90 



Mr. E. Hatschek on some simple Deformations 



IV. Cubo-octahedrou stretched along axis of octahedron. 



(Fig. 4, a & b.) 



E = 



\f 4 sin 2 - ^/*2 cos a 



L= ^E ^/cos a, 



S = q E 2 ( 3 sin a 4- sin 2 - + sin ^ y^2 cos a ) . 



(N.B. — For this polyhedron E = the whole edge of the 

 square pyramid, a the angle at the apex o£ the latter, and L. 

 the distance between the two square faces.) 



A number of values have been calculated, for elongation 

 only, from these formulae, and are given in the table 

 below : — 



II. 



III. 



IV. 



The 





E. 



L. 



S. 



L 



S — S »l 





&m 



90° 



1000 



1-732 



6 000 



1-000 



o-bbo 



75 



1031 



2-194 



6-158 



1-267 



0026 



60 



1112 



2-745 



6-545 



1-585 



0-091 



45 



1-300 



3-499 



7-171 



2 020 



0-195 



30 



1653 



4-732 



8193 



2-732 



0-366 



70° 31' 44" 



1-000 



2-304 



11-313 



1000 



0000 



60° 



1-029 



2-906 



11-564 



1-261 



0-022 



50 



1-094 



3-526 



12037 



1-530 



063 



40 



1-234 



4321 



12-989 



1-876 



0-149 



30 



1-456 



5-420 



14-258 



2-352 



0-260 



25 



1-628 



6-198 



15140 



2-695 



0-339 



108° 88' 16" 



1000 



2-000 



11-313 



1-000 



0000 



100° 



1-012 



2-417 



11-479 



1-208 



0-018 



90 



1041 



2-843 



11-803 



1-422 



0043 



60 



1-251 



4-314 



13553 



2-157 



0198 



45 



1-473 



5-439 



14-960 



2-719 



0322 



60° 



1-000 



0-943 



2-976 



1-000 



o-ooo 



50 



1-073 



1-147 



3024 



1-215 



0-016 



40 



1-200 



1-400 



3-158 



1-485 



0-061 



30 



1-419 



1-761 



3-398 



1-869 



0-142 



20 



1-822 



2-355 



3-735 



2-497 



0-255 



15 



2194 



2-875 



4105 



3-049 



0-379 



values of 





have 



been plotted in 



fig. 5 



as 



ordinates against the values of L/L„, as abscissae. Differ- 

 entiation of the expressions obtained for these two variables 

 leads, of course, to entirely unmanageable equations, but it is 

 sufficiently obvious that the function connecting elongation 

 and increase is the same in all cases, and therefore of the 

 same type as the comparatively simple function found in 



