The day after Bnai Yisrael heard and accepted all the laws that Moshe told them, Moshe built an altar on which the Jews could bring sacrifices. The Posuk tells us that Moshe took חצי הדם, "half the blood", from these sacrifices and put them in basins (to eventually sprinkle toward Bnai Yisrael), and the other half he sprinkled on the altar (שמות כ"ד:ו'). Rashi here says that an angel came down and divided the blood into the two halves for Moshe.
The obvious question is why Rashi was forced to say that an angel split the blood into two. Why can't we say that Moshe himself simply did it, or that perhaps another man did it, as opposed to saying that it was done by an angel? One might say that since a man can't measure the blood so exactly as to know that it was divided precisely in half, and yet the Posuk says חצי הדם, implying exactly a half, Rashi therefore says that an angel must have measured it. But the Gemara in Bechoros (דף י"ז:-י"ח.) concludes that as long as a man does actually split something, it's usually considered as a half even though it might not be a half exactly. We see from here, therefore, that when the Posuk mentions חצי הדם, it could still refer to a division of the blood done by a man.
The Maharil Diskin offers an answer based on a translation of Onkelos two Pesukim later. The Posuk says that Moshe sprinkled the blood on Bnai Yisrael (שם פסוק ח'). Onkelos, however, explains that actually Moshe sprinkled the blood on the altar as an atonement for Bnai Yisrael. We thus see that both halves of the blood were used for the altar and thus must follow the rules relating to blood used for sprinkling on the altar. This is a new approach since the Posuk implies that one half was sprinkled toward Bnai Yisrael (not on the altar) and only the second half was sprinkled on the altar. Onkelos evidently holds, though, that both halves went onto the altar.
The Gemara in Zevachim (דף כ"ה.) teaches that the blood that spills from the neck of an animal being sacrificed into a vessel has to be sprinkled onto the altar from that exact vessel. If, however, one takes the blood out of the originally designated vessel and puts it into another vessel, then the blood is no longer valid for sprinkling. The Maharil Diskin thus explains that Moshe realized that since he had two separate halves of blood to sprinkle, they had to be in their two separate vessels. If the blood from the first half would overflow into the vessel being used for sprinkling the second half, then he'd be sprinkling blood out of the vessel which wasn't intended for that blood, which would be invalid. Moshe thus had to calculate it so that only the blood of the first half went into its correct vessel to be sprinkled, and not into the second vessel for sprinkling. Therefore, since it had to be a precise calculation of exactly a half, no man could accurately do that. Rashi therefore concluded that an angel divided it accurately making sure that each half of the blood went into its originally intended vessel.