198 DISCUSSION OF THE ANNUAL FLUCTUATION 



To shorten the labor, I shall here only present the values of e and s for four 

 epochs of the annual fluctuation, and for three days m each case, viz. : for January 

 20, 21, 22, for April 21, 22, 23, for July 22, 23, 24, for October 21, 22, 23; epochs 

 which correspond respectively nearly to the times of maximum cold, of average 

 temperature, of maximum heat, and again of average temperature. 



Selecting a station near the Atlantic sea-board, one on the western slope of the 

 AUeghanies, and one near the Red River, we have the following results: — 



Probable error (e) of the mean temperature of any day about the periods of 

 maximum cold and heat — 



January. July- 



20th. 2 1st. 22d. Mean. 22d. 23CI. 24tli. Mean. 



Providence, R. I. . . 7°.o 6°.i 7°. 9 ±7°.o 3°. 4 3°. 9 3°. 2 ±3°.5 



Marietta, Ohio . . . 7.0 6.g 7.2 ±7.0 3.4 3.1 2.8 ±3-1 



Washington, Ark. . . 9.8 8.0 7.9 ±8.6 1.6 1.9 1.4 ±1.6 



and about the periods of average temperature — 



April. October. 



2lst. 22d. 23d. Mean. 21st. 22d. 23d. Mean. 



Providence, R. I. . . 4°. 4 4°. 2 3°. 9 ±4°. 2 5°. 9 6°. 3 4°.; ±5°. 6 



Marietta, Ohio ... 5.7 5.8 6.6 ±6.0 6.2 6.4 5.3 ±6.0 



Washington, Ark. . . 5.2 4.6 5.2 ±5.0 5.2 5.5 7.0 ±5.9 



We have also the probable error (g) of our daily normals as given in the preceding 

 tables for Providence (from a series of 28g years), for Marietta (from a series of 32 

 years), and for Washington, Ark. (from a series of 20 years). 



Providence. Marietta. Washington, Ark. 



January 20-22 dzi°.3 ±i°.2 ±i°.9 



April 21-23 ±0.8 ±1.0 ±1.1 



July 22-24 ±0.6 ±0.5 ±0.4 



October 21-23 dzi.o ±1.0 ±i-3 



In midwinter the mean temperature of any day will, therefore, fluctuate, in 

 diff"erent years, from 2 to 5 times as much as in midsummer, and the fluctuation 

 for days in that part of the year where its mean temperature is reached, are inter- 

 mediate between the maxima and minima values, 



In our annual curve of the temperature at Providence, the daily means for any 

 two adjacent days in midwinter, will, therefore, ordinarily diff"er by e -j/2 or by 

 -I- 1°.8, and in midsummer by ^ 0°.8, and at the intermediate times by J^ 1°.3, 

 and mai/ difl'er by three times these amounts, or even more, before positively 

 indicating any abnormal influence in the annual fluctuation. In a series of 

 observations comprehending 100 years, the probable error of the resulting average 

 temperature of any day, in the colder half of the year, would still be J^ 0°.6, and 

 in the warmer half J^ 0°.4, and on the average, the normals for two consecutive 

 days will difl'er -j- 0°.7, thus showing the difficulty of clearly making out small 

 deviations at certain suspected periods of the year. If a series of observations can 

 be had long enough to be divided into two or more parts, and the same apparent 



