WATER-PLANES AND CRUST AL DEFORMATION 355 



Both the average and the maximum deviation in each case are 

 within the probable error of observation and the limit of error respec- 

 tively, so that the difference of 0.30 foot in favor of the broken lines 

 possesses no significance. It may be shown likewise that a curved 

 line would fit the observed points with no greater error than noted 

 above. 



The certain conclusion is reached, then, that either a straight, a 

 curved, or a broken line may be drawn through the points of observa- 

 tion with equal accuracy, and that, consequently, in this distance of 

 35 miles the present attitude of the old shore -lines may be the result 

 either of a uniform tilting, a differential warping, or a differential tilting 

 of the earth's crust. 



It may be said, however, that a distance of 35 miles is too short for 

 a test of this character. We may consider, then, the entire length of 

 the profile from Rock Island to Two Rivers, a distance of about 100 

 miles. In so doing the conclusion that the Algonquin beaches encircle 

 the southern half of Lake Michigan as the "Toleston" beach, instead 

 of descending beneath the level of the lake somewhere north of Two 

 Rivers, will be assumed as correct. 



The first thing to be noted is that a straight line cannot be drawn 

 through the points of observation without far exceeding the probable 

 error of observation. The hypothesis of uniform tilting, therefore, 

 drops out. It appears possible, however, to fit a curve. For the sake 

 of simplicity a circular curve, with a radius of approximately 11.75 

 feet, may be drawn through the points of observation as plotted on 

 Goldthwait's profile, and the deviations of the points measured. The 

 results are as follows : Average deviation of all sure points =1.2 feet ; 

 maximum deviation of any sure point =3 feet. The deviations of all 

 the observed points from the broken profile of Goldthwait were not 

 measured for the entire length of the profile, since it was evident that 

 they would be essentially the same as measured for the profile from 

 Rock Island to Jacksonport, namely, i . i and 4.0 feet respectively. 



The conclusion may be stated, then, that the Algonquin shore- 

 line for the whole length of the profile, about 100 miles, furnishes no 

 evidence in favor of the hypothesis of differential tilting over the older 

 one of differential warping; both are equally probable so far as the 

 observations go. The hypothesis of differential warping, however, 



