MAGNETIC DECLINATION AT TREVANDRUM. 739 



solar diurnal variation in the middle (or third) week. These hourly means were 

 then compared with the observations at the corresponding hours in the third 

 week, and the differences obtained. The hourly means from the second and 

 third sets of four weeks served in a similar manner for the observations during 

 the fourth week. In a like way the differences were found for all the observa- 

 tions throughout the series. 



12. It is still supposed that the hourly means obtained from the observa- 

 tions in four successive weeks represent the solar diurnal variation unaffected 

 by any inequality of the lunar action. The following discussions make it pro- 

 bable that the mean action of the moon at each solar hour during a lunation 

 is constant, or so nearly so, that any error due to this cause may be 

 nesrlected. 



'{V 



Mean Lunar Diurnal Variation for each Month in the Year. 



13. As the diurnal variation of the magnetic needle produced by the moon 

 has generally been found small, it has been usual to combine the results from 

 all the lunations throughout the year, in order to destroy the effects of disturb- 

 ing causes which still remain, even after a considerable portion of the observa- 

 tions has been rejected for this object. Although this combination may give 

 approximations to a general law in high latitudes, it cannot be expected to do 

 so near the equator ; the first discussion of the Trevandrum observations 

 having shown the law to be inverted in the course of six months ; the combina- 

 tion for that locality of all the observations made during the year, gave a result 

 which is purely arithmetical, without any representative in fact. As nothing was 

 known as to the mode in which the law changed from one form to another, it 

 was necessary to determine it for each month in the year. This has now been 

 done by the discussion of nearly eighty thousand hourly observations made 

 during the eleven years, 1854 to 1864. The resulting values, which will 

 be found in the first volume of the Trevandrum Observations, with a more 

 detailed account of the reductions, are projected in curves in the first half of 

 Plate XXVI. 



14. As these curves present some slight irregularities, it is believed that an 

 elimination of the effects of disturbance, as far as they are independent of the 

 lunar action, will be best made in calculating the most probable variation from 

 the deduced quantities by the formula of sines, 



y = a x cos 6 + &! sin + a 2 cos 20 + b. 2 sin 20. 



The following are the resulting equations for each month, together with the 

 probable error of each result as derived from the four terms only : 



VOL. XXVI. PAKT IV. 9 Q 



