172 



DISCUSSION OF THE ANNUAL FLUCTUATION 





Extent of 



Calendar 

















Station. 



Series 

 in Years. 



or 

 Mean Mo. 



A 



^1 



B^ 



■^3 



Ci 



Q 



C3 



Fort Snelling, Min. 



42 



Cal. f 

 Mean 1 



44°-S2 

 44-65 



3o°-03 

 30.02, 



i°.6o 

 1. 71 



o°.65 

 0.69 



238=58' 



239 46 



208°. 8 

 209.4 



i84°.4l, 

 182.7 j 



New Haven, Conn. 



86 



Cal. j 



49.00 



22.66 



0.27 



0-39 



233 37 



298 







139-4 1 

 140.2 j 







Mean 1 



49.10 



22.66 



0.26 



0.41 



234 25 



283 



2 



Marietta, Ohio 



49 



Cal. j 

 Mean | 



52.24 

 52-33 



21.16 

 21.16 



0.79 

 0.80 



0.41 

 0.42 



238 38 



239 25 



284 

 279 



I 



7 



72.6 -1 

 77-6 1 



San Diego, Cal. 



20 



Cal. ( 

 Mean | 



62. 11 

 62. 14 



8.78 

 8.78 



1-59 

 1.58 



0.17 

 0. 19 



224 07 

 224 50 



285 

 285 



7 

 8 



156-7 1 

 161. 7 1 



Key West, Flo. 



26 



Cal. f 

 Mean ( 



77-05 



7-23 



0.29 



0. 20 



228 49 



235 



7 



243.6 \ 







77.08 



7-23 



0.31 



0. 19 



229 34 



233-0 



243.2 j 



' Uncorrected for daily fluctuation. 



The terms in B^ and ^5 are of no practical consequence in the present inquiry. 

 The difference in the angle Cj for calendar and mean months is for Fort Snelling, 

 Min., + 48' ; for New Haven, Conn., + 48' ; for Marietta, Ohio, + 47' ; also (Sill. 

 Journ., May, 1866, p. 377-378) for St. Paul, Min.; New York; and Charleston, 

 S. C., -4- 46', and for San Diego, Cal. + 43' ; for Key West, Flo., + 45'. We can 

 therefore correct our expressions derived from the calendar months, for their 

 inequality in length, by substituting for stations having a range between the hottest 

 and coldest months exceeding 40°, 



A + 0.0043 B, for A and G, + 47' for G„ 

 and for stations having a less range, 



A + 0.0036 B, for A and C, + 45' for 0,. 



The effect on O^ and Cg appears irregular, and may therefore be omitted as of 

 little importance ; the values of B^ and B^ are not sensibly affected. 



The preceding five expressions for the annual fluctuation refer to the middle of 

 December for their epoch ; hence, in order to count the angle 6 from the fii'st day 

 0/ January, we must increase C^ by 15°, C2 by twice 15°, and C-^ by thrice 15°. 



The second correction is nearly zero in April and May, and again in Oct. and 

 Nov., and reaches a maximum (a few tenths of a degree) in July or August, and 

 again in January or February, the monthly amounts changing gradually, with 

 opposite sign for the half year when the temperature is above, and the half year 

 when it is below the mean. Since the mean monthly temperature is numerically 

 less than the temperature corresponding to the middle of the month, the parameters 

 of the fluctuations must be increased, and the correction for curvature is effected^ 

 by multiplying the parameters or values, B^ B^ B^ . . . , as found without regard 

 to this, by the factors, 



7t 27t 07t 



• • respectively. To allow, there 



7t . o7t . 07f 



sm^TFt sm i7=i sm 



^12 ""^ 12 °"^ 12 



fore, for curvature, we increase the co-efficients B^ Bn B^ 



as ordinarily obtained 



' A. Bravais in "Voyages en Scandinavia, etc." 

 ologie, Vol 2, pp. 291 and 325. Paris, 18 . 



Pendant les annees 1838, 1839, 1840. Meteor- 



