314 BEPOET— 1893. 



in which the first part contains the changes due to the variation of the 

 zero-point and P all periodical changes. The period being twenty -four 

 hours, we have 



P — P 



Thus, if we form the differences ^\=f2i—f-3, ^2=/'22— /-2) • • • ^6 

 =/26— A we get six equations, from which we obtain by the method 

 of least squares 



^^2^{'^'+'^'"^'^' + ^^ + ^^ + ^'^}' 



.= 1 I 



y=g7"^Q|-5A,-3^2-A3 + A, + 3A5-h5A6|. 



If the lunar wave be of any importance the harmonic elements of 

 the daily period as deduced from observations in different phases of the 

 moon will show certain regular changes. But as the daily period is in 

 itself very variable, and depends on the radiation of the sun at the place of 

 observation, these latter changes must be entirely eliminated before the 

 changes produced by the superposition of the lunar wave can be distinctly 

 recognised. 



Judging from my own experiments, I believe that the variation of the 

 daily period, which is due to meteorological changes, forms the most serious 

 obstacle to this investigation. The gravitational deflections of the plumb- 

 line are large enough to be discovered by the horizontal pendulum But 

 it requires a very long set of observations to reduce the meteorological 

 effects sufiiciently in the mean results to make the former visible. 



In my investigation contained in No. 3169 of the ' Astr. Nachr.' I 

 have availed myself of the three sets of observations, containing 159, 

 161, and 123 days respectively, of twenty-four readings each.' For each 

 day the time of the upper meridian passage of the moon was taken from 

 the almanac, and groups were formed of those days for which C agrees 

 withni one hour. Thus, each set of observations was divided into twenty- 

 four groups. If we distinguish these by the letters a, b, c, d, . . ., a, for 

 instance, contained all days with C between hours minutes and 1 hour 

 minutes ; d, all days with C between 3 hours minutes and 4 hours 

 minutes; and so on. I then proceeded to form other groups by taking 

 the means ^ (a+h + c), ^ (b + c + d), . . . &c. This was done because the 

 number of days contained in each set of observations was too small to 

 eliminate in a satisfactory manner the irregularities of the cui-ves. 



The twenty-four sets of twenty-four mean hourly values each were 

 now treated as described above, the values of /3 and y were calculated, and 

 the necessary corrections applied, so as to obtain the purely periodical part 

 Pp of the observations. From the resulting numbers, the harmonic con- 

 stants a, b were computed, supposing the daily oscillation to be repre- 

 sented by the expression 



«, cos t + biSint + a^ cos 2t + 7/., cos 2t + a^ cos ^t + h.^ sin 3/ -I- rr , cos 4^ + h^ sin it, 



in which t is either Greenwich mean time or local time. A deflection of 

 the plumb-line to the east of its normal position is considered as positive. 

 In deducing the constants a, b account had to be taken of the process of 



' The readings were taken for the beginning of each hour of Greenwich meantime 

 for the first two sets of observations, and of local time for the third set. 



