Unimolecular reactions in gases have a rather exceptional theoretical interest, because they involve, apparently, the spontaneous change of isolated molecules. One example only has been satisfactorily investigated, the thermal decomposition of nitrogen pentoxide, and an examination of the molecular statistics of this reaction leaves a certain mystery about the method by which the molecules are caused to decompose. It is unwise to infer too much from what might be a quite special instance; hence we have during the last few years searched for other examples. We now find that the thermal decomposition of acetone vapour satisfies the experimental criteria of a homogeneous, unimolecular reaction. Moreover, the peculiarities of the nitrogen pentoxide decomposition are here reproduced, although the absolute temperature at which the acetone decomposition can be studied is approximately three times as high as that at which nitrogen pentoxide reacts with conveniently measureable speed. Since then this analogy exists between the two reactions, taking place at such different temperatures, we may begin to draw theoretical conclusions with more confidence. The theoretical discussion is reserved for the last section, after the experimental work has been described, because the conclusions depend very much upon the actual numerical results.