+-----------------+--------------+------+------+------+------+------+------+------+------+------+------+------+------+
| Place. | Latitude. | Jan. | Feb. | Mar. | Apr. | May | June | July | Aug. | Sep. | Oct. | Nov. | Dec. |
+-----------------+--------------+------+------+------+------+------+------+------+------+------+------+------+------+
| | deg. | | | | | | | | | | | | |
| Hammerfest | 70-1/2 | 20.9 | 17.6 | 8.8 | 0 | 0 | 0 | 0 | 0 | 4.4 | 9.9 | 17.6 | 20.9 |
| Jakobshavn | 69 | 14.6 | 13.0 | 9.2 | .5 | 0 | 0 | 0 | 0 | 9.2 | 15.1 | 18.4 | 20.0 |
| Godthaab | 64 | 15.5 | 12.4 | 9.7 | 4.9 | 0 | 0 | 0 | 1.2 | 8.7 | 13.3 | 17.0 | 17.4 |
| St Petersburg | 60 | 6.5 | 9.1 | 16.8 | 13.8 | 3.5 | 1.2 | 1.4 | 5.9 | 13.8 | 13.1 | 7.6 | 7.3 |
| Christiania | 60 | 8.6 | 11.4 | 14.0 | 11.2 | 0.6 | 0 | 0.2 | 6.5 | 14.6 | 12.2 | 10.3 | 10.3 |
| Upsala | 60 | 8.4 | 12.9 | 14.9 | 7.4 | 0.7 | 0.2 | 0.4 | 7.1 | 12.4 | 14.3 | 10.7 | 10.7 |
| Stockholm | 59 | 7.6 | 10.0 | 14.7 | 16.4 3.8 | 0.0 | 0.0 | 5.6 | 12.9 | 11.4 | 10.0 | 7.3 |
| Edinburgh | 56 | 9.6 | 12.6 | 14.0 | 9.5 | 3.4 | 0.0 | 1.7 | 6.0 | 12.6 | 13.5 | 11.8 | 5.2 |
| Berlin | 52-1/2 | 7.6 | 10.8 | 16.4 | 15.5 | 11.4 | 0.6 | 2.9 | 2.9 | 6.5 | 13.2 | 8.5 | 4.1 |
| London | 51-1/2 | 8.6 | 10.5 | 10.2 | 10.7 | 4.0 | 1.1 | 1.9 | 5.6 | 14.5 | 16.9 | 9.6 | 6.4 |
| Quebec | 47 | 3.6 | 14.8 | 8.3 | 14.2 | 4.1 | 5.9 | 7.7 | 5.9 | 11.2 | 12.4 | 7.7 | 4.1 |
| Toronto | 43-1/2 | 5.4 | 9.5 | 8.7 | 11.8 | 9.0 | 6.2 | 8.0 | 6.4 | 8.5 | 11.1 | 8.7 | 6.7 |
| Cambridge, Mass.| 42-1/2 | 5.1 | 8.2 | 11.8 | 10.2 | 6.4 | 5.1 | 10.3 | 8.5 | 13.3 | 9.2 | 6.8 | 5.1 |
| New Haven, Conn.| 41-1/2 | 7.7 | 7.3 | 8.9 | 8.2 | 7.6 | 5.7 | 8.9 | 8.1 | 11.9 | 7.6 | 10.6 | 7.5 |
| Scandinavia | N. of 68-1/2 | 16.4 | 13.8 | 14.8 | 1.6 | 0.0 | 0.0 | 0.0 | 0.4 | 7.8 | 15.1 | 14.4 | 15.7 |
| " | 68-1/2 to 65| 15.3 | 14.6 | 13.7 | 2.9 | 0.0 | 0.0 | 0.0 | 1.1 | 9.7 | 14.6 | 14.0 | 14.1 |
| " | 65 to 61-1/2 | 13.2 | 12.3 | 14.5 | 5.4 | 0.2 | 0.0 | 0.0 | 2.8 | 13.1 | 14.2 | 12.8 | 11.5 |
| " | 61-1/2 to 58| 9.5 | 11.2 | 13.5 | 10.9 | 1.3 | 0.1 | 0.4 | 5.7 | 13.6 | 13.8 | 10.4 | 9.6 |
| " | S. of 58 | 8.2 | 11.9 | 12.6 | 13.3 | 1.5 | 0.1 | 0.6 | 4.9 | 14.9 | 13.5 | 10.3 | 8.2 |
| New York State | 45 to 40-1/2 | 6.3 | 7.4 | 9.1 | 11.0 | 7.4 | 6.6 | 8.8 | 10.4 | 11.7 | 9.7 | 6.2 | 5.4 |
+-----------------+--------------+------+------+------+------+------+------+------+------+------+------+------+------+
The total number of auroras in the year is taken as 100, and t denotes
the time, in months, that has elapsed since the middle of January.
Putting t=0, 1, &c., in succession, we get the percentages of the
total number of auroras which occur in January, February, and so on.
The first periodic term has a period of twelve, the second of six
months, and similarly for the others. The first periodic term is
largest when t X 30 deg. + 100 deg. 52' = 450 deg. This makes t = 11.6
months after the middle of January, otherwise the 3rd of January,
approximately. The 6-month term has the earliest of its two equal
maxima about the 26th of March. These two are much the most important
of the periodic terms. The angles 100 deg. 52', 309 deg. 5', &c., are
known as the phase angles of the respective periodic terms, while
3.03, 2.53, &c., are the corresponding amplitudes. Table II. gives a
selection of Lovering's results. The stations are arranged according
to latitude.