Accretion disks play a fundamental role in the theoretical models of
active galactic nuclei (AGNs). Investigations indicate that
instability and pulsations in the inner, transonic regions with
parameters in proper ranges have various time scales (for a review see
Wallinder et al. 1992). The time scale of the dwarf nova type limit
cycle instability in AGNs is too long to be observed directly for a
central black hole of mass 
or higher
(Meyer-Hofmeister 1993), but the global thermal limit cycle
(oscillation) time scale in slim accretion disks with 
around a central mass of 
to 
varies from a few years to several hundred thousand years (Honma et
al. 1991). The latter periodic instability may be observed in some
QSOs and BL Lac objects with available observational data for around
100 years.
Rapid and large amplitude variability for BL Lac objects, a special
subclass of AGNs, has fostered considerable interest. The intra-day
variability has been extensively investigated (see, e.g. Wagner &
Witzel 1995 and references therein). Only a few investigations,
however, deal with the long-term variations of BL Lac objects due
to the lack of data available over a long enough time scale.
Therefore, whether periodic or quasi-periodic fluctuations on long
term time scales exist is unclear. Several years ago, we
started collecting observational data on some BL Lac objects and
investigated their long time-scale variability. Liu et al. (1995)
showed that ON 231 is a very active object with a probable periodic
activity of 
years. This was interpreted
as a thermal limit cycle (oscillation) in a slim accretion disk (for an
alternative interpretation to the periodicity of OJ 87, see
Sillanpää et al. 1988a). In this paper, we show that the BL
Lac object Mkn 421 is also very active and probably has periodic
activities.
The X-ray selected BL Lac object Mkn 421, at z=0.0308 has attracted
much attention after it was identified as a BL Lac object. It is one
of the objects simultaneously observed at all electro-magnetic
frequencies and one of the few objects radiating strong gamma-rays.
Many observations to search for its
variability in optical wave-band have been performed. Data from
the archive plate
collection of Harvard College Observatory showed a large range of
variations, 
magnitude (Miller 1975). After
examining the data between 1974 and 1982, Gagen-Torn et al. (1983)
concluded that Mkn 421 varied in B band with an amplitude of 1.5
magnitude on characteristic time scales of days to years. The
purpose of the present paper is to probe
the long time-scale variability of Mkn 421. We collect
all available observational data in B band and give a general
discussion on the light curves in Sect. 2. In Sect. 3 we present
a detailed analysis of the light curve, through the Jurkevich 
test. In order to test the robustness of the Jurkevich method, we
analyze a simulated data set in Sect. 4.
Final conclusions are given in Sect. 5.