It appears from Struve's researches that about one in forty of all stars down to the ninth magnitude is composite, but that the proportion is doubled in the brighter orders.[102] This he attributed to the difficulty of detecting the faint companions of very remote orbs. It was also noticed, both by him and Bessel, that double stars are in general remarkable for large proper motions. Struve's catalogue included no star of which the components were more than 32" apart, because beyond that distance the chances of merely optical juxtaposition become considerable; but the immense preponderance of extremely close over (as it were) loosely yoked bodies is such as to demonstrate their physical connection, even if no other proof were forthcoming. Many stars previously believed to be single divided under the scrutiny of the Dorpat refractor; while in some cases, one member of a supposed binary system revealed itself as double, thus placing the surprised observer in the unexpected presence of a triple group of suns. Five instances were noted of two pairs lying so close together as to induce a conviction of their mutual dependence;[103] besides which, 124 examples occurred of triple, quadruple, and multiple combinations, the reality of which was open to no reasonable doubt.[104] It was first pointed out by Bessel that the fact of stars exhibiting a common proper motion might serve as an unfailing test of their real association into systems. This was, accordingly, one of the chief criteria employed by Struve to distinguish true binaries from merely optical couples. On this ground alone, 61 Cygni was admitted to be a genuine double star; and it was shown that, although its components appeared to follow almost strictly rectilinear paths, yet the probability of their forming a connected pair is actually greater than that of the sun rising to-morrow morning.[105] Moreover, this tie of an identical movement was discovered to unite bodies[106] far beyond the range of distance ordinarily separating the members of binary systems, and to prevail so extensively as to lead to the conclusion that single do not outnumber conjoined stars more than twice or thrice.[107]