300 

 the second differences 



' -ft) 



were taken ; these differences, as in the case of the similar investiga- 

 tion for the solar laws, represent the disturbance at each hour-angle 

 of the moon ; and when the means of the second differences are taken, 

 the law of the lunar diurnal disturbance will be obtained, if any such 

 law exist. 



The small range of the regular lunar diurnal variation, and the de- 

 rangement produced by the larger disturbances, the effects of which 

 cannot be eliminated in short series of observations, would render 

 identical results from different groups of years improbable, especially 

 if the range of the variation to be determined be small. The follow- 

 ing conclusions, however, seem sufficiently confirmed by the discus- 

 sion of different groups of observations to be accepted. 



There is a lunar-diurnal law of disturbance which, from the mean 

 of six years' observation, consists of a 



Principal maximum 5 hours before the moon passes the upper 

 meridian. 



Principal minimum near the moon's passage of the lower meridian. 



Secondary maximum 6 hours after the passage of the upper meri- 

 dian. 



Secondary minimum 1 hour after the passage of the upper meri- 

 dian. 



When the results for each year are compared, the principal maxi- 

 mum and minimum are always shown distinctly; but the values and 

 epochs of the secondary maximum and minimum vary, and that so 

 irregularly, that in the mean for the three years 1857-59 the exist- 

 ence of either is doubtful, only the principal maximum and minimum 

 being well-marked. 



In order to determine if the law varied with season, means of groups 

 for quarters of the year were obtained ; means also for the groups of 

 half-years, October to March and April to September, were taken. As 

 the results for the quarters forming each half-year agreed with each 

 other, and that for the half-year which contained them, the following 

 conclusions may be accepted as probably true. 



