608 Dr. C. Ohree : Applications of 



Table III. 

 Excess of arc over chord, unity = 1//, =0*001 mm. 



Value 

 of a/l. 



Type 

 of bar. 



} A 



E. 



B'. 



C. 



D. 









•757 



135 



•159 



•no 



•409 



05 





0301 



•0054 



•0063 



•0044 



•0162 



0-5594 





•0034 



•0006 



•0007 



•0005 



•0018 



0-5774 





•0064 



0011 



•0013 



•0009 



•0034 



0-6 





•110 



•020 



023 



•016 



•059 



10 





2-287 



•407 



•481 



•332 



1-235 



Broch (7.c.p. B. 70) finds for the minimum difference between 

 chord and arc in the type B the value '0003 //,, or only half 

 that given above for the case a/7 = 0*5594. This is not due 

 to his retaining 9 instead of 4 figures in the critical value of 

 ■a/l, but to his use of '7486 as the value of co/c* instead of 

 "5213 as given in Table I. For this I see no justification. 

 He agrees with Benoit in recording *5213 as the value of 

 <wa; 2 for bending about a horizontal diameter (i. e. in a 

 vertical plane) ; and even if he were correct in quoting *7486 

 (Benoit gives '5444, which looks more probable) as the value 

 of cok 2 for bending about a vertical axis, the result would not 

 apply to the actual problem. This discrepancy, however, 

 hardly affects the conclusion drawn by Broch, that the 

 difference between chord and arc is neo-ligible f or metre 

 prototypes supported so that a/l = 0'55938. At the same 

 time, Table III. shows that a comparatively small departure 

 of a/l from the best position suffices to increase the difference 

 between arc and chord tenfold, and for measurements of 

 the highest accuracy the point should be borne in mind. 

 The rapid increase in the difference between chord and arc 

 as the supports are moved out to near the ends is specially 

 notable. 



§ 31. The absolute difference between the arc and its 

 horizontal projection is greater for the entire length than 

 for any shorter portion ; but the relative difference — i. e. the 

 difference per unit length — is considerably greater for some 

 short portions. The relative difference is greatest where the 



