Meteorological Observations. 127 



Now these numbers apply in particular to the reduction of monthly 

 avt rages. But they may be converted into a formula wh'ch Nvill 

 apply also to the reduction of daily averages, when the period is 

 long enough. A suitable formula for Kenihvorth is : 



K = -462-r-025 sin {nT,o° ~ 162°- -,) ■ — '007 sin (n6o'^ + 2 i4°'5), 



counting from the middle of Januar}. Whence, if we determine 

 the mean minimum temperature, m, and the mean maximum, M, 

 of any day in the year, we can determine the mean temperature, 

 T, of the dav from the formula : 



T = m + K (M — m), 



where K has the value given above. 



Example: For the ten years 1888-1897, on March ist, at Kim- 

 berley. according to the Lee register. M = 86°"6, m = 6o°"o. With 

 sufficient accuracy we may put n=i'^. Therefore 



T = 6o°'o ^ 26°'6 (o"46j — o"o25^o"462 — • o'oo7 — o"824) = 7i'^'8. 



Since in our example the value of h (M -r m) is 73°'3, the differ- 

 ence between this and the computed mean is i°'5, agreeing, there- 

 fore, with the tabular correction for March on the last line but one of 

 Table 3. 



Hitherto we have been discussing mean conditions under a 

 sky whose average cloudiness would fall somewhere between 20% 

 and 30%. The tables at the end, Xos. 6 — 13, give, in addition, 

 material applying to " cloudy " skies whose average cloudiness ex 

 ceeds 50%, and to " clear " skies whose average cloudiness does not 

 reach even 5%. The latter is only likely to be of occasional use 

 in very special cases, chiefly in winter. For probably no station 

 in the world has less cloud than Kimberley. But the former may 

 apply to some extent to such places as (^ueenstown, Umtata, or 

 the Katberg Sanatorium, or even Uitenhage. The secular change 

 whereby temperature and pressure tend to rise, dew-point and 

 humidity to fall under clear skies (and of course vice- versa under 

 cloudy skies), has not been corrected for. Before computing the 

 harmonic terms of the different elements, however, the annual 

 curves were reduced to re-enter. It is doubtful, nevertheless, 

 whether some small extraneous error is not thereby introduced.* 



Kaemtz's factors for clear and for cloudy skies are shewn in 

 Table 15. 



A word of explanation may be acceptable concerning the 

 Tables 6 — 13. 



First, the values under clear skies were picked out one by one 

 from the registers, and arran<i;ed in monthlv sets. The same 



*In the Annual Xormals for clear and for cloudy skies, in Table I., instru- 

 mental errors have been corrected. 



