1879.] Prof. Liveing, On a new spectroscope. 261 



by an arm moveable about the same axis G as the telescope. The 

 plane through the edge of the first prism A and the axis G is 

 made always to bisect the angle between the plane through the 

 edge of B and the same axis and the plane which is the prolonga- 

 tion of the first face of the half-prism attached to the collimator. 

 This is effected by two levers, one working on a pivot e fixed to the 

 table, and the other working on a pivot g fixed to the arm F which 

 carries the prism B. These two levers have at their other ends a 

 common pivot/", which works in a slot in the arm which carries 

 the prism A. The line GA thus always bisects the angle g Ge. 

 By similar levers attached to the arms E and G the line BG is 

 made always to bisect the angle IGh. By this mechanism the 

 prisms are always kept symmetrically arranged. Measurements 

 are taken by moving the telescope until the line to be measured is 

 on the cross wires of the telescope. It is not of any consequence 

 in practice whether the prisms be always exactly at the minimum 

 deviation, provided they be nearly so, but it is important, where 

 measures are taken by readings of the angle through which the 

 telescope is moved, that the readings should always be the same 

 when the same line is on the cross wires. To ensure this the 

 author purposes to have spiral springs attached to the several 

 moveable arms, so as to keep them always up- to their bearings 

 on one side. The instrument has been made by Browning. Were 

 another such instrument constructed it might perhaps be well to 

 replace the flat arm with a slot which may wear to uneven edges, 

 by an arm with its middle part square in section and a tube 

 sliding on it to which the levers should be hinged as in Fig. 4. 

 The wear in this case would be more uniform and of less con- 

 sequence. 



To illuminate the cross-wires when the field is dark the author 

 proposes to place a small collimator, with a pin-hole instead of a 

 slit, so that the light from it may be reflected from the second face 

 of the second prism. Since the angle through which this prism 

 moves is always half that through which the telescope is moved 

 the image of the pin-hole will be in a nearly constant position in 

 the field of view; and it may be conveniently illuminated by a 

 sodium flame. 



(3) Mr C. Taylor, M.A., On the geometrical proof of Lambert's 

 theorem. 



Lambert's theorem on the times of describing portions of an 

 elliptic orbit was proved in the fourth section of his work on 

 comets entitled Insigniores Orhitce Gometarum Proprietates (1761).. 



The author's demonstration although essentially geometrical 

 was encumbered by calculations and reductions which may be seen 



