represents a whole series of spaces, generally non-homogeneous, of which the above-mentioned truly spherical and homogeneous variety is only one particular case.
[35] Quoted from one of the standard text-books of philosophy.
[36] We are endeavouring to explain things as simply as possible, but as a matter of fact the statement we are making that acceleration remains absolute in Einstein’s special theory is not quite correct. The acceleration of a body which in Newtonian science remained the same regardless of our selection of one Galilean frame or another, varies in value in the special theory under similar circumstances. Nevertheless, inasmuch as a sharp distinction still persists between velocity and acceleration, we have felt justified for reasons of simplicity in presenting the problem as we have done.
[37] Subject to the restrictions mentioned in a note in the previous chapter.
[38] This formula
or
can also be written: