We observed 42 molecular condensations within previously identified bright-rimmed clouds in the ammonia rotational inversion lines NH3 (1,1), (2,2), (3,3) and (4,4) using the Green Bank Telescope in Green Bank, West Virginia. Using the relative peaks of the ammonia lines and their hyperfine satellites we have determined important parameters of these clouds, including rotational temperatures and column densities. These observations confirm the presence of dense gas towards IRAS point sources detected at submillimetre wavelengths. Derived physical properties allow us to refine the sample of bright-rimmed clouds into those likely to be sites of star formation, triggered via the process of radiatively-driven implosion. An investigation of the physical properties of our sources show that triggered sources are host to greater turbulent velocity dispersions, likely indicative of shock motions within the cloud material. These may be attributed to the passage of triggered shocks or simply the association of outflow activity with the sources. In all, we have refined the Sugitani et al. (1991) catalogue to 15 clouds which are clearly star-forming and influenced by external photoionisation-induced shocks. These sources may be said, with high confidence, to represent the best examples of triggering within bright-rimmed clouds.