Formation density is calculated from acoustic logging measurements. In some embodiments, a longitudinal axis of a lamp is at an acute angle greater than 0\xb0 relative to a region of the lower base between the lamp and another lamp. 5 mole equivalent, based on the pivaloyl chloride, of a magnesium compound to thereby prepare a pivaloylacetoacetic acid ester and then alcholyzing or alkali-hydrolyzing the pivaloylacetoacetic acid ester to thereby give a pivaloylacetic acid ester having a high purity at a low cost. The non-pen stroke data may particularly be coded as pen strokes in a position area which is not used for the transfer of ordinary pen strokes, e.