1874.] Variation of the Magnetic Declination. 257 



valent equations of sines are carried to four terms, the following results 

 are obtained : 



1854 to 1869. 



Adie. 2/=0'-120 sin (0 + 175) + 0'-076 sin (20+323) 



+ 0'-011 sin (30 + 299) + 0'-022 sin (40 + 181). 



G-rubb.2/=0'-056 sin (0 + 209) + 0'-095 sin (20 + 315) 



+ 0'-012 sin (30 + 293) + 0'-022 sin (40 + 197). 



From these equations we deduce the following epochs of maxima and 

 minima : 



Minima. Maxima. 



Adie. January 26 and May 19. March 14 and October 1. 

 Grrubb. January 13 and May 23. March 18 and September 29. 



The confirmation of the results from Adie's instrument by those from 

 Grubb's, in spite of the errors of the latter, is so marked in each year 

 and group of years, that we can affirm that at Trevandrum, in the south 

 magnetic hemisphere, the magnetic needle obeys an annual law producing 

 a double oscillation, having a minimum towards the end of May, the prin- 

 cipal maximum near the end of September, another minimum in January, 

 and a secondary maximum in the middle of March. Or, taking the results 

 from Adie's instrument as most free from all error, the principal mini- 

 mum occurs about a month before the June solstice, and the secondary 

 minimum about a month after the December solstice ; while the principal 

 maximum occurs about a week after the September equinox, and the 

 secondary maximum about a week before the March equinox. 



In the result obtained by me from four years' observations (1843 to 

 1846) at Makerstoun, in Scotland, the greatest easterly position was 

 attained in the end of April or beginning of May, and the greatest 

 westerly (or least easterly) position in September. If that result, derived 

 from a single instrument, can be accepted*, it would appear that the 

 movements of the north end of the needle, in the annual variations, are 

 in opposite directions at Trevandrum and Makerstoun at the same period 

 of the year. This result agrees with that which I have found for the 

 decennial inequality, or that in the south magnetic hemisphere ; the law 

 for the south end of the magnet is the same as that for the north end of 

 the magnet in the north magnetic hemisphere : but it is opposed to the 

 result obtained by me for the twenty-six day period, in which the easterly 

 and northerly magnetic forces have their maxima at the same time in both 

 hemispheres. 



It follows that the results which are connected with the sun's rota- 

 tion on its axis are the same in both hemispheres, while those related to 



* I have always considered this result a near approximation to the truth, but it 

 was not confirmed by the very limited series of observations made in the three subse- 

 quent years, years of great disturbance. 



