MAGNETIC DECLINATION AT TREVANDRUM. 737 



together, all for the moon on the meridian of one hour, and so on, and the 

 means be taken, we see in each case that the sun will have been on all the 

 meridians for each of these hour angles of the moon ; and the means thus 

 obtained will be equally affected by the solar action. The process is the same 

 as for the solar diurnal variation. 



If, however, the suppositions made are inaccurate, and the solar diurnal 

 action is not constant during a month, the hourly means for the lunar diurnal 

 variation will not be equally affected by the solar action. A similar conclusion 

 holds for the solar diurnal variation, if the law of lunar diurnal variation is not 

 constant throughout the month. 



7. Besides this possible source of error, there is at least another which 

 depends upon unknown causes, the effects of which have been named disturb- 

 ances. In order to determine the extent of the disturbance at different hours, 

 each observed position is compared with the monthly mean for the corresponding 

 hour, and the means of the differences thus obtained give comparative measures 

 of the disturbance or displacement of the needle at the different hours. 



The discussions for this purpose have shown that the disturbance, though 

 irregular in action, yet on the whole obeys a solar diurnal law, so that in the 

 mean of a sufficient number of observations the disturbing action, like the 

 usual solar action, will be eliminated, and this the more easily when the days 

 of greatest disturbance are omitted. 



8. As it is thought probable that the larger disturbances, at least, are inde- 

 pendent of the lunar action, it has been sought to avoid the irregularities which 

 they introduce when limited series of observations are discussed. Three 

 methods have been employed for this end. By one all the observations differ- 

 ing from the corresponding hourly mean by a certain arbitrary limit have been 

 suppressed, the hourly means for the month have been recomputed from the 

 remaining observations, and the differences taken as if the suppressed observa- 

 tions had not existed."" By the second (employed by me in the first discussions 

 for the lunar diurnal variation from the Makerstoun observations for 1844- 

 1845), the observations exceeding a certain arbitrary limit were considered dis- 

 turbed, and quantities were substituted for them, derived from preceding and 

 succeeding observations, which were within the limit. In the third method, 

 which was employed by me in the first discussion of the Trevandrum observa- 

 tions ;t all the observations in clays which were considered days of marked 

 disturbance were omitted. J 



* I have touched on the objections to this method in a note which appeared in the Proceedings of 

 the Royal Society, of London, vol x. p. 479. The Astronomer Royal (Trans. Roy. Soc. Lond., vol. 

 cliii. p. 617), and Dr Lloyd (Dublin Mag. Observ., vol. i. p. 91, foot note) have also both objected to 

 this process. 



+ Proc. Roy. Soc. Lond., vol. x. p. 481. 



X The test for determining whether a day is one of marked disturbance has been obtained in 

 different manners. I believe that the most certain test would be one depending on the value of the 



