2d ' 



' March. 



2d ' 



' April. 



2d ' 



' May. 



ISt ' 



' June. 



2d ' 



' July. 



ISt ' 



' August. 



ISt ' 



' September. 



ISt ' 



' October. 



ISt ' 



' November. 



ISt ' 



' December. 



no DISCUSSION OF THE ANNUAL FLUCTUATION 



Normal months: January ends with 0.44 of the 31st of Calendar month. 



February " " 0.62 " 



March " " 0.06 " 



April " " 0.50 " 



May " " 0.94 " 



June " " 0.37 " 



July " " 0.81 " 



August " " 0.25 " 



September " " 0.69 " 



October " " 0.13 " 



November " " 0.56 " 



December " " with midnight of the 31st. 



To make use of these expressions we require to know the mean temperature of 

 certain days near the beginning of each month ; this may either be taken directly 

 from the observations or may be computed from the monthly means. In Silliman's 

 Journal of Science and Arts, May numbers of 1866 and of 1867, Mr. E. L. De 

 Forest has presented the case in a diiferent and very convenient form^ by using the 

 monthly means already computed and finding corrections thereto, employing the 

 means of the months preceding and following. Practically the results by the two 

 methods are identical. The general effect of the correction for inequality is to 

 increase the annual means by a small fraction of a degree. 



To exhibit the magnitude of the monthly corrections, the results for the New 

 Haven series, extending over nearly 86 years, may serve as a sample. The second 

 column contains the uncorrected or calendar means, the third and fourth the cor- 

 rection to reduce to months of mean length, according to first and second methods, 

 the last column gives the corrected means. 



' On page 316 of Sill. Journ., No. 129 (May, 1867), we find the expressions for the normal months, 

 M, by means of the calendar months, m, as follows : — 



j1/j = m, 4- -0037 ?«, +.0030?«i„ — .0067 ?«2 

 M.^ = ?«2 — .0127 m, — .0031 «/j + .0158 OT3 

 M, ^ ?«3 + .002S ?«3 — .0249 m., 4- .0221 m^ 

 M^ = ?»4 — .0042 m^ — .0200 ;«3 4- .0242 OT5 

 Afr^ = OTj 4- .0016 m^ — .0218 ;«4 + .0202 OTg 

 il/g = W|; — .0039 Pig — .0180 ?«5 + -0219 ?«, 

 M, = w, 4- .0026 /«, — .0200 W|, 4- .0174 ?»8 



Mg ^ 7«s 4- .0025 ?«g .0103 ?«, + .OO7S W/r, 



Mg = nig — .0027 ?«g — .0067 ;«g + .0094 ?«i|, 

 ^/jo = ?»io 4- .0030 ?«,(,— .0085 OTg + .0055 ?«ii 

 jlfjj = ?Kj, — .oo26 7«ji — . 0046 ;«,„+ .0072 ?ni2 



M-^^ = OTjj 4- .0032 ?«j2 .0064 7«i, 4- .0032 OTj 



Mr. De Forest also remarks that the term r = ^ + 5j sin (9 -f Cj) obtained on the supposition of 

 calendar months will be very nearly corrected, for temperate climates, for the inequality of months 

 by taking T=A^ .0041 5, +5, sin (9 + (7^ + 46'). The effect on the periodical terms involving 

 multiples of 9 is small and variable. They are preferred in the form ± J„sin?i (9-— e„), as deter- 

 mined by sin (» 9 + E^) = sin w (9 — ^ (360° — E^ ) or — sin n (9 — ""^ (180 — K) ) according to 



n n 



-E'„>or<thaQ 180°, the arce„ indicates the position of the first intersection, and the ascendmg or 

 descending wave is shown by the sign of the term. In the usual form the signs are all positive. 



