Basically what he means here
But the space of science is neutral as between touch and sight; thus it cannot be either the space of touch or the space of sight
Refers to how there are 2 kinds of "spaces", there's a personal space, an individuals personal view and space, and then there's a "real space" which is the scientific space, different and completely detached from a personal "space".
Now this sounds a bit complicated, but simply said, There is a difference between what someone sees an object is and what it is in reality. Lets take an object for an example: a simple coin. we all know a coin is a circular object but it will look like an oval to a person unless we are directly in front of the coin, this is the persons own "space of sight" but the "real" shape of the coin stays as a circular object, this is it's "Space of science".
Rewording that phrase could be many different things, such as
Space of science is unchanged no matter the observant, it's form does not change based on perception, thus it cannot be defined by the space of touch or the space of sight of an individual.
As Bertrand Russell himself says in the chapter
The space of science, therefore, though connected with the spaces we see and feel, is not identical with them, and the manner of its connexion requires investigation.
Also clears up the meaning of the difference between space of science and space of touch and sight.