576 MR J. A. BROUN ON THE 
those aurorz seen below a line of equal frequency passing through St Peters- 
burg, Makerstoun, and Boston.* The following are the numbers of auroree given 
by Professor Loomis for the period 1790 to 1820 :—t 


Years. Aurore. Years. Aurore. | Years. Aurore. 
1790 82 1800 6 1810 1 
1791 79 1801 5 1811 0 
1792 66 1802 8 1812 0 
1793 23 1803 10 1813 2 
1794 11 1804 12 1814 9 
1795 9 1805 22 1815 3 
1796 3 1806 Wal 1816 3 
1797 15 1807 5 1817 iki 
1798 1 1808 3 1818 18 
1799 a 1809 2 1819 13 


Professor Loomis’s numbers show in general a variation which agrees to a 
considerable extent with that of the numbers of solar spots and the ranges of 
the magnetic variations ; they can be considered, however, in many cases as 
only rough relative approximations for limited periods, depending as they do 
on the attention that may have been bestowed on this phenomenon by different 
observers at different times.{ Whatever weight they may possess is in favour 
of the conclusions at which I have already arrived. We see that in 1797 more 
aurore were observed than in any year between 1793 and 1805, in which latter 
year there is alsoa maximum. With these facts before us, we may now deter- 
mine the mean duration of the decennial period. 
27. Mean Duration of the Period.—If the difference of the intervals for 
successive periods follows no law, we can obtain the best approximation to the 
mean interval by including the greatest space of time possible, consistent with 
a knowledge of the number of periods, and the exact epochs at the commence- 
ment and end of the time considered. If, however, as seems not improbable, 
the durations of the different periods vary in such a way as to repeat themselves 
at equal intervals, we can obtain the mean duration accurately only by com- 
paring epochs in the same phase of variation. This is a consideration which 
can be attended to only when the law of variation is known. Dr Wo Fr appears 
* The principle on which this limitation is founded had been already indicated by me. See 
“Trans. Roy. Soc. Edin.,” vol. xix. pt. ii. footnote, p. Ixxxii. 1850. ; 
t+ “ American Journal of Science,” April 1873, pp. 249, 256. 
t{ I may point out the very few aurore noted for the maximum of 1818, yet as I have shown (15, 
footnote) the diurnal range of the magnetic needle for that year was probably as great (or nearly as 
great) as at any other maximum. It is possible also that the limiting line of equal auroral frequency 
is variable. In any case little confidence can be placed in the relative magnitude of the number for sun- 
spots and for aurore at the epochs under consideration, when compared with those for the half century 
1826 to 1876. 


