I have, during the summer solstice of 1884, carried out an experimental
investigation for the purpose of demonstrating the temperature of the
solar surface corresponding with the temperature transmitted to the sun
motor. Referring to the illustrations previously published, it will be
seen that the cylindrical heater of the sun motor, constructed solely for
the purpose of generating steam or expanding air, is not well adapted for
an exact determination of the amount of surface exposed to the action of
the reflected solar rays. It will be perceived on inspection that only
part of the bottom of the cylindrical heater of the motor is acted upon by
the reflected rays, and that their density diminishes _gradually_ toward
the sides of the vessel; also that owing to the imperfections of the
surface of the reflecting plates the exact course of the terminal rays
cannot be defined. Consequently, the most important point in the
investigation, namely, the area acted upon by the reflected radiant heat,
cannot be accurately determined. I have accordingly constructed an
instrument of large dimensions, a polygonal reflector (see Fig. 1),
composed of a series of inclined mirrors, and provided with a central
heater of conical form, acted upon by the reflected radiation in such a
manner that each point of its surface receives an equal amount of radiant
heat in a given time. The said reflector is contained within two regular
polygonal planes twelve inches apart, each having ninety-six sides, the
perimeter of the upper plane corresponding with a circle of eight feet
diameter, that of the lower plane being six feet. The corresponding sides
of these planes are connected by flat taper mirrors composed of thin glass
silvered on the outside. When the reflector faces the sun at right angles,
each mirror intercepts a pencil of rays of 32.61 square inches section,
hence the entire reflecting surface receives the radiant heat of an
annular sunbeam of 32.61 × 96 = 3,130 square inches section. It should be
observed that the area thus stated is 0.011 less than the total
foreshortened superficies of the ninety-six mirrors if sufficiently wide
to come in perfect contact at the vertices. Fig. 2 represents a transverse
section of the instrument as it appears when facing the sun; the direct
and reflected rays being indicated by dotted lines. The reflector and
conical heater are sustained by a flat hub and eight radial spokes bent
upward toward the ends at an angle of 45°. The hub and spokes are
supported by a vertical pivot, by means of which the operator is enabled
to follow the diurnal motion of the sun, while a horizontal axle, secured
to the upper end of the pivot, and held by appropriate bearings under the
hub, enables him to regulate the inclination to correspond with the
altitude of the luminary. The heater is composed of rolled plate iron
0.017 inch thick, and provided with bead and bottom formed of
non-conducting materials. By means of a screw-plug passing through the
bottom and entering the face of the hub the heater may be applied and
removed in the course of five minutes, an important fact, as will be seen
hereafter. It is scarcely necessary to state that the proportion of the
ends of the conical heater should correspond with the perimeters of the
reflector, hence the diameter of the upper end, at the intersection of the
polygonal plane, should be to that of the lower end as 8 to 6, in order
that every part may be acted upon by reflected rays of equal density. This
condition being fulfilled, the temperature communicated will be perfectly
uniform. A short tube passes through the upper head of the heater, through
which a thermometer is inserted for measuring the internal temperature.
The stem being somewhat less than the bore of the tube, a small opening is
formed by which the necessary equilibrium of pressure will be established
with the external atmosphere. It should be mentioned that the indications
of the thermometer during the experiment have been remarkably prompt, the
bulb being subjected to the joint influence of radiation and convection.
The foregoing particulars, it will be found, furnish all necessary data
for determining with absolute precision the _diffusion_ of rays acting on
the central vessel of the solar pyrometer. But the determination of
temperature which uninterrupted solar radiation is capable of transmitting
to the polygonal reflector calls for a correct knowledge of atmospheric
absorption. Besides, an accurate estimate of the loss of radiant heat
attending the reflection of the rays by the mirrors is indispensable. Let
us consider these points separately.
[Illustration: _Fig._ 2.]
_Atmospheric Absorption._--The principal object of conducting the
investigation during the summer solstice has been the facilities afforded
for determining atmospheric absorption, the sun's zenith distance at noon
being only 17° 12' at New York. The retardation of the sun's rays in
passing through a clear atmosphere obviously depends on the depth
penetrated; hence--neglecting the curvature of the atmospheric limit--the
retardation will be as the secants of the zenith distances. Accordingly,
an observation of the temperature produced by solar radiation at a zenith
distance whose secant is _twice_ that of the secant of 17° 12', viz., 61°
28', determines the minimum atmospheric absorption at New York. The result
of observations conducted during a series of years shows that the maximum
solar intensity at 17° 12' reaches 66.2° F., while at a zenith distance of
61° 28' it is 52.5° F.; hence, minimum atmospheric absorption at New York,
during the summer solstice,
13.7
is 66.2°-52.5° = 13.7° F., or ------ = 0.207 of the sun's
66.2
radiant energy where the rays enter the terrestrial atmosphere.
[Illustration: CAPTAIN ERICSSON'S SOLAR PYROMETER, ERECTED AT NEW YORK,
1884.]
