We present very-high-energy $gamma$-ray observations of the BL Lac object 1ES 2344+514 taken by the Very Energetic Radiation Imaging Telescope Array System (VERITAS) between 2007 and 2015. 1ES 2344+514 is detected with a statistical significance above background of $20.8sigma$ in $47.2$ hours (livetime) of observations, making this the most comprehensive very-high-energy study of 1ES 2344+514 to date. Using these observations the temporal properties of 1ES 2344+514 are studied on short and long times scales. We fit a constant flux model to nightly- and seasonally-binned light curves and apply a fractional variability test, to determine the stability of the source on different timescales. We reject the constant-flux model for the 2007-2008 and 2014-2015 nightly-binned light curves and for the long-term seasonally-binned light curve at the $> 3sigma$ level. The spectra of the time-averaged emission before and after correction for attenuation by the extragalactic background light are obtained. The observed time-averaged spectrum above 200 GeV is satisfactorily fitted (${chi^2/NDF = 7.89/6}$) by a power-law function with index $Gamma = 2.46 pm 0.06_{stat} pm 0.20_{sys} $ and extends to at least 8 TeV. The extragalactic-background-light-deabsorbed spectrum is adequately fit (${chi^2/NDF = 6.73/6}$) by a power-law function with index $Gamma = 2.15 pm 0.06_{stat} pm 0.20_{sys} $ while an F-test indicates that the power-law with exponential cutoff function provides a marginally-better fit ($chi^2/NDF $ = $2.56 / 5 $) at the 2.1$sigma$ level. The source location is found to be consistent with the published radio location and its spatial extent is consistent with a point source.
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