A technique is described and standard integral forms are presented for the application of a new performance criterion for servo mechanisms based upon minimizing the time moment of error-squared of a system in response to a given signal. Examples of its use are given, in the course of which a novel graphical method of analysing servo mechanisms is described.The new criterion is a comprehensive one depending upon the complete error transient. It is related to the minimum-integral-of-error-squared criterion, which has been previously proposed. The latter criterion, while convenient for mathematical manipulation, suffers from the severe disadvantage that systems based upon it do not give the best practical results. As a consequence of considerable practical experience with the simpler types of servo mechanism it is usual to express empirically design requirements which lead to systems yielding the best practical results. Any criterion of practical significance should satisfy these requirements in such cases. It is the purpose of the paper to show that the minimum-moment-of-error-squared criterion does satisfy these requirements although the minimum-integral-of-error-squared criterion does not, and to recommend that the time-weighted criterion be adopted for the design of the modern special-purpose system, where the original empirical requirements are not necessarily appropriate.