Zevachim 37 - Blood Service of Sacrifices
Throwing the blood on the Altar is the fourth and final step of the sacrificial service. For the majority of offerings, the blood has to be thrown from a vessel twice, each time on the lower part of each of the two opposing corners. As the blood is dashed on the corner, it spreads out on the adjacent sides, so that with two applications the blood falls on all four walls. This is called "two applications that are four."
Beit Shammai say that if a Kohen performed only one throwing of the blood, the offerings is valid. Although the second throwing is obligatory, it is not essential for the validity of the offering. In the case of a sin offering, where four applications are initially required, the first two make the offering valid. Beit Hillel disagree in the last case and say that even for a sin offering the first application already makes the offering valid.
Therefore, all agree that the Kohen's intent during the first blood application is what counts, and if he intended to consume the offering beyond allotted time, the offering is rejected. If he had a wrong intent during the second blood application, the offering remains valid.
Art: Karoly Ferenczy - Boys Throwing Pebbles into the River