8 Mr. \V. Brennand. [Dec. 11, 



I have been careful to verify it by numerous observations both at 

 Dacca and in Somersetshire, and also to vary the observations in every 

 way I could devise. Thus the mitrailleuse has been placed in the 

 plane of minimum intensity. In this case all the barrels give the 

 same reading for points not too near the horizon. 



Next the mitrailleuse was placed in planes of great circles through 

 the sun at various angles with the plane of symmetry, by turning it 

 round the line joining one of its tubes with the sun the observed 

 chemical actions agree well with 



ia cosec 0. 



Next by means of stops I made the aperture of each barrel of the 

 mitrailleuse to be 



c sin 0, 



where is the distance of the axis of the barrel from the sun; 

 this mitrailleuse being exposed, the barrel c sin being directed to 

 the sun, the circular darkened spots were found to be very accurately 

 of the same depth. 



Further, I calculated the times of exposure for a (particular) 

 mitrailleuse with barrels of uniform aperture, which ought, on the 

 law ia cosec 6, to give a uniform tint. I exposed this mitrailleuse for 

 these calculated times, first in the plane of symmetry, afterwards in a 

 plane inclined to it at 62 ; the results agreed closely with my antici- 

 pation, and show ia cosec to be a very good approximation. 



22. I have therefore made full use of the expression ia cosec 

 for the chemical action of the light of the sky in a circle 

 from the sun (whose altitude is <*). First, in the following proposi- 

 tion : 



24. Having given ia the chemical action in the circle of minimum 

 intensity, to calculate the total chemical action of the sky on a plane 

 exposed at right angles to the sun. 



N.B. ia is a constant for this calculation, but it varies with the 

 altitude of the sun. 



Let the figure represent a projection on the plane of symmetry, S 

 being the sun, Z the zenith, HBYH' the horizon, AYX the plane of 

 minimum intensity, SH = a. the sun's altitude, the angular dis- 

 tance of the sun from QR. Then the total action of sky throughout 

 the gore HYZSH on sensitised paper at in the plane perpendicular 

 to OS 



-+ 2 



d0 \ 



-T-- > 



*co& 2 J 



The expression cannot be integrated ; but, by using a formula of 

 reduction in series, it gives 



