. 

 8-162 . . . being the square-root of 10, 3102 is of com-se 

 a geometrical mean between 1000 and 10,000 ; and 

 therefore the error rightly has 8 zeros before the 51. 



