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POPULAR SCIENCE MONTHLY. 



so on. All cross-motions above 13" we put together.* The results of 

 this work are shown, so far as described, in the first four columns of 

 the table below. We have here for the various values of t the num- 

 ber of positive, negative and zero apical motions. 



Table showing the number of positive and negative apical motions 

 for different values of the cross-motion. 



The first question that arises in connection with this table is how 

 to count the motions that come out zero; that is to say, those which are 

 too small to be certainly observed. The most probable distribution we 

 can make of them is to suppose that they are equally divided between 

 positive and negative motions. I have, therefore, added one-half of 

 the zero motions to the positive and one-half to the negative column, 

 thus getting the results given in columns P and N. The percentages 

 of positive and negative motions thus resulting are given in the last 

 column. 



We see that there is a fairly regular progression in the percentage, 

 depending on the value of the cross-motion. In the case of the small 

 cross-motions, which presumably belong to the more distant stars, the 

 percentage of negative motions is markedly greater than it is in the 

 case of the nearer stars which have larger values of t. The diminu- 

 tion in the number of zero motions is still more remarkable. This 

 arises from the fact that in the case of the nearer stars the apical mo- 

 tions are necessarily larger, whether positive or negative. 



In the preceding table all the stars were counted, without reference 

 to their distance from the solar apex. The result of this will be that 

 the mean of the apical motions is taken as we see it projected on the 

 sphere, which does not correspond to the actual motion in space except 

 when the direction of the star is at right angles to that of the apex. 

 I have, therefore, made a second partial count, including only stars be- 

 tween 60° and 120° from the apex. These stars were selected in oppo- 



*The author should say that the greater part of the work on these countings 

 was done with great care and accuracy by Mrs. Arthur Brown Davis, to whom 

 he is so much indebted for help of this kind through the present work. 



