330 
Proceedings of Royal Society of Edinburgh. [sess. 
giving an error of + 2'. . 39”, from which, we infer 
{u-v} = 96°. . 10'. . 48" ) 
V field = 25°.. 40'. 
{v} = 42 . . 34 . . 58 ) 
This value of POR, 96° . . 11', differs by six degrees from the deter- 
mination of Mr Uicol ; hut as the surface according to that gentleman 
§is inclined by seven degrees to the position assigned by theory, it 
follows that the value of v, or the position of the plate of balsam in 
reference to the axis of the crystal, is nearly the same in his instru- 
ment, as by the above determination. 
If, indeed, an eye-piece, constructed according to the directions of 
the inventor, be placed so that the light from any object pass in 
the interior parallel to the length of the rhomb, that object will he 
found considerably nearer the limit of the ordinary than that of 
the extraordinary light. 
The above angles are sufficient to guide the operator in the con- 
struction of the eye-piece. But it is to he remarked that the advan- 
tages sought in this construction do not balance the disadvantage 
of a diminished field ; and that Mr Uicol’s dimensions are preferable. 
Having now completed the investigation of the best form for a 
rhomb whose faces are obtained by cleavage, I shall proceed to 
investigate the absolutely best form independent of that considera- 
tion. 
In strictness, this investigation ought to he founded on the above 
values of POU, PO^. It ought to include the solution of the 
equation 
POU + PCh/ = 2(/x - A.) . 
The root of that equation determined, the value of POU - POw 
should he thence deduced. Then the maximum value of that field 
ought to he sought, g and A, being the primary variables. 
Or if the condition of non-refraction of the line of sight be 
included, /x becomes a function of A, and hence the differentiation 
becomes monome. This investigation however is, on account of its 
complexity, almost impracticable : for it I shall substitute another. 
Instead of seeking the maximum separation of the limiting rays 
exterior to the rhomb, I shall seek for that position of the plate of 
balsam which gives the greatest internal divergence, which depends 
