tations in intervals of 10″ (half of 20″), and even of 7″ (third of 21″). Some examples will best illustrate what further remarks we may have to make.
Observation on the 17th August, 1836, for 10ʰ 20′. By Prof. Ulrich.
| 10ʰ 19′ 30″ | 869·9 | ||
| 40 | 871·3 | 870·80 | |
| 50 | 871·7 | 871·05 | |
| 20 0 | 870·8 | 871·35 | 871·35 |
| 10 | 871·0 | 871·60 | |
| 20 | 872·4 | 871·95 | |
| 30 | 872·9 |
The second column contains the several notations; the third, the partial results; 870·80 is the mean between the first and third notation, and therefore corresponds to 10ʰ 19′ 40″, and so forth. It is pleasing to perceive in this example, chosen from a time of rapid change in the declination, how a practised observer can recognize with certainty the changes occurring in 10 seconds.
Observation on the 25th March, 1837, at 0ʰ 5′. Dr. Goldschmidt.
| 0 4′ 32″ | 847·3 | |||||||
| 39 | 847·2 |
| ||||||
| 46 | 847·8 | |||||||
| 53 | 848·7 | |||||||
| 5 0 | 848·9 | 847·91 | ||||||
| 7 | 848·1 | |||||||
| 14 | 847·0 | |||||||
| 21 | 846·9 | |||||||
| 28 | 847·3 |
The first partial result in this case is obtained from the combination of the first and fourth notations; the second from that of the second and fifth, &c.
In this example the submultiple of the approximate time of vibration is an integer number; where this is not the case, the time must be divided into unequal parts, which has, however, no disadvantage, provided such an arrangement is made, that the notations to be combined shall always have for the interval to which they correspond the same approximate value of the time of vibration, and that the time, and also its portions, shall be registered. Thus, for instance, the observations in the astronomical observatory, with a bar of 25 pounds in weight, having a time of vibration of 43ˢ·14, must be arranged according
