0°.1 and 0°.2 alternately from the successive daily means. The monthly mean temperature at the hours 4, 8, noon, 4, 8, midnight, was first made out (if diminished by the above constant 0°.15, their mean would exactly give 19°.55). To obtain the intermediate values for 2, 6, 10, A. M. and P. M., the observations between the 21st and 30th were used as follows:

which, applied to 17°.38, gives 16°.93; in the same way, we obtain from the following hour, 4 A. M., the value 17°.38. The mean, or 17°.15, has consequently been adopted as the mean monthly temperature at 2 A. M. The remaining values were derived in a similar manner.

February, 1858. On the 11th and some following days, there are occasionally pencil figures inserted between the lines. These are neither used nor explained. April, 1858. The daily mean from six observations differs from the daily mean from twice this number of observations by 0°.13, as found from the values between the 1st and 17th; a correction of -0°.13 has, therefore, been applied to the deduced means on and after the 18th, in order to refer the same to the result produced by twelve observations. The hourly means at the bottom of the page were obtained in the manner explained in the note to the hourly means of the month of September, 1857, viz: through a comparison of the hourly means of the full series, and applying the correction (the mean found from the preceding and following column) to the monthly mean at the hours 4, 8, 12, etc.

May, 1858. The temperature at 8 A. M. on the 2d was assumed to be 30°.5. March, 1859. The correction to refer the mean from six observations on each of the last four days of the month to the daily mean as resulting from twelve observations, was found by comparison of the respective means on the twelve days preceding; it was found -0°.16. The mean hourly temperature for the hours 2, 6, 8, 10, was obtained by the process applied on two former occasions.

April, 1859. The bar in the column for 41 and in the column for midnight, indicates that the observations were taken one hour later and one hour earlier, or at 51 and 11 respectively. This practice was discontinued on the 5th of July following.

July, 1859. For the temperatures of the 5th, at the hours 2, 4, 6, 10, A. M., I have adopted the interpolated values 36°, 36°.5, 39°, 43°, respectively. The correction to refer the mean of six observations (hours 5, 8, noon, 4, 8, 11) to the mean of twelve observations (hours 4, 8, 12, A. M. and P. M.), was derived from the tables constructed for Van Rensselaer and Boothia Felix; the latter value having the weight 2, it was found = —0°.21, which quantity was applied in the first column of means, July 1st to July 4th inclusive. To obtain the correct hourly means for the month, the numbers in the column for 51 (first four days) were first referred to the reading at 4h by subtracting 0.5. The same correction was applied to refer the readings from 11 P. M. to midnight. The monthly means for the hours 4, 8, 12, A. M. and P. M., being known, the means for the interme

diate hours were found by comparison of the respective readings on the last twentyseven days of the month, as has been explained in similar cases.

August, 1859. The value 34°.0 for the mean temperature on the 17th was interpolated, which required a corresponding diminution of 0°.08 for each of the hourly means, in order to produce the same monthly temperature of +36°.58.

September, 1859. The means of this month are of little value, the month being incomplete, and the change in latitude (and longitude) very considerable.

The two following tables contain a recapitulation of the results of the preceding abstracts. Table I exhibits the mean monthly temperature at the locality indicated by its latitude and longitude, also the relative maxima and minima, and relative monthly extreme range, as observed in either the bi-hourly or the four-hourly series. The absolute maxima and minima were not recorded. Table II contains the mean monthly temperatures for each observing hour, and is intended to serve as the basis for the discussion of the diurnal variation, while the first table furnishes the means for the discussion of the annual variation of the temperature. The column headed "mean," in Table II, differs from the corresponding column in Table I, for this reason: that, in Table II, no correction has been applied to refer the mean of six or twelve observations in a day (as the case may be) to the reading of twenty-four observations.

TABLE I.-RECAPITULATION OF RESULTS OF MONTHLY MEAN TEMPERATURES OF THE AIR IN SHADE OBSERVED ON BOARD THE YACHT FOX. (Expressed in degrees of Fahrenheit's scale.)

Year.

TABLE II. DIURNAL VARIATION OF THE TEMPERATURE OF THE AIR IN SHADE.
Recapitulation of the preceding mean hourly values for each month, and of their monthly mean temperature.

