Fuly 13, 1871] 
NATURE 
205 

energy. It would be waste of time to enter on any further 
demonstration in refutation of the extravagant assumption 
that a thermometer in contact with the photosphere would 
indicate some 12,000,000° Fahr. higher temperature than 
that which we have established on the basis of the known 
distance and radius of the sun’s photosphere, and the 
ascertained radiant intensity at the boundary of the earth’s 
atmosphere. Nor need we point out the inconsistency of 
the doctrine that the sun’s photosphere possesses less 
radiant power than incandescent terrestrial substances, 
such, for instance, as iron and carburetted hydrogen. But 
the advocates of high solar temperature may urge, that 
the law, agreeable to which the temperature of 4,000,000° 
Fahr. has been determined, is mere ¢/eory, which, although 
true for distances of a few feet, may be wholly erroneous 
when the radiator is millions of miles away. 
It has been one of the principal objects of my researches 
connected with solar heat, during the last three-years, to 
endeavour to determine this question. Accordingly, the 
difference of intensity of solar radiation at midsummer 
and midwinter has been particularly observed.  For- 
tunately, the eccentricity of the earth’s orbit is sufficient 
to produce a marked difference of intensity at different 
seasons ; but, on the other hand, the varying depths of the 
atmosphere resulting from the varying inclination ofthe 
earth’s axis, apart from thevarying distance between the sun 
and the earth, presentserious obstacles. My observations as 
before mentioned have been conducted in lat. 40° 42’, hence 
17° 12’ from the ecliptic at the summer solstice, and 
64° 12’ at the winter solstice. Accordingly, the depth of 
atmosphere has varied during the investigations in the 
ratio of I’o4 to 2'25 ; thus rendering comparisons between 
the actual intensities very difficult. A series of observa- 
tions made at different hours and seasons has ultimately 
enabled me to construct the curve before referred to, 
defining the maximum intensity of the sun’s radiant heat 
for all latitudes at the time when the earth passes the 
aphelion; likewise defining the retardation of solar 
intensity for all zenith distances not exceeding 75°. 
Evidently an accurate knowledge of the solar intensity 
corresponding with given zenith distances removes the 
obstacles attending the varrying inclination of the axis of 
the earth. The variation of intensity consequent on the 
eccentricity of the earth’s orbit has also been accurately 
determined for each day in the year. The detail not 
being immediately connected with the subject under con- 
sideration, it will suffice to state that actinometer observa- 
tions conducted under very favourable circumstances, 
January 7, 1871, proved the sun’s radiant heat to be 
57°25° Fahr., the zenith distance being 63°15’. Referring 
to the table, it will be seen that for equal zenith distance— 
63° 15’—the temperature produced by solar radiation is 
only 51°77° when the earth passes the aphelion. An zucrease 
of solar intensity of 57°25 — 51°77 = 5°48°, when the earth is 
in perihelion, has therefore been established. This im- 
portant fact enables us to test on a grand scale the correct- 
ness of our assumption that the intensity of solar radia- 
tion diminishes in the inverse ratio of the area over which 
the rays are dispersed. 
The aphelion distance of the earth being 218'1 times 
greater than the radius of the sun’s photosphere, while 
the perihelion distance is 2109 times that radius, the 
temperatures produced by solar radiation at the boundary 
of the earth’s atmosphere at midsummer and at mid- 
winter, will be inversely as 218'17 : 210°9°.. Consequently, 
as the ascertained maximum temperature at the former 
period is 84°84° Fahr., the temperature produced by solar 
2181? X 84°842 = 
210°9° 
go'72° Fahr. Let us ascertain if this theoretical tempera- 
ture correspond with actual fact. Our table shows that 
the diminution of solar intensity attending the passage of 
the rays through the atmosphere, when the zenith distance 
is 63°15’, amounts to 15°43° in addition to the diminution 
radiation at the latter period will be 

