The Pole Star has a well-known companion of about the 9th magnitude, which is a favourite object for small telescopes. Burnham finds that the bright star and its faint companion are "relatively fixed," and are probably only an "optical pair." Some other companions have been suspected by amateur observers, but Burnham finds that "there is nothing nearer" than the known companion within the reach of the great 36-inch telescope of the Lick Observatory (_Cat._, p. 299). The well-known companion to the bright star Rigel (β Orionis) has been suspected for many years to be a close double star. Burnham concludes that it is really a binary star, and its "period may be shorter than that of any known pair" (_Cat._, p. 411). Burnham finds that the four brighter stars in the trapezium in the great Orion nebula (in the "sword") are relatively fixed (_Cat._, p. 426). γ Leonis. This double star was for many years considered to be a binary, but Burnham has shown that all the measures may be satisfactorily represented by a straight line, and that consequently the pair merely forms an "optical double." 42 Comæ Berenices. This is a binary star of which the orbit plane passes nearly through the earth. The period is about 25½ years, and Burnham says the orbit "is as accurately known as that of any known binary." σ Coronæ Borealis. Burnham says that the orbits hitherto computed--with periods ranging from 195 years (Jacob) to 846 years (Doberck) are "mere guess work," and it will require the measures of at least another century, and perhaps a much longer time, to give an approximate period (_Cat._, p. 209). So here is some work left for posterity to do in this field. 70 Ophiuchi. With reference to this well-known binary star, Burnham says, "the elements of the orbit are very accurately known." The periods computed range from 86·66 years (Doolittle) to 98·15 years (Powell). The present writer found a period of 87·84 years, which cannot be far from the truth. Burnham found 87·75 years (_Cat._, p. 774). In this case there is not much left for posterity to accomplish. 61 Cygni. With reference to this famous star Burnham says, "So far the relative motion is practically rectilinear. If the companion is moving in a curved path, it will require the measures of at least another half-century to make this certain. The deviation of the measured positions during the last 70 years from a right line are less than the average errors of the observations." Burnham once saw a faint companion to Sirius of the 16th magnitude, and measured its position with reference to the bright star (280°·6: 40"·25: 1899·86). But he afterwards found that it was "not a real object but a reflection from Sirius" (in the eye-piece). Such false images are called "ghosts."