Complement of the critical angle

We label meridional rays with the angle 0 between the path and the z-direction, as used in Section 1-2. Accordingly, the ranges of 0 for bound and refracting meridional rays are given by Eq. (1-5), where for the step profile of Eq. (2-2), the complement of the critical angle 0 retains the definition of Eq. (1-3). 

We recall from Fig. l-4(a) that bound rays propagate along a zig-zag path at angle 6 to the axis in the core of the waveguide. The range of values of 6 for bound rays is given by Eq. (l-5a) as 0 < 0, < 6, where 6 is the complement of the critical angle defined inside the front cover. The transit time of Eq. (1-14)... 

The waveguide parameter and the complement of the critical angle in this situation are defined in terms of the real parts of the profile by... 

The proton transfer properties of organic molecules in strong aqueous acids is a major area of physical organic chemistry with many practical and theoretical implications. Research in this field has been documented in at least 2000 separate publications over the past two decades and the results have been collected in critical reviews, (Paul and Long, 1957 Arnett, 1963 Deno, 1964 Boyd, 1969 Rochester, 1970 Liler, 1971), several of which have appeared quite recently. It is not our intention here to provide yet another. Instead, we hope to take advantage of the accessibility of the data to approach the subject from a somewhat different angle, so that this article will complement the material presented elsewhere with the least possible redundancy or overlap. We intend to limit our tabulations to material related directly to our principal aim, which is an interpretative one. 

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