This is the so-called "shield-name", the heraldic motto or device of the Pharaoh, occurring in many variations on the obelisk.
The two diadems referred to are 1) the crown surmounted by an Uræus snake or cobra, symbolizing the king's power over life and death, and 2) the crown with the vulture—usually worn by goddesses and queens—to proclaim him the "nourisher" or "protector" of his people.
This is the longest of any Egyptian cartouche, and is written in two vertical columns. It stands for the second cartouche given on page [36].
The last hieroglyphs of the two columns of the cartouche form the regal name: Thoth-mes.
The custom of erecting obelisks in pairs in front of the gates of temples has already been alluded to on page [20] (cf. the picture).