308 DR. S. CHAPMAN ON THE DIURNAL VARIATIONS OF THE 



whole effect. This is not surprising when the minuteness of the lunar variation is 

 considered. The tables showed some outstanding features, however, in particular 

 the constancy (within reasonable limits) of C 2 and a ; C It C s , C 4 are generally smaller 

 and rather more irregular in amount for the eight phases. The phase angles 0, 

 showed a fairly regular increase through 2-* with the moon's age, while 0, showed a 

 less regular decrease of the same amount. No regular change in 4 was noticed, 

 partly because C 4 is small and 4 therefore not well determined, till the Batavian 

 summer declination results were considered ; in this case the fourth harmonic 

 happened to be exceptionally large, and the phase therefore better determined. 

 This clue having once been obtained, the same feature, viz., a monthly increase of 

 4ir in the phase angle 9 4 , was verified to be present in most other cases, where C 4 

 was not too small. The examination of the phase laws followed by the harmonic 

 components was first undertaken by means of vector diagrams, and independently of 

 the theoretical considerations which suggested themselves later, and which are 

 embodied in 12, 23. 



The real test of the phase laws suggested by the vector diagrams was made, of 

 course, by correcting the phases by the amount through which the law indicated they 

 had changed from the period of new moon. The corrected values, tf (where 



V 2 = &i> 



v being the moon's age, in angular measure, at the particular lunar phase considered) 

 should then all be the same (for the same value of the suffix and different 

 values of v), apart from accidental error. The Tables III. to X. show that this 

 is the case, generally, as far as we have any right to expect, though, in some 

 instances, the agreement is not very apparent. Even in these cases, however, 

 the mean value of & frequently agrees so closely with the mean value of tf a as to 

 show that the phase law is acting, though its manifestation is obscured by large 

 accidental error. This agreement between tf lt tf 2 , & 3 , and 0' 4 is a noticeable feature, 

 of which, as well as of the monthly changes of phase, the theory of the lunar variation 

 gives a satisfactory account ( 23). On general grounds, too, it is to be expected 

 that if any simple relation exists at all between the phase angles of the four harmonic 

 components, this relation should assume the simplest form (which proves to be 

 equality) at new moon, when the sun and moon are on the same meridian. The 

 equality of the phase angles at new moon points to a single exciting cause (the lunar 

 atmospheric tide being suggested) of the four components. 



The regular monthly change in the values of 0,, 3 , and 4 results in the 



