304 Prof. Balfour Stewart and Mr. W. L. Carpenter. 



together, and if, moreover, not only the years of the series but also 

 the type of the Inequality be different in the two records, we should 

 require a much longer series before we could so disentangle the 

 influence of Inequalities upon each other as to point by this means 

 unmistakably to a physical connexion. 



The case is different, however, in a comparison of phase. If we 

 are able to show a nearly definite relation in phase between each 

 couplet of these associated phenomena, then the greater the number 

 of such couplets the greater will be the evidence. Were there only a 

 single Inequality we could have no evidence whatever of this kind, 

 but if there be a good number of Inequalities in each couplet of 

 which there is a constant relation in phase between the two members, 

 the evidence of a connexion becomes very strong, because the 

 likelihood that such a relation should constantly repeat itself without 

 a physical connexion is extremely small. Again, as a matter of fact, 

 it is much more easy to alter slightly the position of a maximum than 

 it is sensibly to affect the phase of the Inequality. We have already 

 mentioned in Art. 10 that we have only deemed it necessary to make 

 separate and complete settings for every third of the small stages 

 herein employed. Now suppose that by such treatment we have a 

 maximum at some point, say, for instance, 36. By employing the 

 more laborious method of a complete setting for each small stage 

 we might in some cases shift the position of such a maximum (if 

 only slightly in excess of its neighbours) one or even two places, say 

 to 37 or 38, but we should not by this method of treatment 

 materially alter the phase. In fine, the comparison by periods is sub- 

 ject to greater uncertainty than the comparison by phases, inasmuch 

 as while the maximum has been displaced by a slight difference 

 of treatment, through two divisions, the phases for 36, 37, 38 

 by the old method are practically the same as those by the new. We 

 have already (Art. 9) sufficiently indicated the method of dealing 

 with an Inequality of one period so as to bring it to represent in 

 phase one of a slightly different period. In the above instance, 

 therefore, we may imagine the true period of the Inequality to be 

 36, or we may with equal propriety imagine it to be 38; in 

 either case we shall have the same phase for our Inequality, 

 provided that in the latter we reduce 38 so as to represent in 

 phase the period 36, or, in fine, bring both to one common 

 period. 



It thus becomes manifest what we ought to do. We ought to 

 reduce in phase the two members of a couplet to the same time-scale 

 and then make our comparison. It is possible that if the series of 

 years had been precisely the same for the celestial and the terrestrial 

 members of the couplet, and if both had presented only one oscillation 

 in 24 days, we might have found a constancy of phase between 



