Three machines have been simulated using an optical scanner and the IBM 704 computer. Each of these simulated machines has read documents containing rows of handwritten Arabic numbers. Sample numbers were produced by at least 20 people for each simulation study. The three machines simulated differ in the control required of the writer during document preparation and in the complexity of the machines. Writing controls were required for the preparation of the first two types of documents. A section of this paper concerns experiments with and a mathematical model of controlled writing. The third simulated machine was applied both to numbers written within preprinted boxes and to numbers written without any guide marks. About one per cent of 2180 of these numbers were misread as the wrong character. This error rate is based on a sequential experiment in which the recognition logic is constructed from all characters not recognized and thus rejected prior to each input character. Numbers, when rejected, cause the programn to identify them from a table. Their structure is then entered into the recognition logic. The rejection rate decreased throughout the experiment. The last rejection rate was about 10 per cent.