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The differences O—C are now no longer systematically positive or negative in the first and second zone; in the third they have become negative, instead of positive. We thus find that the anomaly is wholly explained by the irregularities introduced by a few extremely large proper motions.

For this reason it seems preferable to adopt a system of values for q which vary with sin X in the way postulated by theory. The procedure has the advantage of accomodating itself closely to the real variations in the average proper motion in the different parts of the sky, whereas, if we use the etnpirical values of q the average proper motion is artificially brought to equality over the whole of the sphere.

We will therefore adopt a system of values of q for which the variation with sin X is determined by the theoretically calculated values. For that purpose we multiply the

values of q0 for every zone by the quotients -- . The values thus obtained will be

ZêtMJo

called q'0'

Having thus fixed the variation of the values of q with sin X, let us now inquire into the variation of these quantities with the value of p. The following tables embody the whole of the data at our disposal for that purpose.

Table 20.

1.00 > sin X > 0.80 (mean 0.94).

. mean / _ r\ c „

p p qo qc O — n

i i

O 0 O

o to 15 7 1.20 1.18 +0.02 364

15 to 45 30 1.21 1.13 | +008 539

45 to 75 60 0.95 1.03 | — 0.08 220

75 to 105 90 081 0.89 —0.08 158

105 to 135 120 0.80 0.78 -f 0.02 164

135 to 165 150 0.57 0.70 —0.13 95

165 to 180 173 0.68 0.69 — 0.01 48

0.80 > sin X > o 60 (mean 0.72^.

mean > r\ C

p p q 0 qc U — ^ n

|

000

o to 15 7 1.04 i.ii —0.07 | 83

15 to 45 30 | 1.10 1.07 +0.03 j 160

45 to 75 60 0.96 1.00 i —0.04 102

75 to 105 90 0.97 0.89 + o 08 57

105 to 135 120 0.91 0.80 +0.11 37

135 to 165 150 0.72 0.75 —0.03 39

165 to 180 173 0.67 0.72 — 0.05 14

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