''Their study gave us the first conclusive evidence that the afternoon nap is internally generated by the brain as part of the biological clock for sleep/wake cycles,'' Dr. Broughton said. Theory on Need for Naps

It was Dr. Broughton who in 1975 first proposed the then radical notion that naps were are a natural part of the sleep cycle. He speculated that the body's built-in sleep rhythm included, in addition to a major period at night, a smaller period of sleep in the afternoon. Dr. Broughton's proposal challenged the conventional wisdom in the field, which saw naps as either a sign of laziness or a social artifact, irrelevant to the scientific study of sleep.

But soon evidence on napping began to mount. Dr. Broughton cites several other lines of evidence pointing to the importance of naps. One is that babies, who begin by napping frequently through the day, usually have developed the habit of a single afternoon nap just before they give it up entirely at school age. Another is that in cultures where the siesta is a custom, its timing is always in the midafternoon.

In addition, studies of Americans who often take naps show that most do so in midafternoon. Other evidence Dr. Broughton cites is that there is a well-documented drop in people's performance at work in midafternoon, along with a simultaneous increase in accidents resulting from sleepiness.

He said he believes that a believes that the natural rise in sleepiness in midafternoon is at play in the fact that the midafternoon period is also when the highest number of deaths occur, presumably because of an increase in accidents at that time.

In more recent research, reported in the newly published collection, Peretz Lavie, a sleep researcher at the Technion Israel Institute of Technology in Haifa, found another kind of evidence for the need to nap. In Dr. Lavie's studies, volunteers are kept on a 20-minute sleep/wake cycle, where they sleep for 7 seven minutes and stay awake for 13 minutes for several days at a time. This allows Dr. Lavie to determine how quickly, if at all, they can fall asleep at different times throughout the day.

Dr. Lavie found that in addition to the regular night-time propensity to go right to sleep, there is a midafternoon peak in the readiness of people to sleep. That heightened sleepiness falls between peaks in alertness that occur in the morning and early evening. During these peaks it is much harder for people to sleep, even those who have been deprived of sleep the night before. But Dr. Lavie's volunteers readily fell asleep during their usual bedtime or afternoon nap time.