Plano-convex ingot problematic in the case of the stamped examples as this would require the furnace to be dismantled or else have a short shaft to allow access for stamping (Merkel 1986, Tylecote 1986, 22.) As a solution the furnace could have been tapped into a mould at the completion of smelting. It is possible that both methods were used as several of the ingots seem to have had additional metal poured onto the top in order to allow stamping (Tylecote 1986, 23-4.) Plano-convex ingot Plano-convex ingots are lumps of metal with a flat or slightly concave top and a convex base.
Luneburg lens one side, and formula_14 only on the other: The parameter formula_19 is a constant for any given ray, but differs between rays passing at different distances from the centre of the lens. For rays passing through the centre, it is zero. In some special cases, such as for Maxwell's fish-eye, this first order equation can be further integrated to give a formula for formula_14 as a function or formula_13. In general it provides the relative rates of change of formula_14 and formula_13, which may be integrated numerically to follow the path of the ray through the lens. Luneburg lens A