Frequent use is made of the short term “solar constant” to denote the derived values of the intensity, expressed in appropriate thermal units, of solar radiation as if measured just outside the atmosphere of the earth when at its mean distance from the sun.

Determinations of the solar constant show small but important fluctuations from day to day. This investigation is a search for evidence as to what part, if any, of these and of other short-period fluctuations, should be ascribed to solar changes, and what part, if not all, must be assigned to the inevitable errors of derivation.

Unusual methods of analysis are required, because the total variation due to all causes is so small that it is entirely plausible that all of it may be nothing but errors of measurement. At the same time it is possible some solar variation may exist.

SECTION I. The mathematical equations for computing the solar constant are given with extensions drawn from statistical theorems for impersonally measuring, comparing, and correlating variations in observational data.

SEC. II. Securing highly accurate values of the solar constant in absolute magnitude is a difficult problem by itself and is wholly foreign to this study.

Evidence for and against day-to-day and other variations in solar intensity can be secured from pyrheliometer readings alone.

How this is done is shown by a sample analysis of the latest and best observations thus far published in full, namely, for Calama, Chile, July, 1918, to July, 1919. The pyrheliometer is the basic instrument for all solar constant measurements. Its errors are smallest, most certainly known and most constant, and when properly standardized it is the most comparable of all the instruments employed.

It is not difficult to show that nothing but the sun and errors of derivation can cause variations of the solar constant at a single station. If half the total variation found at Calama is assumed to be due to the sun, analysis shows the probable departure of any daily value from the mean for the year due to the sun to be ± 0.0083 calorie. To ascribe this small possible variation to the sun is to assume that the total variation at the Calama station due to all causes is the irreducible minimum of total variation to be found when values are available from many equally good stations.

SEC. III. A graphical tabulation is given to aid in the interpretation of correlations between pyrheliometer and other observations.

SEC. IV. Consecutive values of solar constant values from 1902 to 1924 are charted and probable variations evaluated and illustrated.

SEC. V. Any annual periodicity in solar constant values is prima facie evidence of terrestrial influence. Small but important summer and winter effects of this kind based on fully 3,000 daily values are shown in a striking manner, including the physically inconsistent values for the station at Harqua Hala, which are found to be correlated with the values at Montezuma in an artificial way.

SEC. VI. An example is given of how solar variations can be segregated from variations due to errors, when simultaneous observations are available from one or more pairs of independent stations by the solution of three simultaneous equations between solar variation and the two other unknown variations caused by station errors. Incidentally, it is shown how to ascertain whether the three unknowns are interdependent and thus how to interpret in a rational way the results secured.