Elastic Solids to Metrology. 



60£ 



slope is greatest, its greatest value being the maximum 

 value of 



(ds/dx-1) or %{dy/dx)\ 



We have seen in § 24 that the largest value of dyjdx 

 occurs either at the end of the bar or at x = x if where x 1 is 

 given by (76); and equations (77) and (79) supply the values 

 of dyjdx at these two points. From these we find the corre- 

 sponding values of (ds/dx — 1) given in Table IV. Of the 

 numerical results given, those not in brackets are the 

 absolutely largest values met with throughout the bar. To 

 avoid decimals as much as possible the factor 10 9 has been 

 applied. 



Table IV. 

 Largest values of 10 9 x (ds/dx — 1). 



Bar. 



Value 

 of .r. 



all- 



•5774 



10 



- {? ::: 

 B{r'::: 



° {f ::: 



1126 872 305 



206 159 56 



242 188 



169 131 



66 



46 



[0] 

 70 



6 

 6 



17 

 [0] 



36 



L7] 



973 

 [953] 



4504 

 4504 



[0] 

 13 



11 



1-1 



30 



[0] 



[1-3] 



178 

 [174] 



822 

 822 



[0] 

 15 



13 

 1-3 



36 



[0] 



8 

 [1-5] 



210 



[205] 



970 

 970 



[0] 

 11 



09 

 0-9 



25 



[0] 



5 

 [M] 



146 

 [143] 



677 

 677 



A is the only bar of the four in which the difference between 

 a short arc and its horizontal projection can exceed one part 

 in a million. So far as Table IV. is concerned, the standard 

 yard compares unfavourably with modern types. 



§ 32. As the angle of slope may be more easily grasped' 

 than the difference between the arc and its horizontal pro- 

 jection, I give in Table V. (p. 610) the particulars as to 

 the slope corresponding to the data in Table IV. A plus 

 sign means that the slope is downwards in the direction of 

 x increasing, or towards the end of the bar, a minus sign 

 implies the re^ erse. To avoid decimals the angles are 

 measured in seconds. 



