All observational data in B band on Mkn 421 are available in the following
studies: Miller (1975), Ulrich et al. (1975), Veron & Veron (1975),
Veron & Veron (1976), Miller et al. (1977),
O'Dell et al. (1978),
Mufson et al. (1980), Puschell & Stein (1980),
Zekl et al. (1981),
Gagen-Torn et al. (1983), Sitko et al. (1983),
Cruz-Gonzalez &
Huchra (1984), Moles et al. (1985),
Sitko et al. (1985), Makino et
al. (1987), Xie et al. (1987), Sillanpää et al. (1988),
Xie et al.
(1988), Sillanpää et al. (1991),
Sitko & Sitko (1991), Takalo
(1991), and Takalo et al. (1992). Data for Mkn 421 consist of 565
observations, dating back to 1900. Since we are searching for the long
time variability, we include those data estimated from Miller's
figures with relatively large date uncertainties (less than one month).
The B-band observations are used in this paper because there are more
data available in B-band than in other bands. We
translate the photographic magnitude 
by the approximate relation
and the flux density, 
, by 
(Sitko et al. 1985).
The error caused by the conversion from photographic to photo-electric
values is not larger than 0.2 magnitude. The object does not produce a stellar
image in deep photographic exposures, so photometric data obtained
with different entrance sizes are different. About half of our data are taken
from Miller's paper (Miller 1975), where the uncertainty of the iris
photometry measures are typically 0.1-0.2 magnitudes. A large fraction of the
remaining data are
obtained with a diaphragm of about 26'', within which the
contribution of the host galaxy is less than 0.2 magnitude. Thus the difference
between magnitudes derived through different entrance diaphragm sizes is
less than
about 0.2 magnitude. Therefore, the photometric and photo-electric data
are consistent within 0.2 magnitude, a very small value
compared to the large range of variation of the object,
mag. The magnitude uncertainties introduce
noise and introduce an uncertainty on the parameters of the temporal features possibly detected on the Jurkevich plot (see next section).
The long-term light curve is shown in Fig. 1 (click here)a. Because of our
purpose to investigate large-amplitude variations, we do not show individual
error-bars. The effect of errors on the periodicity analysis
will be discussed in Sect. 3. Mkn 421 is
very active, with a range of variation of 
mag. The
source reached a maximal brightness of 11.6 mag in 1934 January and
was brighter than 12.5 mag on three occasions in 1901, 1916 and 1936
(Miller 1975). After reaching
a maximum B=12.75 in 1982 April, Mkn 421 faded out until 1986.
There are fewer observations available for Mkn 421 after 1986, in B
band. The observations, however, still show that the source brightened
again (Takolo 1991; Takolo et al. 1992).
Figure 1: a The long-term light curve of Mkn 421 from 1900
to 1991. The discontinuity of the light curve between 2435000 and
2439000 is due to lack of observations
Figure 1: b The mean light curve of Mkn 421 over
a 100-day mean
To reduce small amplitude intra-day's fluctuations, we averaged the light curve over 1 day. No significant difference has been found. In order to probe the long-term behavior of the variations, we averaged the light curve over 100-day (Fig. 1 (click here)b). Because of the different quality of our data at different epochs, the impact of flickering in recent data is washed out,while still significant in the early data. As the object varies in intensity by about 0.5 mag on a time scale of several hours (Xie et al. 1988), the largest difference between early epoch data point and the mean value can be estimated only within an uncertainty of 0.5 mag. We have averaged the light curve. The resulting light curves are similar. The peaks in 1934, 1975 and 1982 remain unchanged. The difference between Figs. 1 (click here)a and b is quite significant. It indicates that Mkn 421 suffers large intensity variations on a time scale of a few months. The variability of Mkn 421 shows two modes: a short one with a time-scale of a few months to several years and a longer one with a time scale of the order of ten years. We will analyze the repetition of the bursts in the light curve using the Jurkevich method (1971) in Sect. 3.