Solid Cylinders of Elliptic Section. 79 



Table II. 





Value of co 2 a -j- 



s/m/ P . 







b/a. 



rj= 0. -2. 



•25. 



•3. 



•5. 







1-732 1-732 



1-732 



1-732 



1-732 



•2 



1-721 1721 



1-721 



1-7215 



1-722 



•4 



1-693 1-698 



1-699 



1-701 



1-708 



•6 



1-661 1-684 



1-691 



1-698 



1-732 



•8 



1-639 1-703 



1723 



1-744 



1-849 



10 



1-633 1-768 



1-812 



1-851 



2-138 



The results are only approximate*. The value of b/a 

 represents a disk whose minor axis, though extremely small 

 relative to the major axis, is not absolutely zero. Assuming 

 that the stress-difference and greatest-strain theories really 

 apply to all distributions of stress, the values to be attached 

 to S and Ei in determining the limiting speeds are the same 

 in any one material. 



§ 9. A few hints on the practical application of the tables 

 may assist the reader. If 8 and E be given in absolute 

 C. Gr. S. units, i. e. dynes per sq. cm., then substituting for p 

 the number which denotes the ratio of the density of the 

 material to that of water, we deduce from the tables the 

 values of the velocities o^a and (o 2 a in centimetres per second. 

 If S and E be given in grammes weight per sq. cm., then 

 multiplying their numerical measures by 981 we obtain their 

 values in dynes and so find the velocities as before. To 

 reduce the velocities in these two cases from centimetres per 

 second to feet per second, we divide by 30*480. If S and E 

 be given in tons weight per sq. inch, the reader may avail 

 himself of the following result. Let S = Es = t tons weight 

 per sq. inch, and let p = d times the density of water, then 

 the velocities coia and co 2 a may be found in feet per second 



bv replacing v S/p and \/ Es/p in the tables by 

 407*8 x s/tjd~. 



* Numerical results will here be termed exact or approximate according 

 as they are the complete values supplied by the formulae, or only the 

 first figures of a decimal. The decimal has in every case been calculated 

 to a greater number of figures than appear in the text. 