-32.28

37.90

+39.18

+35.40

+-26.45

9.03

O

O

O

O

O

17.15

75.2 67.9

-17.15-17.23 +16.75
-17.23 16.75 +18.78

-20.42 22.07 +23.1623.10
22.07+23.16

4.37 4.315.29 + 6.29 6.867.39 7.32 6.55

O

+44

20.1619.63 -19.63 +18.63-17.38 5.68 5.29 4.81 Nov. 74.8 69.1 4.93 4.58 4.98 4.98 4.63 4.42 4.62 4.38 4.82 5.00 5.17 66 Dec. 74.3 67.4-22.00-22.23 -21.47-21.10-21.00 -21.00-21.21-21.48-21.45 -21.44 -21.44-21.14 -21.14-21.86-22.24-21.55 1858 Jan. 73.2 63.7-25.01-25.07-24.92-24.72-24.39-24.16-24.52-25.08-24.97-25.21-25.08-25.00-24.84 Feb. 71.5 60.9-16.55-16.18 -15.98 -15.55-15.14-14.11-13.95 -14.66-15.43-15.04 -15.43-15.70 -15.31 March 69.4 59.1 5.43 6.03 5.60 3.44 1.34 + 0.47 + 0.74 0.13 2.49 4.79 5.57 3.31 3.354.13+7.50 +10.14 +12.62 +13.37 +12.45 +10.38 7.776.145.63+ 8.04

72.0 94.2—11.53—11.20-10.60-10.33 -10.03 -10.32 -11.07 -11.57 -11.87-12.17-12.23-12.57-11.29
94.2-32.52-32.41-32.60-33.32 -32.78
-33.32 -32.78 -32.81 -32.74-33.18 -33.27-33.35-33.40-33.29-32.97
94.2-33.78 -34.26-33.97-33.97-33.52-33.31-33.55-33.26-32.85-33.10-33.11-33.78-33.54

-36.64-36.32-36.32-35.97-35.86-35.25-35.25 -35.82-36.28 -36.07-35.96 -35.96-36.59-36.03 94.2-21.06-21.00-21.57-19.45-14.79 -11.89-12.03 -13.77-18.43-19.22 -19.52-20.66-17.78

2.27

+16.50
-38.05

+1.25
-18.81
-39.82

+0.60
+18.21

-36.92

- 4.07
14.26

+33.93

-5.82 2.45 +11.39 +15.42 +31.0835.52

July 72.0 94.236.51 +37.24+39.24 +41.29 +42.90 +43.48 +42.34 +41.98 +41.07 +40.02 +38.56+36.98+40.13

37.97 +47.60

-37.65

-37.10

+47.30 :: -45.60

+35.52 +36.58 +45.00+45.80

Discussion of the Annual Variation and of the Temperature at Different Seasons

of the Year.

The monthly means brought out in Table I refer to different localities and years,
and require to be combined with reference to these changes. The "Fox" remained
stationary at the winter quarters for nearly a whole year-between August, 1858,
and August, 1859-and we will, therefore, first examine the annual variation, the
mean temperature of the seasons and of the whole year, for Port Kennedy, in north
latitude 72° 01', west longitude 94° 14', near the eastern entrance to Bellot Straits,
which separates North Somerset froom Boothia Felix. Our monthly means for
August, 1858 and 1859, require to be corrected for difference of position. For this
purpose, I have projected on a suitable chart the two isothermal lines for the month
of August, constructed by me on the basis of Dove's investigation, and published
in the 2d volume, Appendix No. XIII, of Dr. Kane's Narrative of his Arctic Ex-
pedition (north of Smith Straits), in the years 1853-54-'55. By means of these
curves, we find that the positions of August, 1858 (viz., latitude 73°.1, longitude
88°.5), and of August, 1859 (viz., latitude 71°.9, longitude 79°.8), can be assumed
as lying nearly on the same isotherm, with a temperature of 1o.4 Fahr. relatively
colder than the isotherm passing through Port Kennedy in that month; the nor-
mal distance between the isotherms differing 4°.5 in temperature being nearly 6°
of arc.
In the following table, the temperature for the month of August is derived
from the mean of the respective observations of 1858 and 1859 increased by 1°.4,
in order to refer the value to the locality of Port Kennedy.

