Observed times of equal altitudes by watch:—
| Polaris | 3h | 33m | 54s·2 |
| α Columbæ | 3 | 42 | 40 ·8 |
| ε Canis majoris | 4 | 24 | 35 ·8 |
Polaris.
| Watch time | 3h 33m 54s·2 | |
| Watch fast | 2 22 ·0 | |
| L.S.T. | 3 31 32 ·2 | |
| Star’s R.A. | 1 25 9 ·1 | |
| t | 2 6 23 ·1 | = 31° 35′ 46″·5 W. of meridian. |
| φ = 24° 20′ 50″ | log sin | 1·6151769 | |||
| δ = 88° 48′ 33″·1 | log sin | 1·9999062 | |||
| 1·6150831 | log cos δ | 2·3177 | |||
| Nat. (1) | 0·4121764 | log sin t | 1·7193 | ||
| 2·0370 | |||||
| φ = 24° 20′ 50″ | log cos | 1·9595488 | log cos h | 1·9560 | |
| δ = 88° 48′ 33″·1 | log cos | 2·3176870 | log sin A | 2·0810 | |
| t = 31° 35′ 46″·5 | log cos | 1·9303179 | log cos φ | 1·9595 | |
| 2·0405 | |||||
| 2·2075537 | Nat. = | 0·011 | |||
| Nat. (2) | 0·0161270 | ||||
| Nat. (1) | 0·4121764 | log cos A | 1·9999 | ||
| 0·4283034 | Nat. = | 1·000 | |||
| log sin h | 1·6317515 | ||||
| h | = | 25° 21′ 35″·8 |
Whence the equation for Polaris is
35·8 + 1·000 dφ − 0·011 dT − h0 = 0 (1)
α Columbæ.
| Watch time | 3h 42m 40s·8 | |
| Watch fast | 2 22 ·0 | |
| L.S.T. | 3 40 18 ·8 | |
| Star’s R.A. | 5 36 15 ·6 | |
| t | 1 55 56 ·8 | = 28° 59′ 12″·0 E. of meridian. |
| φ = 24° 20′ 50″ | log sin | 1·6151769 | |||
| δ = 34° 7′ 45″·7 | log sin | 1·7490118 | |||
| 1·3641887 | |||||
| Nat. (1) | 0·2313070 | log cos δ | 1·9179 | ||
| log sin t | 1·6854 | ||||
| φ = 24° 20′ 50″ | log cos | 1·9595488 | 1·6033 | ||
| δ = 34° 7′ 45″·7 | log cos | 1·9179112 | log cos h | 1·9560 | |
| t = 28° 59′ 12″·0 | log cos | 1·9418753 | log sin A | 1·6473 | |
| 1·8193353 | log cos φ | 1·9595 | |||
| Nat. (2) | 0·6596830 | 1·6068 | |||
| Nat. (1) | 0·2313070 | Nat. = | 0·404 | ||
| 0·4283760 | |||||
| log sin h | 1·6318196 | log cos A | 1·9523 | ||
| Nat. = | 0·896 | ||||
| h | = | 25° 21′ 51″·1 |