176 PROCEEDINGS OF THE AMERICAN ACADEMY 



from each other 19.22 inches. The horizontal axis consists of two 

 reversed cones, which terminate in a cube whose single edge is 4.43 

 'nches. The instrument is provided with three positive eye-pieces, 

 magnifying, respectively, 36, 67, and 99 diameters; this last being the 

 one employed in the longitude observations. The reticule of the 

 instrument consists of a series of twenty-five lines ruled by Prof. W. 

 A. Rogers. They are arranged in tallies of five lines each ; the equa- 

 torial interval between the lines being 3'.543, and between the middle 

 lines of the separate tallies 21'.258. This form of reticule is found ex- 

 tremely convenient in practice ; since a circumpolar star may be observed 

 over the five lines of a single tally, and the instrument can be easily 

 reversed in time to observe a symmetrical tally with the circle oppo- 

 site its first position. The equal spacing of the lines possible, when 

 they are ruled on glass, reduces by one step the computation of tlie 

 results. And, by a slight movement of the eye-piece, it is possible in 

 this reticule to obtain a spurious image of a line remarkable for its 

 blackness, without sensibly disturbing the focal image of the star. This 

 is especially convenient in observing faint stars, where it becomes 

 necessary to reduce the illumination so much that the line would ordi- 

 narily be invisible. On the other hand, the loss of light by reflection 

 is objectionable ; and the writer has not been able to use lines on 

 glass with bright-line illumination for faint stars. 



The chronograph by Bond & Sons, situated in the computing room 

 of the observatory, was used. 



At Waltham, the observations were made with a transit instrument 

 by Alvan Clark & Sons. It is of the ordinary pattern, has a clear 

 aperture of 2.55 inches, and a focal length of 38.0 inches nearly. 



The pivots, 0.972 inches in diameter, rest upon journal bearings 1.00 

 inch in length. These bearings are distant from each other 17.25 

 inches. The telescope is provided with a diagonal eye-piece magnify- 

 ing 64 diameters, and it is reversed by means of a reversing carriage. 



The chronograph used is also from the shop of Alvan Clark & Sons ; 

 it is of the cylinder pattern, and is controlled by the conical pendulum 

 governor so successfully used by the Messrs. Clark in this connec- 

 tion. 



For portable instruments, the formula expressing the relation be- 

 tween the apparent place of a star and its observed place, as affected 

 by errors of observation, may be written 



a = T-\-r-{-Jr-\-8T{T— T,) -\- A a {or A' a') -\- B b -{- C c 

 — 0'.021 cos cp sec d, 



