68 Royal Society : — 



It appears from these values that the range of the lunar diurnal 

 period varies from year to year according to the same law (nearly) as 

 the range of the solar diurnal period ; and we may conclude that the 

 range of lunar diurnal variation obeys the "decennial" law. 



It is well known that the declination needle obeys two diurnal laws 

 due to the solar action ; the first of these governs the movement of 

 the north end of the needle from east to west and from west to east, 

 the second determines a superposed movement resulting from the 

 relative amounts of displacement of the needle from its normal posi- 

 tion at each hour ; the latter is usually termed the diurnal law of 

 disturbance. In order to obtain this law and the values of the dis- 

 turbance, the quantities d oi d v d 2 . . . . (Proceedings, vol. x. p. 477) 

 are summed for each hour and the means are taken. No similar in- 

 vestigation, as far as I am aware, has as yet been undertaken for the 

 lunar diurnal variation. 



I have now arrived at the following conclusions in the discussion 

 for this object of six years' observations of magnetic declination made 

 at the Trevandrum Observatory. 



Having arranged the differences containing the lunar effect, 



dj d x ' d 2 ' 

 do" *» d 2 » 



according to the moon's hour- angles from the meridian, and obtained 

 the means, 



2^0 _ z , K&) a^ . s; 3 Qe") 



t</ -J- — !(,, -f ■ ...» j 



n— 1 n—l'n—l n—\ 



the second differences 



<tf-w.«v -&) 



<-{K),<t"-(K) 



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. 



