At moderate air masses, it makes a separation of a minute in time about equivalent to a degree on the sky. This estimator is computed for the two sky samples closest in time to each star observation, one before the star and the other after it. The angular part of S is necessary to prevent problems when groups of variable and comparison stars are observed. It can happen that the sky is observed only after two stars in a group have been observed, if only a single sky position is used for the whole group. If sky was measured after the last star before the group, that previous sky may be closer to the first star of the group, in time alone, than the appropriate sky within the group.
Similar effects can occur at the end of a group, of course.
While this problem can be prevented by careful observers, not all observers are sufficiently careful to avoid it. The crude separation used here is adequate to resolve the problem without going into lengthy calculations. This brings us to the sky model. The airglow and scattered starlight are proportional to the airmass, to a first approximation. Actually, extinction reduces the brightness of the sky light near the horizon.