Hes Vase with Cover Faience, 8 1/16 x Diam. 2 3/16 in. (20.5 x 5.6 cm) Thebes, Egypt, New Kingdom, late XVIII Dynasty, ca. 1350-1295 B.C.E. Brooklyn #48.55a-b, Charles Edwin Wilbour Fund Photo © Joan Lansberry, May 2012-2016

(From info card) "Ritual vessels known as hes-vases were commonly used in temple rituals of purification and in libations, or liquid offerings, which the priest poured to the gods. Their shape resembles the hieroglyph hes, which can mean 'to favor' or 'to praise.'" The glyph for 'water jar', heset, shows one of these vases with water streaming from it.

Detail created from "Thin gold plaque with embossed ba-bird holding a hes vase in one hand." at the British Museum, Registration number: 1952,1213.2

In Lepsius' drawing, which I've adapted here, Thutmose III is running in his Heb Seb race, while carrying two heset jars. He has passed by Horus, who holds three ankhs and holds a palm branch. He approaches Amun, Set is behind Amun. Set also has palm branches. The presentation of palm branches ensures a long reign.