156 Proceedings of the Royal Society 
period, as shown by preceding magnetical observations connected 
with bis own. The relation of the frequency and area of sun-spots 
to the amplitude of the diurnal movements of the magnetic needle 
gives an increased value to this investigation. 
Two very different results have been obtained ; — one by Dr 
Lamont, showing a period of 104 years ; the other, by Dr ft. Wolf, 
gives 11J years. Dr Lamont’s result depends on the assumption 
that three periods occurred between 1787 and 1818 — an assump- 
tion which is opposed to the conclusions which have been deduced 
from the sun-spot, auroral, and magnetic observations for that 
interval. Dr Wolfs result has therefore been accepted very gene- 
rally by many of the most eminent scientific men in England and 
on the Continent. 
The author determines the epochs of maximum and minimum 
range of the diurnal oscillations of the magnetic needle by the 
more exact method, in which the mean for twelve months corre- 
sponding (at its middle point) to each month of the year is obtained. 
Commencing with the Trevandrum observations, from the present 
time, proceeding backwards to the earliest series, showing a maxi- 
mum, that of Cassini (Paris 1784-1788.) The maximum at this time 
(1787'25) is confirmed nearly by Gilpin’s observations (London, 
1786-1806). The latter do not show the minimum in 1792 and 
maximum in 1797, which should satisfy Dr Lamont’s assumption, 
and they are considered by him, like the observations of sun-spots 
at the time, as worthless for this investigation. Dr Wolf, on the 
other hand, finds support in both for a minimum in 1798. 
It is concluded by the author, from an examination of Gilpin’s 
observations, that a maximum really happened in 1797*7, but so 
little marked as to make it probable that any slight corresponding 
increase of sun-spots would not be noticed by the single, not very 
accurate, observer at the time. Evidence, however, of a slight 
maximum is also found in Professor Loomis’s investigation for the 
frequency of the aurora borealis. As it is certain that another 
maximum occurred about 1804 to 1806, the author finds that 
Gilpin’s observations, which agreed with Cassini’s at the commence- 
ment of the series, showed in all probability the true magnetic 
variations afterwards. 
It results from these investigations that the mean duration of the 
