10 Photometric Observations of the Sun and Sky. [Dec. 11, 



Table E. 



Twilight. 



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

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



= (2- sin at + 4 cos *)t. 

 This vanishes when 



2ir sin a. + 4 COS at = 0, 



i.e., when 



en- 



tan * = , 



TT 



* = -32 29'. 



This gives an absolute value for twilight, supposing daylight to 

 cease when the diffused daylight of Roscoe entirely vanishes. 



The extreme limit at which twilight has been certainly observed is 

 when the sun is 24 below the horizon ; at which time the formula 

 ta(2jr sin a + 4 cos *) would show the chemical action of diffuse day- 

 light to be only -^ of what it was just after sunset. 



In other words, the formula 



(2ir sin a. + 4 cos )ta 



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



34. Taking as co-ordinate planes the plane of symmetry, the plane 

 of minimum intensity, and the plane through the sun at right angles 

 to these (which last I call the plane of the sun's altitude), it is found 

 (as a corollary in Article 34) that [U], [V], [W], representing the 

 total chemical effect of the sky, resolved on these co-ordinate planes. 



This suggested the construction of the octant actinometer, which 



