During a non-central eclipse the centre line of the moon's shadow does not touch the surface of the earth. The graph below shows the distribution of non-central eclipses (in blue) during from -1999 until 3000. A least square fit gave a period of 5.9 centuries Again this seems to be the same period that governs many other distributions (e.g. lunar tetrads, total penumbral eclipses, duos, double duos, and off course the frequency of solar eclipses in general).
Comparing the distribution of non-central eclipse with the distribution of eclipses that are part of a double-duo (4 eclipses in a 7 lunation period) shows that non-central eclipses occur mainly in periods with no or few eclipses that are part of a double duos series. (Note the different scales on the y-axis)
The table below lists the non-central eclipses. For subsequent
non-central eclipses in the same Saros series, the eclipse has to occur near
the perihelion passage. These are always non-central annular events. Some
Saros series (27, 64, 103) have 3 subsequent non-central eclipses. Saros 153
will even have 4 subsequent non-central annular eclipses (17 Dec 2104, 28
Dec 2122, 8 Jan 2141 and 19 Jan 2159). The following 2 eclipses in this
Saros will also have no northern limit, but will be central. (see Morsels IV, ch. 12)