Photometric Observations of the Sun and Sky. 273 



32. Since in table E the value of i a for = 42 1 3' is found from 

 Roscoe's observations to be 016, from mine to be 0'012, it follows 

 that Roscoe's unit of chemical action is yf of my Dacca candle unit. 

 This is merely a first attempt to correlate these units. 



33. The resultant chemical action of the sky on a horizontally 

 exposed piece of paper, the Sun's altitude being , is found 



= (2w sin a. + 4 cos )t' a . 

 This vanishes when 



2-n- sin a. + 4 cos = 0, 



2 

 t.e., when tan = _, 



77- 



* = -32 29'. 



This gives an absolute value for twilight, supposing daylight to 

 ease when the diffused daylight of Roscoe entirely vanishes. 



The extreme limit at which twilight has been certainly observed is 

 when, the Sun was 24 below the horizon ; at which time the formula 

 ta(27r sin a, + 4 cos x) would show the chemical action of diffuse day- 

 light to be only -^ part of w r hat it was just after sunset. 



In other words, the formula 



a(27T sin +4 cos ) 



. 



gives a very good agreement with the observed duration of twilight, 

 supposing, that is, the illumination and the chemical action to follow 



uch the same laws in this extreme case. 



34. Taking up the expressions for U, V, W at the end of Art. 26, 

 I integrate them for the octant of the sphere contained by the three 

 coordinate planes, viz., the plane of symmetry, the plane of minimum 

 intensity, and the plane of the Sun's altitude ; i.e., I take and 6 each 

 from to \TT which gives 



. 



[V] = [W]'= 





suggested the construction of the octant actinometer, which 

 requires only one-fourth of the visible sky 'to be clear for observation, 

 and gives the value of ia. directly, requiring no calculations of re- 

 duction. 



135. The octant actinometer (fig. 3) consists of three quadrantal 

 ancs, MOS, MOI, and IOS, joined at their edges so as to form a hollow 

 trihedral, and mounted so that one of the edges, OS, can be brought to 

 int to the Sun, and the plane MOI will then coincide with the 

 >ne of minimum intensity. The instrument has another adjustment 



