central processing, which differentiates these effects from those of preparation, discussed below. Preparation Another observation first made by early chronometric research was that a "warning" sign preceding the appearance of a stimulus typically resulted in shorter reaction times. This short warning period, referred to as "expectancy" in this foundational work, is measured in simple RT tasks as the length of the intervals between the warning and the presentation of the stimulus to be reacted to. The importance of the length and variability of expectancy in mental chronometry research was first observed in the early 1900s, and remains an important consideration in modern research. It is reflected today in modern research in the use of a variable foreperiod that precedes stimulus presentation. This relationship can be summarized in simple terms by the equation: where and are constants related to the task and denotes the probability of a stimulus appearing at any given time. In simple RT tasks, constant foreperiods of about 300 ms over a series of trials tends to produce the fastest responses for a given individual, and responses lengthen as the foreperiod becomes longer, an effect that has been demonstrated up to foreperiods of many hundreds of seconds. Foreperiods of variable interval, if presented in equal frequency but in random order, tend to produce slower RTs when the intervals are shorter than the mean of the series, and can be faster or slower when greater than the mean. Whether held constant or variable, foreperiods of less than 300 ms may produce delayed RTs because processing of the warning may not have had time to complete before the stimulus arrives. This type of delay has significant implications for the question of serially-organized central processing, a complex topic that has received much empirical attention in the century following this foundational work. Choice The number of possible options was recognized early as a significant determinant of response time, with reaction times lengthening as a function of both the number of possible signals and possible responses. The first scientist to recognize the importance of response options on RT was Franciscus Donders (1869). Donders found that simple RT is shorter than recognition RT, and that choice RT is longer than both. Donders also devised a subtraction method to analyze the time it took for mental operations to take place. By subtracting simple RT from choice RT, for example, it is possible to calculate how