Blunt, of New York,) reading by two verniers to 10". The level attached to the alidade of the circle has a run of one-thirteenth of an inch for 5"; and this being the smallest division of the scale, single seconds and fractions have to be estimated by the eye-a defect which will be further noticed in another connection.

The graduation of the circle is very accurate. The difference between the readings of the opposite verniers seldom amounts to to 15′′, and from its law of variation, it is manifestly due, in the main at least, to a very slight excentricity in centering the circle on the graduating engine, not to imperfection in the engine itself. The micrometer-screw has 75 threads to the inch, or one revolution of the head equal to 78"-74.

The optical performance of the instrument is very satisfactory. Transits of Polaris are readily taken at midday, and in favorable states of the atmosphere, at that hour, even by reflection in mercury. Transits of Aldebaran have been taken when the star was within 6° of the sun's center. The eye-piece commonly used is a diagonal one of four lenses, with prismatic reflector,-the magnifying power about 190.

The method of observing for latitude with the transit instrument is of course essentially the same as with the zenith telescope. A pair of stars having been selected, which culminate within a few minutes of each other, but on opposite sides of the zenith, and having their zenith distances nearly equal, the instrument is set for the star first to culminate, the level clamped, the bubble brought to zero by the slow-motion screw which turns the whole instrument, the star bisected with the micrometer wire, and the readings of the level and micrometer noted. The axis is then reversed, the bubble brought to zero as before, and the other star observed in the same manner.

The pairs for the observations now to be considered, were ta ken from the Catalogue of the British Association. The stars are to the sixth magnitude, and mostly within 25° of the zenith, the difference of zenith distances of the stars of a pair being usually less than 25'-averaging about 12'.

The individual results of 92 pairs are exhibited in the following table, which includes, with two exceptions, all the observations made, whether in favorable or unfavorable states of the atmosphere. In a few cases where the B. A. C. differs widely from other catalogues, the B. A. C. results are enclosed in brackets [] and are omitted in computing the mean. That the fault is in the B. A. C., is obvious from the accordance of the corresponding results from other catalogues with the general average. The contents of the table are as follows:

Col. 1 and 2. The numbers from the British Association Catalogue designating the stars of a pair.

3. The dates of the observations.

4. The mean results for latitude from each pair, using the positions of the B. A. C.; the seconds of the individual results, where the same pair was observed on different evenings, being placed at the left hand side of the column, and connected with their mean by a brace.

5. The differences, 4, between these mean results of pairs and the mean of the whole.

6. The results for latitude from the same observations, the position of one or both the stars of the pair being taken from some other catalogue than the B. A. C.; the arrangement as in column 4.

7. The names of these other catalogues; G. standing for Greenwich Twelve Year Catalogue; B. that of the British Association; R. the catalogue in Radcliffe Observations for 1856; and A. the English Nautical Almanac. A. G., for example, signifies that the position of the first star of the pair is from the Nautical Almanac, and that of the other from the Twelve Year Catalogue; etc. 8. The differences between the results in column 6 and the mean of the whole.

If we divide these 92 pairs into four sets of 23 each, as indicated in the table by the lines after Nos. 5336, 6623, and 7119, the mean of each set respectively, and of the whole, will be as follows; column 1, giving the number of the set; col. 2, the number of results of pairs in the set by B. A. C.; col. 3, the mean of these results; col. 4, the number of results of pairs by other catalogues; col. 5, the mean of these; col. 6, the number of results by both B. A. C. and other catalogues taken together; col. 7, the mean of the same; col. 8, the probable error, E, of this mean; col. 9, the probable error, E', of a single result for latitude.

We may regard 41° 18′ 42′′-41, then, as a close approximation to the latitude of the point in New Haven, where the observations were made, the probable error of this result, as given by the observations, being less than a tenth of a second. In taking the arithmetical mean of the results for the several pairs, we assume, of course, for each of these results equal weightsno discrimination having been attempted between errors of observation and of star-places, or between different catalogues. Such discrimination, however, in so large a number of independent pairs, would not have materially changed the result.

It will be seen, from the above table, that any one of the four sets would have given a latitude almost identical with the mean of the whole-in no case differing from it so much as a tenth of a second, or ten feet on the earth's surface. That this extremely close accordance, however, of results from sets composed of so few pairs, is in a measure accidental, may be inferred from the larger probable errors of these results as given in column E. Had there been three sets, instead of four, the differences would have been somewhat greater, though still not exceeding a few tenths of a second.

The probable error of a single result for latitude, as given in the last column, (about nine-tenths of a second on an average), includes, it will be understood, the accidental error of observation, (depending on observer, instrument, state of the atmosphere, etc.), together with the error of the stars' places, as given in the catalogues. The experience of the observers of the Coast