AMPLITUDE OF THE SOLAR-DIURNAL VARIATION 



1 The hours refer to mean local time, reckoned from midnight to 24 hours. 



* The mean given is the simple mean of the four readings, and at 14h- of five readings, and is here inserted for 

 comparison with the corrected mean in the line below, which would have been obtained if there had been no omis- 

 sions in the observations. 



' To obtain the normals referring to January of the mean year, the readings for the defective years 1840 and 1843 

 have been interpolated in the following manner : 1. For the even hours. The normals for any two consecutive years 

 differ simply by the annual effect of the secular change, which may be regarded as uniform when the same hours 

 and months are compared, as in the present case. The values derived from the comparison of the several months 

 of any two years differ, however, by the accidental errors of the observations ; thus, taking the difference of the 

 normals for 1840 and 1841, we obtain for the several mouths the values 



June 

 July . 

 August 



20.5 

 18.5 



September 



October 



November 



12.7 



17.5 



December 



+20' J .0 



Mean 



16.86 



Which mean corresponds exactly to the difference of the constant terms in Part I, for 1840 and 1841. By adding, 

 therefore, 16.9 scale divisions to the normals for 1841, we obtain interpolated values for 1840. The values from 

 January to May, 1840, were thus supplied. The normals for 1843 were supplied in a different manner, by making 

 use of the readings at 2 P. M., which were taken for the purpose of keeping up the continuity of the series. Sub- 

 tracting 0.6 scale division from the hourly readings of 1842, we obtain those for 1843 this being the difference at 

 14 h - ; in like manner, adding 2.2 scale divisions to the readings of 1844, we obtain a second value for the normals 

 of 1843. The mean of these two independent determinations has been used in supplying the readings for 1843. 

 The normals for 1840 and 1843 being thus supplied, the figures in the last line of the preceding table are obtained 

 by simply taking the mean of the six readings at each even hour. 2. For the odd hours. The difference in the 

 mean readings for any given odd hour, in 1844 and 1845, from the two adjacent even hours, was applied to the 

 normals of these hours, and the mean taken as the normal of the intermediate odd hour. Thus, the mean 

 reading at noon of 1844 and 1845 is 538.55, at 13 h , 538.80, difference +0.25; which, added to the noon normal 

 557.72, gives 557.97 ; and, in like manner, by comparison with 14 h -, the correction to its normal is 0.90, and the 

 normal for 13 h - becomes 556.65. The mean of the two results, 557.31, is the resulting normal for this hour as given 

 in the table. 



The same principle of interpolation was applied throughout the tables. Due attention must be paid, in the 

 deductions, for the unequal weight of the normals for the even and odd hours ; these weights being generally as 

 5 : 2, or proportional to the number of separate readings. The application of a nearly constant quantity to refer 

 means from a defective number of years to the mean epoch of all the years, is not of much consequence in regard 

 to the diurnal and annual inequalities, which depend mainly on differences of readings, but it is essential that no 

 changes should have occurred in the zero of the scale during any interval under discussion. 



