so on. All cross-motions above 13" we put together.[1] 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 τ the number of positive, negative and zero apical motions.
Table showing the number of positive and negative apical motions for different values of the cross-motion.
| Values of τ | Special Motions, σ | Percentage. | |||||
| Pos. | Zero. | Neg. | P'. | N. | N. | P. | |
| 0, ± 1, 2 | 1,013 | 261 | 425 | 1,143 | 555 | 0.33 | 0.67 |
| ± 3, 4 | 360 | 56 | 160 | 388 | 188 | 0.33 | 0.67 |
| ± 5 to 7 | 285 | 37 | 107 | 303 | 125 | 0.29 | 0.71 |
| ± 8 to 12 | 215 | 7 | 52 | 218 | 55 | 0.20 | 0.80 |
| ± 13 + | 216 | 2 | 61 | 217 | 62 | 0.22 | 0.78 |
| Total | 2,089 | 363 | 805 | 2,269 | 985 | 0.30 | 0.70 |
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 τ. The diminution 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 motions 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 between 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.
