To the Editor:
I t is a great pleasure for the author to know that some readers are interested in the author's articles and in testing them to express their frank opinions. Now the author would like to answer the auestion sent in from the reader. I t is clear ---in a crystallograpiy texthook that a cuboctahedron can be observed in a cubic closest packed structure. From this viewpoint, the observation of the reader is correct, and i t is selfevident truth. However, this does not lessen the valuesof the two articles previously puhlished by the author (J.Chem. Educ. 1985.62.1088 and 1987,64,1040). I t is needless to say that the authoks methods of folding envelopes are useful f i r various reasons, one of which is to train thinking ahility of a pupil, in addition to using the model ohtained in class (Yamana, S. 8th International Conference on Chemical Education, Tokyo, 1985 and 31st IUPAC '87, Sofia, 1987). This is applied to the present case, as follows: (A) Although these two methods produce the same shape (euhoctahedron), the processes of them are quite different from each other. (B) The model produced by the first article is not the same as the one by the second article in their magnitude. (The first method produces a slightly Larger model than by the second method.) (C) The author thinks it is proper to treat the cubic closest packed structure together with the hexagonal closest packed structure in class. This leads to the conclusion that the second article should he read together with the third one (J. Chem. Educ. 1987,64,1033), whose processes are quite similar to those of the second article and the scales of models obtained in the second and third articles are the same. In this case, the first article is powerless. (D) From these standpoints,the second method can he considered to he a modified method of the first one. On the other hand, since 1968, the author has invented and published methods of making ahout 30 kinds of polyhedra from a (or two) business envelo~e(s).Among them, three methods bf producing three kindsof polyhedra (tetrahedron. octahedron. and twin ~entahedralconessharing a face) have been revised and rep"hlished. The author always thinks that even if a method is devised and published, it should be revised for its better use, if possible. Shuklchl Yamana Depsrtrnent of Kyoushoku Education Kinki University Kowakae. Higashi Osaka 577. Japan
Side view of the inverted tube.
where
and
are the principal radii of curvature a t the point P, and a,R, and x denote the surface tension of the water, the radius of the tuhe and the vertical displacement AP (or QB), respectively. Equations 2 and 3 are obtained by assuming that the vertical cross sections of the surface of the water through AB, and through P perpendicular to AB, are arcs of circles. T o determine the maximum allowed diameter of the tuhe to prevent water from flowing out, it is necessary to substitute eq 2 and eq 3 into eq 1and set
where p is the density of the water andg the gravity constant. T o achieve this, Sasaki assumes, quite rightly, that x
