ON EARTH TREMORS. 313 



Cavendish Laboratory at Cambridge, no observer is likely to expect much 

 from a short series of observations, however complete it may be, for the 

 demonstration of gravitational or tidal efiFects of the moon. Holding this 

 view, I was much surprised to find, when first inspecting the photographs, 

 that in the curves obtained at Wilhelmshaven a lunar wave was distinctly 

 visible, which produced a decided change in the general aspect of the 

 curves in different phases of the moon. This led me to make a careful 

 reduction, with the object of finding a lunar wave in all the three sets of 

 observations. The final results of this investigation I have lately pub- 

 lished in No. 3169 of the ' Astronomische Nachrichten.' But as it re- 

 quired a good deal of calculation before the conclusions there given were 

 arrived at, it may be useful to say a few words about the way in which 

 the influence of the moon has been determined. 



We owe to Professor Darwin the evaluation of the principal effects 

 the moon may produce on the solid earth, apart from the well-known 

 deflections of the plumb-line due to the tidal forces of the moon. All 

 these different indirect and direct lunar influences form a complex pheno- 

 menon, the general forms of which have to be ascertained before one may 

 try to analyse it. The first object of our investigation, therefore, is to 

 find whether the observations require the assumption of a lunar wave, 

 what is its form and its position referred to the meridian passage of the 

 moon, and how the size of the wave varies with the declination of the 

 moon. 



The problem is apparently identical with the problem of the ocean 

 tides, if, instead of the heights of the water, the ordinates of the curves 

 are introduced. The same method might therefore be employed which 

 was indicated by Professor Darwin and Professor Boergen for the reduc- 

 tion of the ocean tides. But there is this difference between tidal obser- 

 vations and observations of the plumb-line, that in the former the principal 

 changes in the height of the water are due to the attraction of the sun 

 and moon, the mean level remaining very nearly constant, whilst in the 

 latter the changes due to solar and lunar influence are extremelij small 

 compared with the periodical changes which arise from thermal effects 

 and the very marked variations of the mean daily position of the plumb- 

 line. Thus the principal difficulty in reducing a set of observations with 

 the object of determining the lunar influence is to eliminate as much as 

 possible the zero-point and the daily period. 



The following is a very simple method for eliminating the zero- 

 point, which I constantly employed in determining the mean daily oscil- 

 lation of a group of days. It gives very satisfactory results provided 

 that care be taken to exclude such days on which the motion of the zero- 

 point is too irregular to admit the assumption of a simple mathematical 

 formula. 



If /o, /i, . . ./23 is a series of twenty-four equidistant values, which in 

 the present case would represent the means of a number of single readings 

 of the curves, it is always possible, when the readings form an uninterrupted 

 series, to add to those twenty-four values the following six: f_^, /_2, 

 J-\i • ■ • fa, /26» /26. the meaning of which is clear from the sufiBxes 

 given. These thirty values may be represented with sufficient accuracy 

 by the following formula : — 



