OF ARTS AND SCIENCES. 273 



to it, or would coincide with its shortest dimension. According to this 

 theory, then, the axes of rotation would be directed towards the poles 

 of the Milky Way. If now we suppose that a great number of varia- 

 ble stars, of the form described above and rotating around parallel 

 axes, were distributed over the iieavens, it is evident that those seen 

 in the direction of their axes would not appear to vary, since as they 

 turned they would always present the same portion of their surfaces 

 to the observer. Those at right angles to this direction would show 

 ihe greatest variation, and, other things being equal, would appear to 

 be more numerous since they would be more likely to be detected. 

 If then the axes are coincident, we should expect that most of these 

 variable stars would lie along the arc of a great circle whose pole 

 would coincide with their axes of rotation. An inspection of a plot of 

 the stars of Class IV. showed that they agreed closely with a great 

 circle whose pole is in R. A. 13* and Dec. -|- 20°. To compare 

 these stars in this and in other respects, they are arranged in the order 

 of their periods in Table XIII. They are divided into three sections ; 

 first, those known to be of the fifth class ; secondly, those of the fourth 

 class, including all of a shorter period than /3 Lyrce ; thirdly, the re- 

 maining variables of longer period, whose position in Class IV. may be 

 open to question. The first column gives the name of the star, and 

 the second its period in days. The distance from the great circle 

 whose pole is in R.A. 13* and Dec. -|-20° is given in the third 

 column. It was found by measurement on a globe, instead of by 

 calculation, and is not therefore exact to the nearest degree. 



In measuring the stars of the fifth class at the Harvard College 

 Observatory, much difficulty was experienced from the absence of 

 adjacent comparison stars. Stars of the fourth class, on the other 

 hand, have, in almost all cases, stars near them. An unprejudiced 

 comparison is made in the next two columns, by giving the magnitude 

 and distance, in minutes, of the nearest- star of the Durchmusterung. 

 The lines for the southern stars are therefore left blank. If the stars 

 of the fourth class lie near the Milky Way, we should expect an in- 

 creased number of companions due to this cause. Accordingly, a count 

 has been mf.vie of the Durchmusterung stars in a square degree, in 

 which each star is contained. This area is defined as the portion of 

 the Durchmusterung zone in which the star is situated, having an 

 average length of one degree, one half preceding, the other half follow- 

 ing, the variable. The results are given in the sixth column. If these 

 stars were connected with the variables, we might expect that they 

 would lie, approximately, in a plane at right angles to the axes of rota- 



