4 squared x 1,680,000
-------------- = 2,986,000 deg.  F.
3

The writer has established the correctness of the assumption that “the temperature is as the density of the rays,” by showing practically that the diminution of solar temperature (for corresponding zenith distances) when the earth is in aphelion corresponds with the increased diffusion of the rays consequent on increased distance from the sun.  This practical demonstration, however, has been questioned on the insufficient ground that “the eccentricity of the earth’s orbit is too small and the temperature produced by solar radiation too low” to furnish a safe basis for computations of solar temperature.

In order to meet the objection that the diffusion of the rays in aphelion do not differ sufficiently, the solar pyrometer has been so arranged that the density, i. e., the diffusion of the reflected rays, can be changed from a ratio of 1 in 5,040 to that of 1 in 10,241.  This has been effected by employing heaters respectively 10 inches and 20 inches in diameter.  With reference to the “low” solar temperature pointed out, it will be perceived that the adopted expedient of increasing the density of the rays without raising the temperature by converging radiation, removes the objection urged.

Agreeably to the dimensions already specified, the area of the 10-inch heater acted upon by the reflected solar rays is 331.65 square inches, the area of the 20-inch heater being 673.9 square inches.  The section of the annular sunbeam whose direct rays act upon the polygonal reflector is 3,130 square inches, as before stated.

Regarding the diffusion of the solar rays during the investigation, the following demonstration will be readily understood.  The area of a sphere whose radius is equal to the earth’s distance from the sun in aphelion being to the sun’s area as 218.1 squared to 1, while the reflecter of the solar pyrometer intercepts a sunbeam of 3,130 square inches section, it follows that the reflector will receive the radiant heat developed by 3,130 / 218.1 squared = 0.0658 square inch of the solar surface.  Hence, as the 10-inch heater presents an area of 331.65 square inches, we establish the fact that the reflected solar rays, acting on the same, are diffused in the ratio of 331.65 to 0.0658, or 331.65 / 0.0658 = 5,040 to 1; the diffusion of the rays acting on the 20-inch heater being as 673.9 to 0.0658, or 673.9 / 0.0658 = 10,241 to 1.

The atmospheric conditions having proved unfavorable during the investigation, maximum solar temperature was not recorded.  Accordingly, the heaters of the solar pyrometer did not reach maximum temperature, the highest indication by the thermometer of the small heater being 336.5 deg., that of the large one being 200.5 deg. above the surrounding air.  No compensation will, however, be introduced on account of deficient solar heat, the intention being to base the computation