NO. 3 RADIATION OF THE ATMOSPHERE ANGSTROM 59 



sensitiveness of the bolometer changes with its position, the con- 

 ductivity of heat from the strips through the air being different for 

 vertical and horizontal positions. On the other hand, the sensitive- 

 ness of my apparatus, used in this way, was not very great. When 

 the instrument was directed to points near the horizon the deflection 

 of the galvanometer seldom amounted to more than about 2 mm., 

 and for zenith position the deflection was about 6 mm. The prob- 

 able error in every measurement is therefore about 5 per cent. In 

 spite of this disadvantage, a comparison between the values of the 

 total radiation observed and the total radiation computed from the 

 observations of the radiation to the different zones shows a fairly 

 close agreement. 



If the dimensions of the strips can be regarded as negligible in 

 comparison with the radius of the screen, we may assume the effec- 

 tive solid angle to be equal to the solid angle under which the central 

 point of the instrument radiates to the hole. Now this is not exactly 

 the case, and in computing the total radiation from the radiation to 

 the limited parts of the sky, we must apply a correction with regard 

 to the position of the strips. The mean solid angle is obtained 

 through an easily effected but somewhat lengthy integration process 

 given in the foot-note. 1 It is found to be 768.6 . 



The correction term will make 1.5 per cent in the solid angle, a 

 quantity that is not negligible when we wish to calculate the total 

 radiation. 



When the instrument is pointed in different directions, different 

 parts of the strips will radiate to slightly different regions of the 

 sky. In the process used for finding the distribution of radiation 



1 Let us consider a circular hole of the radius p, radiating to a plane surface, 

 parallel with the hole and at the vertical distance R from it. We wish to find 

 the radiation T to a little elementary surface, dx, whose distance from the 

 perpendicular from the central point of the hole, is /. Using cylindric coordi- 

 nates, and defining the element of the hole (do), through the relation: 



do=pid(pdpi 



, T _ R 2 pid4>d P 



we get : dl — , „„ . — 2 , ?2 — - — ; -y= ■ or 



& [R 2 +Pl-{-l 2 — 2/3i/cOS0] 2 



and for the radiation from the entire hole : 



' a [ 2ir aidadcp 



Jo [i+a?+/3 2 — 2a 1 f3cos<p] 2 ' T 



T= 



where we have put: 



P . a — Pi. R — 1 

 ~R' ai -R' P-li 



