To use the table, let the mean of observations at 7 a. m., for the month of April be 42°.57; apply the correction for that month and hour in the table, 5.97, and you have this sum, 48.54, which is the mean of the 24 hour observations for that month.

For the two hours, 7 and 7, in April, you would have— 42.5750.23 2

+

5 971.69 48.54
=

the same mean.

,

2

For the three hours, 7, 2, and 9, in March, take out the three means30.1943.15 + 32.92 35.42, and corrections from the tables are

3

NOTE.-At the foot of the preceding table are given the corrections for observations, made at various different hours of the days, to show the nearer or more remote approximations to the mean of the 24 daily results.

The first of these is for the hours 3 and 9 a. m., and 3 and 9 p. m., the hours adopted by the Royal Society for obtaining the approximate mean temperature. These hours are convenient, except that of 3 a. m.

The next corrections are derived from one-fourth of the observations at 7 a. m., 2 p. m., and 2 (9) p. m., the last being twice the temperature of 9 p. m. A very near approximation is easily obtained in this way: Thus, the mean of the year, in Amherst observations

420.46

At -
Twice

Sum

2

p. m., is

55°.29

9 p. m., is

91°.40

1890.15

0°.05, onlyth of a degree.

Mean of the 24, hourly =

Difference

Using the same formula for the Leith observations, the approximate mean differs from that of the 24 observations onlyth degree.

The advantages of using the fourth part of the observation at 7 a. m., at 2 p. m., and twice that at 9 p. m., are obvious. The preceding cases are ample illustration.

This table of corrections will have a special value in our country from the locality in the heart of New England, where the observa

tions were made. No similar table has before been derived from them. While it presents the analogies of other similar tables, it will be better adapted to a large district of our country where meteorological observations are being made systematically. Some gratification will result to Professor Snell in such an application of his laborious and scientific efforts, in this particular, in 1839.

Such tables, it is evident, avail nothing where one or more times of observation, as sunrise or sunset, have a constant change, even though they may give an approximate mean. In different latitudes sunrise has different hours, as well as sunset, and the corrections must require a far greater series of observations and far more labor. Though the four hours used at the military posts for several years give an approximate mean, no correction for the sunrise observation is yet obtained. So great is the labor of making the observations, and of discussing them for practical purposes, that the fewest practicable hours, not exceeding three, should be adopted for the observations of meteorologists generally. Only a few observers, who are favorably situated also, can afford to make hourly observations for a year or for years; and when such have been made, as enable observers to make the corrections from prepared tables, the great object will be attained by using only three hours of observation. The last line of corrections in the preceding table is derived from six hours of observation, used for some time at the Toronto Observatory, viz: six and eight a. m., two and four and ten p. m., and twelve, or midnight. Though the corrections are very small for these six hours, they are too numerous for ordinary object or advantage. The same objection lies against the use of any four hours separated by six hours, as one and seven, both a. m. and p. m.; which, however, give very nearly the mean of 24 observations a day. Some of these hours will be very inconvenient and troublesome. Take even the hours adopted by the Royal Society, 3 and 9 a. m., and 3 and 9 p. m.; 3 a. m. is a very inconvenient hour, though the four give very nearly the mean of the daily 24 observations, as shown in the first line of particular hours.

In a series of observations of twelve years, like those in the "Army Meteorological Register" of 1856, these four hours, or any four hours, would require a million more observations than the three hours, besides increasing the labor of the reductions one-third more than is necessary to attain the same approximation to accuracy.

It is hoped that adequate evidence of the value of observations at the hours 7, 2 and 9, has been presented, and that a near approximation to the true mean is attainable. The results may be corrected, if need be, by the prepared tables.

ROCHESTER UNIVERSITY, March 31, 1858.

METEOROLOGICAL OBSERVATIONS AND RESULTS.

BY J. WIESSNER.

1st. The daily results of mean temperature of the air in shade, as observed on a farm in the District of Columbia.

2d. The monthly results.

3d. A trial adjustment, assuming that the mean motion of temperature may be represented by the motion of an elastic ball jumping up and down.

4th. A comparison of the Washington summer with the summers at Naples, Rome, Constantinople, Petersburg, and Savannah.

The probable error for the Washington series being very small, shows that the observations were made carefully and in large number; also, that the last summer was a very regular one.

The figures in the former table for adjusting the daily observations have the probable error 0°.3, so that ten years' further observations will make them correct to the last figure.

Next, a table containing p for each day of observation. By using the three tables and the simple formula tot + pw, all the observations now at the end of 1857, 4,500 in number, may be recomputed and compared with the individual records, which will give an average probable error of a single observation and reduction, ± 1°.4.

Mean temperature of the air in the shade of the District of Columbia.

A table, [w], of use for the reduction of observations for temperature of the air in the shade, made at different hours of the day by the formula

p. A factor depending on the disposition of the atmosphere for solar heat, the mean factor of the month being unit.

p w. The correction to the mean temperature of the day to get out the observed one.

t and p are to be found for each day by the method of least squares, or by a good approximation to it, by a calculation shown on the next page.

2