Who was the 3rd brother in deathly hallows?

well, when Hermione is reading the book it says that when the 3rd brother reached old age he pasted it down to his son. and i thought that harry has a cloak of invisibility and so was the third brother james? and he ped his cloak onto harry. or was it dumbledore's dad and he ped it onto dumbledore who ped it down to harry?