The labial surface in the vertical plane was investigated in 3 sections: center, mesial, and distal edge of an ideally positioned bracket. The material consisted of 28 casts taken from 14 female and male individuals with a mean age of 26.8 years. 2. After trimming each cast, the resulting surface was photocopied, enlarged 8 times, then digitized under a 2.0 mm grid (corresponding to 0.25 mm of the original size). 3. Using a statistical computer program, mean curves including standard deviations and non-linear regression curves were calculated from the individual data. In accordance with their anatomy 3 groups of teeth were formed in each jaw: front teeth, premolars, and molars. The curves, including the comparison of the squared regression curves, provide an accurate mathematical description of the labial tooth crown in the above-stated sections. 4. The angle differentials between a reference tangent and 20 other tangents were calculated. From a practical standpoint, information is obtained on the extent to which the torque of a tooth would be changed if a bracket was to be positioned vertically (in 0.5 mm increments) from its ideal position. These changes of torque fluctuate on average between 1.3 degrees (mandibular front teeth) and 3.3 degrees (mandibular molars) for every 0.5 mm of vertical deviation. 5. The calculated comparisons of the curves permitted the construction of bracket bases filling-at least in the vertical dimension-the tooth surface most accurately in the "optimal" position.