TABLE III.-MEAN MONTHLY TEMPERATURE OF THE AIR IN SHADE OBSERVED AT PORT KENNEDY, IN LATITUDE 72° 01' N., AND LONGITUDE 94° 14' W., IN THE YEARS 1858 AND 1859.

To express the above and other periodic results in an analytical form, Bessel's formula of interpolation for periodic functions, and depending on the method of least squares,1 will be made use of throughout the discussion; a practice which has now become almost universal in meteorological and many other physical investigations.

The above numbers will be found represented by the formula

T=+2°.17+ 38°.70 sin (0 + 248° 4′)+0°.58 sin (20 + 279° 57′)+1°.14 sin (39 + 275° 53′) Trepresenting the monthly values of the annual variation, and the angle 0 counting from January 1st at the rate of 30° a month. According to this expression, the mean annual temperature at Port Kennedy is +2°.17 Fahr.

The strict application of Bessel's formula requires the intervals between the successive observations or means to be of equal length, and a small correction, therefore, becomes necessary on account of the unequal length of the months. This correction, generally too small to be noticed in low latitudes, is of sufficient magnitude in very high latitudes not to be neglectable. The following numbers show the quantity, in days and fractions of a day, by which the middle of each actual month differs from the mean of each month of average duration (30.4 days for a common, and 30.5 days for a leap, year), and for which interval a correction, —depending, also, on the magnitude of the variation of the temperature—is to be applied. A positive sign indicates that the middle of the actual month occurs earlier than the middle of the normal month; a negative sign indicates the reverse. Commencing with January, and proceeding in regular order, these intervals are as follows:-2

-00.3 +0.6 +1.5 +1.5 +1.4 +1.3 +1.2 +0.7 +0.6 +0.5 +0.4 +0.3 -0.2 +0.2 +0.8 +0.8 +0.8 +0.8 +0.8 +0.2 +0.2 +0.2 +0.2 +0.2

The upper line is for a common year, the lower line for a leap year.

These num

bers suppose the angle 0 to be zero for the commencement of the civil year, and that the daily mean temperature, so far as the annual fluctuation is concerned, refers to the middle of the day. The corrections become greatest for the spring and autumn months, when the annual variation is most rapid. To obtain an ap

1

Explained at length by Sir J. Herschel in the article "Meteorology," Vol. XIV, 8th edition of the Encyclopædia Britannica.

2 These numbers were given in my discussion of the meteorological observations of the second Grinnell Expedition, under command of Dr. E. K. Kane. See Vol. XI of the Smithsonian Contributions to Knowledge, 1859.

proximate value for the diurnal change for the middle of each month, the above formula was used, the increase in the value of for one day being 59'.2. Multiplying the daily change into the above intervals, we obtain the following mean monthly temperatures corrected for unequal duration, to which numbers the correction for index error has been added, as given in the third column of the table.

PORT KENNEDY. MEAN TEMPERATURE OF THE AIR IN SHADE IN EACH NORMAL MONTH.

The maximum corrections for inequality in the length of the month were +0°.94, in April, and -0°.32, in October. The above monthly means, as corrected for index error, will be found represented by the expression (II)—

T:

T= +2°.02 + 39°.20 sin (0 + 249° 5′) + 0°.80 sin (20 + 256° 56′) + 1°.06 sin (30 + 274° 43′). The numerical coefficients differ but slightly from the corresponding values in the first expression. The observations are represented as follows (the hundredths have been omitted as having no real value) :

The differences between the observed and computed mean monthly temperatures are greatest in winter, which is due to the greater fluctuations of the temperature in that season. The same result was found from my reduction of the Van Rensselaer Harbor temperatures, as observed by Dr. Kane. The average probable error of representation of the mean temperature of any one month is accordingly ±2°.1, and of the result for the mean annual temperature +0°.6.

The following table contains the temperature of the several seasons at Port Kennedy; December, January, and February being reckoned as winter months (and so on for the other seasons), in accordance with meteorological usage. The results by Formula II refer to the corrected normal months; the results headed "by observation," are corrected for index error.