  We present multiwavelength, multi-telescope, ground-based follow-up
photometry of the white dwarf WD 1145+017, that has recently been suggested to
be orbited by up to six or more, short-period, low-mass, disintegrating
planetesimals. We detect 9 significant dips in flux of between 10% and 30% of
the stellar flux from our ground-based photometry. We observe transits deeper
than 10% on average every ~3.6 hr in our photometry. This suggests that WD
1145+017 is indeed being orbited by multiple, short-period objects. Through
fits to the multiple asymmetric transits that we observe, we confirm that the
transit egress timescale is usually longer than the ingress timescale, and that
the transit duration is longer than expected for a solid body at these short
periods, all suggesting that these objects have cometary tails streaming behind
them. The precise orbital periods of the planetesimals in this system are
unclear from the transit-times, but at least one object, and likely more, have
orbital periods of ~4.5 hours. We are otherwise unable to confirm the specific
periods that have been reported, bringing into question the long-term stability
of these periods. Our high precision photometry also displays low amplitude
variations suggesting that dusty material is consistently passing in front of
the white dwarf, either from discarded material from these disintegrating
planetesimals or from the detected dusty debris disk. For the significant
transits we observe, we compare the transit depths in the V- and R-bands of our
multiwavelength photometry, and find no significant difference; therefore, for
likely compositions the radius of single-size particles in the cometary tails
streaming behind the planetesimals in this system must be ~0.15 microns or
larger, or ~0.06 microns or smaller, with 2-sigma confidence.
