188 PROCEEDINGS OP THE AMERICAN ACADEMY 



plate. To determine the zenith distance and azimuth of this point 

 it is necessary to measure the zenith distance and azimuth of the 

 corresj^onding point of the reticule, as seen from tlie second principal 

 point of the objective. P'or that purpose the mirror A, Fig. 1, is 

 temporarily removed, and a transit instrument is set up in front of 

 the objective B, and in tlie prolongation of its axis. The objective 

 thus becomes a collimator to the transit instrument, through the 

 eyepiece of which the lines of the reticule may be observed as if they 

 were at an infinite distance. It should be remarked, however, 

 that, as the reticule is slightly inside the visual focus of the objective, 

 it is not generally possible to obtain perfectly distinct vision of its 

 lines and of the wires of the transit at the same time. This difficulty 

 is obviated by mai'king the intersection of the middle vertical and 

 middle horizontal lines of the reticule in such a distinct manner that 

 the slight mal-adjustment of focus does not prevent it from being 

 seen. Then, by means of the transit, the reticule is adjusted so that 

 the point in question is very approximately in the meridian, and at 

 a zenith distance of ninety degrees. Finally, the exact azimuth and 

 zenith distance of the point are measured. 



If the photoheliograf)h is employed to depict any object whose 

 linear magnitude is such that it subtends an angle a at the first 

 principal point of the oljective, and if the centre of the image 

 coincides with the centre of the plate upon wliich it is taken ; then, 

 no matter what may be the solar focal distance of the objective, the 

 magnitude of the iuiajje will be 



2 tan la (Z> + E" — T) (1) 



where D is the distance between the back surfice of the objective 

 and the sensitive surface of the photograi>hic plates, E" the distance 

 from the back surface of the objective to its second principal point ; 

 and T A correction due to the thickness of the reticule plate. It is 

 thus evident that, in all calculations involving measurements of pic- 

 tures taken with this apparatus, the value to be employed as the focal 

 distance of the objective is 



D-\- E" — T (2) 



D is obtained by direct measurement, the accuracy of which must 

 be such that the uncertainty of the resulting value will not exceed 

 one part in ten thousand, and it is desirable that it should not ex- 

 ceed one part in forty thousand. To obtain E" we put 



n = refractive index of crown -jjlass lens. 



n' = refractive index of flint-glass lens. 



