190 PROCEEDINGS OP THE AMERICAN ACADEMY 



n 



and as i oannot exceed half a degree, its cosine will be very nearly 

 unity, and it will be sufficiently accurate to write 



T= '-i^i^ (7) 



If we assume the reticule plate to be of crown glass, and its refractive 

 index to be 1.53, then T =: 0.347 t; and it is evident that, in order 

 to make 7" small, the reticule plate should be as thin as possible. 



From the experience thus far had with the horizontal photohelio- 

 graph, it appears that, if the focal distance of the objective is F, its 

 clear aperture should be 0.0100 i^. The clear aperture of the helio- 

 stat mirror, which is circular in form, should be 0.0142 i^. The plates 

 upon which the pictures are taken should be square, and of such a 

 size that their sides, as seen from the centre of the objective, may 

 subtend an angle of about sixty minutes. This should also be the 

 size of the reticule plate, and the distance between any two consecu- 

 tive lines of the reticule should subtend an an^le of about four minutes. 

 Throughout the remainder of this paper it will be assumed that these 

 are the proportions of the apparatus. The actual focal distance of the 

 objectives of the instruments heretofore constructed has generally been 

 about twelve meters. 



To avoid repetition, the notation which will be employed through- 

 out the remainder of this paper is here given. Let PA, Fig. 4, be 

 the meridian of the place of observation; P being the pole, and Z 

 the zenith. Let S be the position of the sun as seen from the centre 

 of the earth, and S^ its position as seen from the place of observation. 

 Hereafter, to avoid circumlocution, S will be designated as the true, 

 and S^ as the apparent, sun. Let v be the vertex of the apparent 

 sun, and V the position of Venus as seen from the centre of the earth. 

 Also, let M be the point where the normal to the heliostat mirror 

 pierces the heavens, and V, S', S'^, and v', the positions of the re- 

 flected images of Venus, the true sun, the apparent sun, and the 

 vertex of the apparent sun, as seen from the second principal point 

 of the photographic objective. Then the following notation will be 

 adopted : — 



(^ = latitude of the place of observation. 



cp' = co-latitude of the place of observation = PZ = 90° — gj. 



As =■ polar distance of true suu = PS. 