In order to determine the loss of energy attending the reflection of the
rays by the diagonal mirrors, I have constructed a special apparatus,
which, by means of a parallactic mechanism, faces the sun at right angles
during observations. It consists principally of two small mirrors,
manufactured of the same materials as the reflector, placed diagonally at
right angles to each other; a thermometer being applied between the two,
whose stem points toward the sun. The direct solar rays entering through
perforations of an appropriate shade, and reflected by the inclined
mirrors, act simultaneously on opposite sides of the bulb. The mean result
of repeated trials, all differing but slightly, show that the energy of
the direct solar rays acting on the polygonal reflector is reduced 0.235
before reaching the heater.
In accordance with the previous article, the investigation has been based
on the assumption that _the temperatures produced by radiant heat at given
distances from its source are inversely as the diffusion of the rays at
those distances. In other words, the temperature produced by solar
radiation is as the density of the rays._
It will be remembered that Sir Isaac Newton, in estimating the temperature
to which the comet of 1680 was subjected when nearest to the sun, based
his calculations on the result of his practical observations that the
maximum temperature produced by solar radiation was one-third of that of
boiling water. Modern research shows that the observer of 1680 underrated
solar intensity only 5° for the latitude of London. The distance of the
comet from the center of the sun being to the distance of the earth from
the same as 6 to 1,000, the author of the "Principia" asserted that the
density of the rays was as 1,000² to 6² = 28,000 to 1; hence the comet was
subjected to a temperature of 28,000 × 180°/3 = 1,680,000°, an intensity
exactly "2,000 times greater than that of red-hot iron" at a temperature
of 840°. The distance of the comet from the solar surface being equal to
one-third of the sun's radius, it will be seen that, in accordance with
the Newtonian doctrine, the temperature to which it was subjected
indicated a solar intensity of
4² × 1,680,000
-------------- = 2,986,000° 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 218.1² 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 /
218.1² = 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°,
that of the large one being 200.5° above the surrounding air. No
compensation will, however, be introduced on account of deficient solar
heat, the intention being to base the computation of solar temperature
solely on the result of observations conducted at New York during the
summer solstice of 1884. It will be noticed that the temperature of the
large heater is proportionally higher than that of the small heater, a
fact showing that the latter, owing to its higher temperature, loses more
heat by radiation and convection than the former. Besides, the rate of
cooling of heated bodies increases more rapidly than the augmentation of
temperature.
The loss occasioned by the imperfect reflection of the mirrors, as before
stated, is 0.235 of the energy transmitted by the direct solar rays acting
on the polygonal reflector, hence the temperature which the solar rays are
capable of imparting to the large heater will be 200.5° × 1.235 =
247.617°; but the energy of the solar rays acting on the _reflector_ is
reduced 0.207 by atmospheric absorption, consequently the ultimate
temperature which the sun's radiant energy is capable of imparting to the
heater is 1.207 × 247.617° = 298.87° F. It is hardly necessary to observe
that this temperature (developed by solar radiation diffused fully
ten-thousandfold) must be regarded as an _actual_ temperature, since a
perfectly transparent atmosphere, and a reflector capable of transmitting
the whole energy of the sun's rays to the heater, would produce the same.
The result of the experimental investigation carried out during the summer
solstice of 1884 may be thus briefly stated. The diffusion of the solar
rays acting on the 20 inch heater being in the ratio of 1 to 10,241, the
temperature of the solar surface cannot be less than 298.87° × 10,241 =
3,060,727° F. This underrated computation must be accepted unless it can
be shown that the temperature produced by radiant heat is not inversely as
the diffusion of the rays. Physicists who question the existence of such
high solar temperature should bear in mind that in consequence of the
great attraction of the solar mass, hydrogen on the sun's surface raised
to a temperature of 4,000° C. will be nearly twice as heavy as hydrogen on
the surface of the earth at ordinary atmospheric temperatures; and that,
owing to the immense depth of the solar atmosphere, its density would be
so enormous at the stated low temperature that the observed rapid
movements within the solar envelope could not possibly take place. It
scarcely needs demonstration to prove that extreme tenuity can alone
account for the extraordinary velocities recorded by observers of solar
phenomena. But _extreme tenuity_ is incompatible with low temperature and
the pressure produced by an atmospheric column probably exceeding 50,000
miles in height subjected to the sun's powerful attraction, diminished
only one-fourth at the stated elevation. These facts warrant the
conclusion that the high temperature established by our investigation is
requisite to prevent undue density of the solar atmosphere.
It is not intended at present to discuss the necessity of tenuity with
reference to the functions of the sun as a radiator; yet it will be proper
to observe that on merely dynamical grounds the enormous density of the
solar envelope which would result from low temperature presents an
unanswerable objection to the assumption of Pouillet, Vicaire,
Sainte-Claire Deville, and other eminent _savants_, that the temperature
of the solar surface does not reach 3,000° C.