  The radio signature of a shock travelling through the solar corona is known
as a type II solar radio burst. In rare cases these bursts can exhibit a fine
structure known as `herringbones', which are a direct indicator of particle
acceleration occurring at the shock front. However, few studies have been
performed on herringbones and the details of the underlying particle
acceleration processes are unknown. Here, we use an image processing technique
known as the Hough transform to statistically analyse the herringbone fine
structure in a radio burst at $\sim$20-90 MHz observed from the Rosse
Solar-Terrestrial Observatory on 2011 September 22. We identify 188 individual
bursts which are signatures of bi-directional electron beams continuously
accelerated to speeds of 0.16$_{-0.10}^{+0.11} c$. This occurs at a shock
acceleration site initially at a constant altitude of $\sim$0.6 R$_{\odot}$ in
the corona, followed by a shift to $\sim$0.5 R$_{\odot}$. The anti-sunward
beams travel a distance of 170$_{-97}^{+174}$ Mm (and possibly further) away
from the acceleration site, while those travelling toward the sun come to a
stop sooner, reaching a smaller distance of 112$_{-76}^{+84}$ Mm. We show that
the stopping distance for the sunward beams may depend on the total number
density and the velocity of the beam. Our study concludes that a detailed
statistical analysis of herringbone fine structure can provide information on
the physical properties of the corona which lead to these relatively rare radio
bursts.
