ing to observe the agreement, in general character, between each of these curves and the mean curve for the summer and winter period to which it belongs. This agreement is, without exception, in the six months from May to October inclusive; and in the other six months the only deviation, (and that not a remarkable one,) is in the month of April, the curve of which corresponds, as before observed, with that for the mean of the twelve months. November is the month whose mean temperature approaches nearest to that of April, but the flattened form of the curve, indicating a restricted range of temperature, marks it as belonging to the winter set, although the mean minimum of November exceeds the mean maximum of March, the nearest winter month.

The gradual diminution of temperature, uniformly observable on the approach to the minimum, shows that there is not, as some have imagined, any sudden increase of cold about the time of dawn; the opinion has doubtless originated in the feeling caused by the action of the greatest cold of the night, (which is found to be at the time referred to,) on the body previously chilled by exposure.

On the Hours of Daily Mean Temperature.

This may be regarded as the most interesting and useful part of the discussion of such observations as we are now considering, since the determination of the hours, before and after noon, at which the thermometer indicates the mean temperature of the day, will enable us to ascertain the mean temperature at any place, by two observations during the day, or even by

one.

The hours of mean temperature are given in Table II., for each of the several periods of time embraced in the table, and need not be here repeated; it will be seen that with one exception, that of the morning mean for November, the results agree remarkably well with each other. The hours of mean temperature for the twelve months are 8h. 36m. A. M., and 7h. 55m. P. M., the interval between them being 11 hours. The interval of 114 hours is found between the mean hours for the six summer months, and 10 hours for six winter months.

It is worthy of remark, that the interval between the morning and evening means, as shown by these observations, agrees with that found by the results of similar observations, made during two years, by Sir David Brewster, at Leith, in Scotland, and by Mr. Snow Harris, at Plymouth, England, although the hours of mean temperature are very different in the three cases, viz:

As a guide for observations on the temperature during the year, in the vicinity of Philadelphia, the hours here stated might no doubt be safely used; but it would probably be better, (in the absence of more extended observations for the mean times,) to use the hours stated in table II., as obtained from the mean of observations during shorter periods, say for the six

30.00 13.54 13 00 34.85 34.50 41.23 40.25 55.56 55.00 35 75 4.04 5.25 23.22 22 75 47.54 48.25 65.41 66.75 137 50 5.92 7.00 27.40 26.25 48.79 48.25 71.27 72.75 136.75 8.23 7.75 34.00 35.25 44.00 44.25 65.12 63.75 37.75 4.04 5.00 31.46 32.75 43.67 44.00 58.09 59.00 32.50 7.40 7.25 29.06 30.25 34.06 33.50 58.74 58.50 31.50 24.79 23.00 33.34 33.38 38.17 38.50 59.23 60.00 35.75 33.67 33.00 32.01 29.75 46.20 45.00 58.65 57.75 34.25 30.19 30.00 30.67 29.50 61.54 62.00 55.40 55.75 31.50 32.6531.75 38.22 38.25 50.60 46.25 57.84 57.13

755

852

9 45

11 55

12 60

13 55

15 50

10 50 33.75 27.73 27.25 35.00 33.00 36.73 36.75 61.91 61.00]
35.50 29.04 29.75 19.79 20.00 35.90 37.00 67.75 68.25
40.00 34.71 36.00 27.23 25.50 41.94 42 50 60.55 57.75
33.25 24.13 21.00 42.17 42.25 49.88 50 75 51.42 52.00
14 48
26.00 22.31 20.25 30.52 29.50 44.69 44.00 55.71 55.75
15.25 23.52 24.00 30.53 29.25 43.61 44.13 66.57 65.00
16 50
16.25 18.85 16.50 37.1637.25 44.77 45.50 71.54 71.75
17 55
29.50 9.58 8.50 38.67 36.50 55.90 55.00 72.86 72.75
23.00 13.72 8.75 29.52 28.50 50.83 50.25 67.13 67.00
20.00 30.26 29.13 32.63 32.50 51.77 52.50 65.02 64.00
20 72
20.00 36.1237.00 33 82 34.00 54.56 55.75 70.94 73.50
36 25 37.31 38.50 34.11 33.63 44.41 43.38 75.42 74.50
18.50 36.81 36.25 30.48 31.75, 48.51 46.75 79.90 76.00
516 75 38.91 39.75 39.60 39.25 50.77 51.060 61.81 61.00
$26.00 31.60 32.25 33 65 32.50 47.45 47.00 59.46 59.25

18 61

19 69

21.60

22 56

23 52

24 52

27 65

252 24.75 21.76 22.75 30.10 50.75 61.77 60.38 56.22 56.00
26 71,
15. 25 22.48 23.00 40.42 40.75 62.34 61.25 50.05 49,75
11. 06 20.21 20.25 43.65,43.25 58.21 57.50 57.41 57.75
15.75 25.63 25.13 40.52 40.25 63.17 64.00 59.02 57.50
36.01 35.50 56.40 53.25 50.16 49.75
41.25 41.25

28

70

29 71 27.75

X

irs

ng

the

ith

te

ons

on,

ob.

alts

193830

Pair

era

..

