(Yakeishi ni mizu; “Water on a hot stone”)
A situation where you shouldn’t expect much. A drop in the bucket. A negligible amount of aid or effort, like a little splash of water against a hot stone, which quickly turns to steam and disappears without cooling the stone noticeably.
We begin with the verb 焼く (yaku), “to burn,” “to heat,” in prenominal form and prefixing the noun 石 (ishi), “stone.” The heated stone is marked by the directional/location particle に (ni) as the target of the noun 水 (mizu), “water.” One can imagine that a verb (such as 掛ける, kakeru, “to throw something against something”) follows, but any verb is elided in the idiom itself.
This phrase is apparently related to a 焼き石 (yakiishi), a stone heated and placed inside a bowl of soup. Apparently one of these could be used to bring a meal to boiling without any need for direct heating from a fire, so it stands to reason that a little splash wouldn’t do much to cool one off.
The origins of this phrase are unclear, but possible sources I’ve seen cited include two 17th-century poetic treatises, the 世話焼草 (Sewayakigusa), and the 毛吹草 (Kefukigusa).
(“Erai bengoshi wo yatotta ga, yakeishi ni mizu datta. Mushiro gyakukouka datta you na ki ga suru.”)
[“I hired a hot-shot lawyer, but it didn’t help at all. On the contrary, I think he made things worse.”]