320 Mr. J. H. Vincent on Models and Diagrams to 



Ellipsoid of Elasticity. 



Man by 



XO Y plane : 



by ZOX 



plane : 



by ZOY 



plane. 



X. 



V- 



&. 



z. 



y- 



z. 



000 



4-00 



o-oo 



6-00 



0-00 



6-00 



1-00 



3-77 



0-50 



5-92 



0-50 



5-95 



1-98 



3-00 



1-00 



5-66 



1-00 



5-81. 



200 



2-93 



1-50 



5-20 



1-50 



5-56 



2-00 



2-00 



1-66 



5-00 



2-00 



5-20 



2-90 



1-00 



2-00 



4-47 



2-21 



5-00 



3-00 



0-00 



2-24 



4-00 



2-50 



4-68 







2-60 



3-00 



2-98 



4-00 







2-83 



2-00 



3-00 



3-97 







2-96 



1-00 



3-46 



3-00 







3-00 



000 



3-50 

 3-77 

 3-94 

 4-00 



2-91 

 2-00 

 1-00 



o-oo 



FresneVs Wave Sui'face. 

 The quantities a, b, c in the equation 



the usual form in which the equation is met with, are to be 

 taken proportional to the reciprocals of /j, : , /x 2 , yu. 3 . This will 

 be the case if a, b, c are proportional to the numbers 4, 3, 2. 

 A model or diagram illustrating this surface will show the 

 properties of a body whose ellipsoid of elasticity has the same 

 shape as that constructed above. 



Fig. 4 shows a series of curves which are the sections of 

 the surface by planes parallel to the XOY plane. If z = 

 the sectional curves are the ellipse 



a^ + l>Y = a' 2 b 2 

 and the circle 



The radius of the circle is 2. The foci of the ellipse are 

 indicated by crosses ; the ellipse may be set out from the 

 table given above for the section of the ellipsoid of elasticity 

 by the XOY plane. Jt need hardly be remarked, that the 

 ellipses in the same principal section of the indicatrix and 

 wave-surface are similar. 



In this figure the sections of the inner surface are shown 

 by broken lines. 



The ellipse and circle are marked O. 



The curves 1, 1 are obtained by putting z=l in the equa- 

 tion to the surface. 



