738 J. A. BROUN ON THE LUNAR DIURNAL VARIATION OF 



There are objections to all these methods, in as far as the rules for rejection 

 or substitution are empirical, and have really no scientific basis. The objections 

 to the second method are probably the least important, since the interpolated 

 values depend on those preceding and succeeding ; and in this respect the 

 operation is somewhat similar to that, where the observed quantities are 

 deduced from photographic registration, by drawing a line among the 

 points. 



9. It has been stated that the third method, that of rejecting all the obser- 

 vations in days considered disturbed, was that employed in the first discussion 

 of the Trevandrum observations. It was, however, found, after the discussion 

 had been performed, that nearly all the days rejected were simply days much 

 affected by the lunar action; the lunar diurnal variations probably amounting 

 on some occasions to upwards of five minutes, while the mean solar diurnal 

 variation did not exceed the half of that amount. In consequence of this 

 discovery, the discussion was made finally including all the observations." 5 ' 



10. The differences, obtained by deducting the hourly means from the obser- 

 vations for the corresponding hours, which are equally positive and negative 

 for a given solar hour during a month, are still affected by the whole lunar 

 action ; so that they will in a given day be positive or negative, more or less 

 positive, or less or more negative, according as the lunar action tends to increase 

 or diminish the deviation of the needle. These differences which are required in 

 the discussion for the solar disturbance serve also for the determination of the 

 lunar diurnal variation, as well as the observed values from which they are 

 derived, with the advantage, that having the mean solar diurnal variation 

 already deducted, they can be combined more readily with reference to any 

 given argument. 



11. The supposition that the law of solar action is constant throughout a 

 month can be considered only approximately true : near the magnetic equator, 

 especially in the months near the equinoxes, the law varies rapidly. To avoid 

 as far as possible any error due to this cause in the discussion of the Trevandrum 

 observations, the mean solar diurnal variation was calculated corresponding 

 to each week in each year in the following manner : — The hourly means were 

 obtained from the observations in the 1st, 2d, 3d, and 4th weeks of the year 1854; 

 from those in the 2d, 3d, 4th, and 5th weeks ; from those in the 3d to 6th weeks ; 

 and so on to the end of the series in 1865. The means obtained from the first 

 series of four weeks were then combined with those from the second series, and 

 the means derived from this combination were considered to represent the mean 



mean difference obtained by comparing each hourly observation with that immediately following it ; 

 the characteristic mark of what is termed a disturbance being the irregular movement of the needle. 



* With a single exception (in about 80,000 observations) in which the mean of the preceding 

 and succeeding observations was substituted. 



