NO. 5 SOLAR VARIATION AND FORECASTING ABBOT 1 5 



CONSTRUCTIVE ARGUMENTS 



Having considered the objections: (i) That it is futile to seek 

 meteorological correlations with imperfect solar observations; (2) 

 that the most naturally to be expected solar variation does not appear : 



(3) that terrestrial sources of error are obviously still in evidence ; 



(4) that for the past six years our results have shown so small a 

 scatter about the mean that there is no room for solar variation ; 

 and (5) that our two stations, intended to check each other's findings, 

 are not really independent, I am ready to take up the constructive 

 part of my paper. 



Thesis (a). — The theory of probability admits of the belief in 

 the real existence of short-period solar variations, some of which 

 exceed 2 per cent in amplitude. 



It is not material to this argument to prove that the scale of Smith- 

 sonian measurements is exactly in terms of the 15° calorie. If the 

 average value of the solar constant which we find tO' be 1.94 calories 

 is really as little as 1.90, or as great as 1.98 calories, it matters not. 

 By expanding or contracting the true calorie slightly, the mean solar 

 constant can be expressed as 1.94. The only question at issue is 

 whether, after this adjustment is made, there are real fluctuations 

 of short period as large as 2 per cent in this conventional value. 



Conceive, if you please, an angel to have brought us from heaven 

 the true curve of solar variation covering the period 1920 to 1924, 

 expressed on the same scale as our determinations. We are to inquire, 

 first of all : What will be found to be the average deviation and 

 probable error of our observed curve from the angel's curve? 



To determine this question, we have 327 differences between 

 independent daily solar-constant determinations of good character, 

 made at Harqua Hala and Montezuma."" I may remark, in passing, 

 that since there is almost three hours difference in longitude, these 

 daily differences are greater, owing to solar variations occurring 

 between measurements, than they would be if the stations observed 

 simultaneously. So our investigation is "too liberal to our critics, 

 but I am wilhng to grant them this advantage. 



The average daily difference, Harqua Hala minus Montezuma, 

 is ±0.011 calorie. This is the average daily difference between two 

 series of measurements both affected by accidental errors, and, let 

 us assume, equally affected thereby. Evidently, therefore, the average 

 deviation of either station from the angel's curve is less than o.oii 



calorie. It is, in fact, — T/T^ ^^ ■'■ have demonstrated both theo- 

 ^ See Smithsonian Misc. Coll., Vol. 77, No. 3, table 4. 