of 17°64° on the ecliptic, together 33°07°. Adding this 
to the temperature 57'25°, observed January 7, 1871, we 
establish the fact that the temperature at the boundary of 
the atmosphere is 90'32° Fahr. Agreeable to the fore- 
going theoretical determination, the temperature ought to 
be 90'72°, difference = o'4° Fahr. This discrepancy 
is accounted for by the fact that the sky, although un- 
usually clear, was not quite free from cirrus haze on the 
day of observation, as proved by the indication of the 
solar calorimeter, an instrument by which the presence of 
any obstruction in the atmosphere is ascertained with 
absolute certainty. In addition to the proof thus fur- 
nished in support of the theory on which our calculations 
are based, that the temperature at the surface of the 
sun’s photosphere does not much exceed 4,000,000° 
Fahr., other tests have been adopted with nearly identical 
results, an account of which, together with necessary 
delineations, has been published in Engineering. These 
tests prove that, unless the photosphere of the sun 
possesses relatively less radiating power than incan- 
descent cast iron, or metallic substances coated with 
lampblack, and maintained at ordinary boiling heat, the 
temperature indicated by a thermometer “ dipped inside 
the solar envelope in contact with the photosphere” will 
not exceed 4,100,000 deg, Fahrenheit. 
Table showing the depth of atmosphere, and intensity of solar 
radiation, for cach degree of zenith distance, when the earth passes 
the aphelion. 

| 
1 







Ae ae ES ay oars ER 
fe | s@ Ea 2G 6. Ea 
a | As |} sa a ee S45 
| : | | 
| =| E 
Deg. | Fah. |] Deg. | Fah 
fe) 1'000 67-20) ||) 38: 1°265 62°11 
I 1‘000 67°20 39 1°283 or'Sr 
2 | 1-000 67°19 40 | 1°302 61°50 
3 I‘OO1 67°15 41 |) 322 61°19 
4 | 1'002 67°16 2 | 1-342) 60°88 
5 1°003 67-12) Sie 43 | 14363 60°57 
6 1'005 67°08 || 44 1°384 60°25 
7 1007 | 67'02 45 1°406 59°93 
8 I‘010 66°96 | 40 1431 59°60 
9 1-013 66:90 || 47 1457 59°25 
10 1010 66°84 | 48 | 1485 58°88 
II I’019 66°77 || 49 1°514 58°51 
12 1°023 66°70 || 50 1°545 5812 
13 1'027 66°62 ) 51 1'577 57°72 
14 1°031 66°54 || 52 1612 57°31 
15 1'036 66°44 53 1°648 56°89 
16 1-041 66°33 54 1686 56°46 
U7 i ak.O40 66°21 55 1°726 5602 
18 1‘O51 66:08 || 56 1°769 55°50 
19 | 1'057 65°95 57 | 1°815 55°09 
20 1063 65°82 || 58 17864 54°60 
21 1‘070 65°68 59 1'916 54°10 
22 1'077 | 65°53 || 60 1970 | 53°58 
23 1'085 65°38 || 61 2°037 53°05 
24 1°093 65°22 62 27098 52°50 
25 I*102 65°04 63 2*164 51°90 
26 I'll 64°86 64. 2'235 | 51°40 
27 I‘I2I 64°67 || 65 2°312 50°81 
28 1°132 64°48 66 2°398 59°20 
29 114r | 64°28 67 2490 | 49°57 
30 I‘I52 64°07 68 2°5QI 48°01 
31 1°164 63°85 69 2°701 48°25 
32 1176 63°63 70 2°82z1 47°55 
33 1189 63°40 71 2°952 | 46°34 
34. 1°203 63°16 2 3°097 46°12 
35 1217 62°92 || 73 3°255 | 45°37 
30 |) SIe232 62°67 | 74. 3°428 | 44°60 
37 1-248 62°40 || 75 | 3°24 | 43°78 
| 

J. ERIcsson 
