Hugh is more than likely correct that the figure 109 is the tonnage of the vessel but without looking at the document in question, it is impossible to ascertain without doubt.
There were at least a dozen vessels named THAMES around in 1850. The only one I can find with a tonnage of 109 tons, is a sailing vessel registered in St. Ives official number 13487. Built in 1843.
Could you give us any more information such as the location of your apprentice, where he was domiciled etc. so we may be able to narrow down the search as to which vessel named THAMES he served on.