OF OBSERVATIONS FOR TEMPERATURE. 



1!) 



Table III.— Mean Monthly Temperature of the An: in Shade observed at Port Kennedy, 

 in Latitude 72° 01' N., and Longitude 94 c 14' W., in the years 1858 and 1859. 



1858-'9 

 1858 



1859 



August 



September 



October 



November 



Deoember 



January 



+36°.95 

 4-25.43 

 4- 7-59 

 — 11.17 

 —32.97 

 — 33.. r .7 



1859 



February 



March 



April 



May 



June 



July 



— 36°.0(S 



—17.76 



— 2.62 



4-15.04 



4-35.11 



4-40.12 



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 investi- 

 gations. 



The above numbers will be found represented by the formula — 



T= +2°.17 + 3S°.70 sin (fl + 248° 4') + 0°.58 sin {1o + 279° 57') + 1°.14 sin (So + 275° 53') 

 T representing the monthly values of the annual variation, and the angle 6 count- 

 ing from January 1st at the rate of 30° a month. According to this expression, 

 the mean annual temperature at Port Kennedy is 4- 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 he 

 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 



-0 d .3 

 -0.2 



+ 0.6 



+ 0.2 



+ 1.5 

 + 0.8 



+ 1.5 



+ 0.8 



+ 1.4 

 + 0.8 



+ 1.3 



+ 0.8 



+ 1.2 

 + 0.8 



+ 0.7 



+ 0.2 



+ 0.fi 

 + 0.2 



+ 0.5 

 + 0.2 



+ 0.4 



+ 0.2 



+ 0".3 



+ 0.2 



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

 bers suppose the angle 6 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. XIY, 8th edition of the 

 Encyclopaedia Britannica. 



8 These numbers were given in my discussion of the meteorological observations of the second Grinndl 

 Expedition, under command of Dr. E. K. Kane. See Vol. XI of the Smithsonian Contributions to 

 Knowledge, 1 859. 



