94 Mr. C. Chree on Rotating Elastic 



The results are only approximate, except for b/a = and 

 for 97 = 0. The thickness a—x of the area of radial com- 

 pression at an end of the major axis is seen to increase with 

 b/a and with 77, but even in a circular disk of material 77 = * 5 

 it is less than 3a/25. 



Table IX. gives y , the distance from the centre of the points 

 where the curve of no radial strain cuts the minor axis. This 

 distance is finite only when b/a exceeds the b 2 /a of Table VI. 



Table IX.— Value of y /b. 



b/a. 



v = -2. 



•25. 



•3. 



•5. 



•5 



•511 



— 



— 



— 



•6 



•718 



•650 



•509 



— 



•8 



•898 



•872 



•844 



•680 



1-0 



•943 



•931 



•920 



•882 



The results are only approximate. In the case of the 

 blanks the curve still passes through the centre of the disk. 

 Comparing this Table with Table VI., we see that the points 

 in which the curve cuts the minor axis retire from the centre 

 with great rapidity as b/a increases from b 2 /a. Thus for 

 7] = *25 we have y /b increasing from to *65 as b/a increases 

 from '5 to *6. 



§ 27. The investigation of the vectorial angles of the points 

 where the curve of no radial strain crosses the rim, and the 

 determination of the limiting values of b/a for which such 

 points of section exist, lead to some very simple and interest- 

 ing relations. 



From (1) and (56) we find the vectorial angles in question 

 to be given by 



a 2 b\ A 3 + C 3 tan 2 6 + B 3 tan 4 <9) - (A x + B x tan 2 6) (b 2 + a 2 tan 2 6) = 0. 



Substituting their values for A 1? B 1? A 3 , B 3 , and C 3 , it will be 

 found that there exists a factor a 4 — 2na 2 b 2 + b* , which clearly 

 cannot vanish for a permissible value of rj. Dividing out by 

 this factor we reduce the equation to 



V aHan i e-{{a 2 -b 2 ) 2 -2r ] a 2 b 2 \ tan 2 <9 + ^ 4 =0. . (60) 



Now substitute for 6 the eccentric angle <£ from 



a tan 6 = b tan c/> 7 



