Rbo = radius of curvature at the vertex of the (non-spherical) surface of revolution obtained when n (and therefore Bo) is finite. Note that Ro is defined as the radius of curvature of the circular cross section when Bo = 0, and R^ is defined as the radius of curvature at the vertex when Bo (which is proportional to the acceleration of the system) is a very small quantity indeed. Hence, for the systems under consideration, which are accelerated only by such tiny forces as gravity gradient, self-gravitation and solar wind, the difference between Ro and R^ is an infinitesimal of yet higher order. Neglecting this infinitesimal we may write R^ = Ro. Substituting the latter (close) approximation in (8) we find Now the a; are functions of the dimensionless parameter Bo, and the ratio (x/2Ro) is also dimensionless since x and Ro are measured in the same units. Hence the units of 5 are the units of Ro. Combining (9) and (10) and taking the deviation 5 positive we have from the first non-zero term of this rapidly convergent series: Substituting for the Bond Number, Bo, from (3), reducing and neglecting higher- order terms, this becomes: If the liquid meniscus surface is considered an optical surface (reflector or refractor) we may redefine the parameters of 8 as follows: R3 = Ro = radius of curvature of an optical mirror or lens,
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