Then, given the one line just above what you quoted is "A walker in hate who has dull facilities should practice the four immeasurable" I would say my answer is wrong.
By looking at the index under 'sphere' I see only the four formless sphere of 'space', 'consciousness', 'nothing', and 'neither perception nor non perception' and discussion of the sense spheres. Perhaps one of those spheres is what is referenced, so perhaps reading each page indexed there would be helpful? I'm not sure.
But it seems possible that the four formless attainments are just the meaning here, as discusses each mode in terms of what is not there; that is, in terms of the disturbances that have been cut off.
Give it a read if you have the energy and give it some thought.
Hopefully someone else here can be of greater help.