Periods could be determined for many other stars. However, due to lower signal to noise their periods are less secure. The results are subdivided into two groups, 21 have FAPs between 1% and 5%, 26 have FAPs between 5% and 20%. These results are summarized in Tables 2 and 3. I expect that of the 47 periods listed in these tables, up to ten of them deviate from the true period by more than 5%. Figure 6 is a histogram of all the periods observed by this program. The darker regions indicate the stars with the more secure period determinations. In the histogram, the stars with the less secure period determinations trace the other stars well. While specific stars may be wrong, the trends seem consistent between the more secure and less secure periods. Note the large clumping of periods at the rapidly rotating end of the diagram, with a small hump near 8 days. This could be interpreted as a continuous distribution with statistically insignificant deviations which give the appearance of gaps or a real gap. The continuous distribution peaks sharply at 2 days, and then is fit with long Lorentzian shoulders. Such a fit expects between one and two stars in the five and six day bins. The peak at 0 -- 2 days is not as abrupt as it first appears. This height of this peak is an artifact of the binning. Since the duration of the rotation period is an observable, the data are binned by period length in days. However, periods of less than two days cover the bulk of the rotational phase space. All stars with rotational velocities greater than about 50 km/s are put in one of these two bins. Stars with rotational velocities less than this are spread among all the other bins.
In Figure 7, the data from the stars in the Orion
OB1a association are
shown separately from the stars near 
Orionis.
Data from the ONC
(Choi & Herbst 1996) are also shown.
As displayed, the data show an evolution
in time from less than 1 Myr in the top panel through about 2 Myr in
the middle panel to about 10 Myr in the third panel. There is a
trend which shows a bimodal distribution at early time with a fast
rotator (FR) to slow rotator (SR) ratio of about 1:2 moving to
a bimodal distribution with FR:SR=2:1 in about half a dex. At an age
of about 10 million years, most of the SR group is gone.
A two--sided Kolmogrov--Smirnov (KS) test of the distribution of the
ONC data with all the stars measured in this study
shows a probability of 
% of the sets being drawn from the same
distribution. This indicates that the distributions are not at all similar.
It should be noted that the comparison of the two data sets is not entirely
fair. This is because the data set presented here and those
from the ONC have
different edge conditions. The data here are sensitive to periods
below a day and insensitive to periods longer than 13 days.
When the distributions of periods less than
four days are compared, the KS test gives a higher probability of the
distributions being drawn from the same parent population, but the probability
is still < 1%. However, the ONC data have a different low--end
cut off than the data reported here.
When the distributions of periods greater five days are compared
for the ONC stars and those near 
Orionis
the KS test gives a 47% probability of these distributions being drawn
from the same population.
The distribution of the slow rotators looks similar. Differences in the high end distribution are accounted for by the duration of the J95 run which limited the longest measurable period to about 13 days. The Choi & Herbst data have a much longer observing run and are sensitive to longer periods. If long periods do exist among the PMS stars in Orion, I am not sensitive to them here. The Choi & Herbst data were monitored irrespective of colors or X--ray and spectral properties. However, they limit their sample to objects in the Jones & Walker (1988) catalog of proper motion ONC cluster members. Differences in the selection criteria may be important for the fast rotators.
The distributions of the fast rotators look somewhat different. This is
probably a function of our high speed sampling.
The period searches conducted on this data were
sensitive to periods up to four times faster than those in the surveys
summarized in Figure 
.
However, the data presented here show a dearth of three and four day
rotators. Undoubtedly, some of the fast rotators indicated here (especially
the ones with higher FAPs) are high frequency aliases of the true period.
It is also likely that many rotational periods in the literature are
low--frequency aliases. In these cases, the FAP or power measured
would not be a
proper measurement of the likelihood since the range of the true period was
excluded from the calculation.
