tokens: value . This gives 3785 proper motion slices. A slice then contains all stars for which holds. The number of stars per slice strongly varies and depends on the total proper motion. The maximum number of 44 000 stars is at (, ) = (), whereas the number of stars is less than 150 at the borders of our square. About 90% of all slices contain less than 6000 stars. These slices represent a seven-fold overlap of the proper motion plane, with the effect that the same over-density on the sky may appear in neighbouring slices, but not necessarily with the same signal-to-noise ratio. (b) In the second step we searched for over-densities in the proper motion slices. For each star in a proper motion slice, we counted all its neighbours within a radius of 0.5 deg (called sky circle) and determined the surface density (stars/square degree). Surrounding each star’s sky circle we chose an area of 9 sq. deg, where we determined the background surface density . We only retain stars if / of their sky circle is larger than 3.0 and their is larger than 5 per square degree. If the angle between two stars is less than 0.5 deg, each of them is in the other’s sky circle. We discard the one with the lower . This cleaning goes on until only “isolated” sky circles are left, which we call Level-0 centres. As our system of proper motion slices represents a seven-fold overlap of the sky, a Level-0 centre in slice could have the same or a neighbouring Level-0 centre in slice . If they are within the radius of a sky circle and the difference of their actual proper motions is less than 1.5 mas/yr, only the Level-0 centre with higher / is retained. These survivors are called Level-1 centres; they are disjunct and are possible candidates of new open clusters. Of course, many of the Level-1 centres could be related to known open clusters. Therefore, we cross-matched them with the MWSC clusters ( Kharchenko et al. 2013 ) and with the most recent cluster list DAML02 VERSION 3.5 of 2016 Jan. 28 ( Dias et al. 2002 ). We discarded all the Level-1 centres within 0.7 deg of a known cluster, if the radius of the known cluster was larger than 0.2 deg. If the radius of a cluster in MWSC or in DAML is smaller than 0.2 deg, it cannot be identical to one of the objects found here. About 200 Level-1 centres surviving this process (called Level-2 centres) were then subject to a photometric check of their existence as clusters. Table 1 New open clusters. 3.2. Photometric steps. (a) We first made a quick and coarse check in the CMD of the stars in a sky circle around a Level-2 centre using TOPCAT 2 ( Taylor 2005 ). A Level-2 centre was selected for a more careful treatment if stars with showed a tendency towards building a part of a main sequence or a turn-off region. The Level-2 centres were immediately rejected if, on the CMDs, their stars showed a random distribution, mostly at the limiting magnitude of Tycho-2. So, we could quickly check the Level-2 centres found in the previous step. Fig. 1
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