TRANSACTIONS OF SECTION A. 003 



where h, M, N afe tte direction cosines of the star with respect to their 

 rectangular axes, of which the first is axis I. and the third is the intersection of 

 the circles II. and I., and we have L, M, N expressed in terms of g, r, R, lij by 

 these equations: — 



L = — sin q sin r + cos q cos r sin Hj ^ 

 M sin R + N cos R = cos r cos Rj r ' • ^'^^^ 



— 31 cos R + N sin R = sin r cos 5 + sin y cos r sin Rj j 



AVhen R and Rj are observed then from (iii) we have L, M, N, and from (ii) 

 a, 5 are known, and as there are three equations there is no ambiguity. 



If R and Rj are given real quantities, then a and S are real quantities, but 

 the converse is not necessarily true. If a and 5 are given, then from (ii) we have 

 L, M, N, and from the first equation of (iii) we have sin JFlj. It may happen that 

 sin R, >1, in which case the instrument cannot be pointed on a, 5. If sin R, <1 

 there will be two values, R^ and 180 — Rj, each of which by substitution in the 

 last two equations of (iii) will give real values for sin R and cos R, so that 

 there will be two methods of pointing the generalised instrument on a given 

 point. This is, of course, the familiar process of reversal in the altazimuth, or of 

 observing upper and lower culmination in the meridian circle. 



3. A New Form of Divided Object- Glass Telescope, 

 By Sir Howard Grubb, F.R.S. 



For certain purposes it was necessary to produce a divided object-glass tele- 

 scope, in which the rays forming the images on one half of the field should be 

 due entirely and solely to the corresponding half object-glass, and the rays form- 

 ing the other half field to the other half object-glass. Moreover, it was necessary 

 to utilise circular revolving wedges over one of the half object-glasses for the 

 purpose of producing a deviation of the rays in one half field as regards the 

 other ; and, furthermore, the images were required to be erect. 



These conditions, though theoretically solvable by introducing a thin dia- 

 phragm in whose plane the optical axis of the telescope would lie, are not prac- 

 ticable, as the light impinging on this diaphragm at very long incidence intro- 

 duces false light into the field and destroys the brilliancy of the images. 



With this form it is not possible to use circular revolving wedges without a 

 considerable loss of light. 



By reversing the two half object-glasses and placing them back to back, the 

 introduction ot an eflFective series of diaphragms is rendered possible without 

 cutting off from the cone of rays which form the images, while the positions of the 

 half object-glasses render the application of circular wedges quite possible and 

 convenient. 



With this arrangement the two semicircular pencils of light being each reversed 

 in themselves by the erecting prisms, emerge from the eye-piece as one single disc, 

 just fitting the pupil of the eye with the lower powers." 



4. The Neva Spectroheliograph foy the Madrid Observatory. 

 By Sir Howard Grubb, F.R.S. 



The necessary conditions to be fulfilled in designing this spectrohellograpli 

 were somewhat limited, owing to the fact that some apparatus (including a 45° 

 prism and a coelostat) already existing had to be utilised. 



Vaiious designs were submitted, and these are mostly described in the Paper. 

 That which was finally accepted did not vary very much, so far as its optical 

 arrangements are concerned, from some of the well-known instruments. 



Most of the novel features are to be found in the mechanical arrangements. 



The whole instrument, which is very heavy and massive, rests on three feet, 

 sliding on three accurately worked planes. 



