MARQUETTE DIABASE DIKE 375 



The slope of the zone of increasing grain or that of a tangent to the 

 curve of the grain is obviously near .0005 + , the average increase from 

 50 millimeters to 761 millimeters being .392/711 or .00055. In the Isle 

 Royal report I neglected to consider the chance that this might be (7, 

 and assumed that there was no contact zone^that is, that B was prac- 

 tically 0. Substituting the corresponding values of g" and x' in equation 

 (8) and any value of A over .0005 we get values of B mainly negative, 

 that is impossible, so that if s is A we must most plausibly assume B to 

 be 0, and our best value of s will be .000539, and then we shall have for 

 uj Uo the value of .286. But if we assume that s represents (7, then we 

 shall find for u / Uo .748. The correction for h is not worth Avhile. We 

 have then to settle the question whether the curve. is of type of curve 

 .30 of plate 57 or curve .60 or .90 of plate 58. To settle this question we 

 may note that, supposing B and y are practically 0, from page 393, if 

 x' be 1622, we shall have Wo equal to 16460 m/1622 or more. But this 

 will be true if mo is about 2.64 and m about .26. Now, in case u / Wo is 

 .286, as supposed above, it is also true that uj iio is P^, and accordingly 

 that the equation g^ = Ax -{- B should still be reasonably applicable. 

 This is, however, not the case. Besides this, we have all the arguments 

 which we used in the Palisade trap for not assuming the small ratio 

 of 21 to Uo. 



On the other hand, if we wish to get an idea of the width of the con- 

 tact zone, we may suppose s is C, and substitute the values : g' = .669 ; 

 E = 1.1013, and we shall have the following equation : 



nn^^imS {x'=lQ22)+y 1 

 .45 • 16,460 + 22/ .68* 



From this equation we find the value of y about 3,000 millimeters, and 

 it is worth noting that this will change the value of c, which we have, in 

 finding u I u^, taken as '2w, from 16,460 to 22,060. Substituting this cor- 

 rected value, we can find more accurate values of the other data. For in- 

 stance, 2 uju^ becomes 1 + (1.013/.45 + .88 -|- .000539 + 22,060)* (2 ujuy 

 or ulu^= .70. 



The relative grain of the other constituents is given later. 



We have K= 2.68 and kjai/'u'^ = .00012. 



The three equations of the three tangents to curve of grain are ac- 

 cordingly : 



2/ = / --.000539 a:'. 



g'' = .0001665 (^ a:'+ 3000] = .0001 x + .5. 



^'''= 1.013. 



