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In this paper we describe a new technique for obtaining the conversion factor between the molecular hydrogen column density and the CO(J=1-0) integrated antenna temperature. This factor, typically known as X$_{CO}$, is often taken to be of order a few times 10$^{20}$ cm$^{-2}$ [K km s$^{-1}$] for the molecular clouds in the Galaxy and is one of the primary means of determining the molecular cloud mass from CO observations. However, for the low-extinction molecular clouds known as the translucent molecular clouds, estimates of X$_{CO}$ vary by up to a factor of 60 depending on the object and techniques employed to calibrate X$_{CO}$. Since the cloud mass is directly proportional to X$_{CO}$, uncertainties in mass estimates of translucent clouds can be more than an order of magnitude. We calibrate the H$_2$ content in translucent clouds by using the linear relationship between the CH and H$_2$ column densities. The CH column density is readily determined from observations of the CH ground state hyperfine main line transition at 3335 MHz. Using CH as a surrogate tracer for H$_2$ and CO(J=1-0) observations of a sample of translucent and dark molecular clouds we find a wide variation in values for X$_{CO}$. For translucent clouds, X$_{CO}$ ranges from 0.3 to 6.8 $\times$ 10$^{20}$ and for dark clouds the values range from 0.8 to 8.6. Although the average values for both types of cloud are typical of the canonical value determined for the Galactic molecular cloud ensemble (2 - 4 $\times$ 10$^{20}$), the scatter in individual X$_{CO}$ values may indicate that X$_{CO}$ for a given translucent cloud cannot be determined a priori and must be obtained for each cloud so that a reliable mass determination may be made.
