8 AMPLITUDE OF THE SOLAR-DIURNAL VARIATION 



To the observations between January 1 and January 10 a correction of +18''.7 

 was applied, as explained in the preceding note. 



In the month of December the declination changed so rapidly as to require the 

 use of half monthly means; the mean of the two results is inserted in the above table. 



For the purpose of comparing the annual means of the normals, or the mean 

 march of the regular solar-diurnal variation for each year, the preceding results 

 have been expressed analytically by means of Bessel's formula, and by the applica- 

 tion of the method of least squares. 



In these formulte the angle 6 is reckoned from midnight (Philadelphia), at the 

 rate of 15° for each following hour. It was found unnecessary to carry the expres- 

 sions beyond the third term, the fourth being generally smaller than the probable 

 error of an hourly normal. We obtain accordingly — 



A. d. d. d. 



For 1S40 D = 586 73 + 6.214 sin (9 + 36° 35') + 4.588 sin (2 6 + 217° 33') + 1.640 siu (3 9 + 68° 50') 



" 1841 JQ = 569.87 + 4.888 sm (9+30 05 ) + 4.380 s/h (2 9 + 212 38 ) + 1.581 S('n (3 9+ 50 14) 



" 1842 D = 563.33 + 4.944 sin (9+33 49 ) + 4.211 sin (2 9 + 217 12 ) + 1.463 sin (3 9 + 64 42 ) 



" 1843 Z> = 562.01 + 4.449 sin (9 + 36 00 ) + 3.918 s»i (2 9+ 218 05 ) + 1.811 sai (3 9 + 68 18) 



" 1844 Z> = 648.89 + 4.486 siK (9+34 35) + 3.872 sm (2 9+222 23) + 1.802 sm (3 9+68 53) 



" 1845 /) = 628.12+ 4.548 s»i (9+35 33 ) + 4.S72s;h (2 9 + 225 35 ) + 1.987 stn (3 9 + 61 20) 



• As indicated by the annual change in the readings, it was considered preferable to obtain the annual 

 mean by deducing the correction to the mean of the first six months, from the readings of the preceding 

 year and those of the year 1842. 



