Step 1: The task is to recall the precise statement of Henry's law, a gas-solubility principle relevant to anaesthetic gas uptake.
Step 2: The law fixes temperature and then links dissolved gas to pressure: the concentration of a dissolved gas is directly proportional to its partial pressure above the liquid. In symbols, $C = k P$, so doubling the partial pressure doubles the dissolved amount at the same temperature.
Step 3: Checking the wrong choices, temperature and fat solubility are not the variables Henry's law uses to define dissolution at constant temperature. Only the statement tying dissolved gas to partial pressure at constant temperature is correct.
\[\boxed{\text{At a constant temperature gas dissolves in proportion to its partial pressure}}\]