30 67 31 672

50.78 50.25

ked

31.75

Mean 59

3:27.72 23.07 22.72 33.58 33 54 48.65 48.30 61.83 61.51

20si

M.. cond

.68. berarrec

ap

ir of

summer months 84h. A. M. and 74h. P. M.; for the six winter months 9h. A. M. and 74h. P. M. To obtain further data for ascertaining the hours of daily mean temperature, it is not necessary to embrace the whole day in our observations, for the results in Table I. furnish evidence of a striking fact, which enables us to determine the mean temperature of the day, by observations of the maximum and minimum, which are little liable to error, and which may even be made by means of self-registering thermometers, if the indications of those instruments can be relied on. The fact alluded to is that the mean of the maximum and minimum of each day is very nearly the mean temperature of the whole day.

By examining Table II., where the general means of hourly observations and the means of diurnal extremes are exhibited together, we see that this holds not only for the whole year, but for each of the periods of six and three months, into which the year is distributed, and also for each separate month; and still further, by Table I., we see that this agreement extends, with little variation, to the results of each day's observations.

Having then a method of ascertaining the mean temperature of the day, by two observations, it will be sufficient, in order to determine the hours of mean temperature, to make two or three observations in the morning and evening, at short intervals, about the time when we know that the mean temperature must occur, and the two observations which agree with each other, and with the mean of the maximum and minimum, will indicate the time of mean temperature.

Since my hourly register was discontinued, I have made observations according to this method, taking as my guide for the hours of observation, the results previously obtained. Thus for the month of June, 1836, observations were made at 4 and 8, A. M., and at 2 and 8, P. M., the results of which are perfectly satisfactory: they are as follows, viz:

Comparison of the Mean Temperature of each Hour, and each similar pair

of Hours, with the General Mean of the Year.

The bottom line in Table II. exhibits the deviation of the mean temperature of each hour from the mean of the year; the differences are marked negatively when the mean of the year exceeds that of the hour, and positively in the contrary case; the first occurs between 8 P. M. and 8 A. M., both inclusive,the greatest difference during that time being 6°.68; the second between 9 A. M. and 7 P. M., inclusive, the greatest difference being 7o,68. This line of differences might be used for ascertaining the mean temperature by one observation, applying to the observed temperature the correction from the table, by changing its sign. But for this purpose a better approximation may be made from observations made at any similar pair of hours, by applying the proper correction from the following table.

VOL. XIX.-No. 1.-JANUARY, 1837.

2

Table IV. shewing the relation of the Mean Temperature of each pair of Hours, to that of the whole year.

From this table it appears that the mean temperature of the six pairs of hours from 11h. to 4h. inclusive, exceeds the mean temperature of the year, the greatest difference being 10.03; and the mean temperature of the six pairs, from 5h. to 10h. inclusive, is less than the mean of the year, the greatest difference being 1°.44. The mean temperatures of 4h. and 4b., and 10h. and 10h. approach nearest to the general mean of the year; therefore, according to these results, those would be the proper pairs of hours for making observations for the mean temperature.

Discussion of the curves of Mean Hourly Variation of Temperature.

The curve projected for the mean hourly temperature, during the twelve months, is that which will be first discussed. It naturally divides itself into four branches, viz:

1. The morning branch, ascending from the minimum to the line of mean temperature.

2. The noon branch ascending from the line of mean temperature to the maximum.

3. The afternoon branch descending from the maximum to the line of

means.

4. The night branch, descending from the line of means to the mini

mum.

Sir David Brewster and Mr. Harris having discussed the curves given by their observations, on the supposition of their being parabolas, each branch having a distinct type, I have applied the same method to the curve under consideration.

Regarding then each of the four branches as an arc of a separate parabola, the vertex of which is at the point of maximum or minimum respectively, we have in each curve the abscissa and ordinate of the point in which it intersects the line of mean temperature, and therefore we can readily calculate the intermediate points, or the temperature of each hour, on the supposition of the curves being parabolas.

The following have been assumed as the data of the calculation, viz:

These terms, differing slightly from those given in Table II., are taken for greater convenience, as approximating sufficiently to the results of observations. Table V. gives the results of the calculated and observed temperature for each hour, together with the differences.