354 



Mr. G. Forbes. 



[Feb. 22 



Again, we see from (7) that the error arising from want of adjust- 

 ment of the prisms 



= — i a (sin <£ 2 — sin <^> 1 ), 



which is clearly a maximum for a fixed value of i, if <j> 2 -<f>i = J71-, 

 when 



<f>2 = + and <£ 2 = -Jtt. 



This occurs when the plane parallel to the axes of the two prisms is 

 at right angles to a plane cutting the prisms symmetrically. 



And, if I be the greatest possible inclination of the axes of the two 

 prisms to each other, through bad adjustment, then the error in the 

 angle used for finding the range cannot exceed 



J2 . lac for the half-base and 2 J2 . la. for the whole base. 



Also it appears that there is no error in this angle when the axes of 

 both prisms are in one plane cutting the prisms symmetrically. Simi- 

 larly, if the plane of the axes is at right angles to this plane there is 

 no vertical displacement of the image. 



It is found that with ordinary care in use the maximum value of I 

 need never exceed one or two minutes of arc for a long period after 

 the adjustments have been made. Now, in order to attain an accu- 

 racy of 2 per cent. (60 yards) in 3000 yards, we may not have an 

 error greater than 2 -8 seconds of arc. Hence, if I amount to 1', we 

 must have 



2" -8 



a. less than = = 0*0165 = nearlv 1°, 



r x 2 J2 J 



but the diameter of field of view of the instrument is 2°. Hence it is 

 possible to observe the object in any part of the field of view, without 

 error amounting to the prescribed limit, if the inclination of the axes 

 of the prisms to each other does not exceed 1'. And by bringing the 

 object viewed to the centre of the fields limited by the outer prisms 

 the accuracy of the base is practically perfect. 



The only defect of the hinge which can lead to error is due, as stated 

 above, to a rotation of one-half of the base with respect to the other 

 half of the base, about the line of the base. When this occurs, the 

 two fields of view seen by the two eyes are not the same, although the 

 object whose distance is required may be in both fields. The conclu- 

 sions arrived at in this section prove that, if the prisms in each half 

 base were parallel to within 1', then, if one image can be seen in any 

 part of its field when the other is in the centre of its field, the error is 

 under the limits assigned, and this would involve an error of 1° in the 

 allignment of the two halves of the base. It would be very incon- 

 venient to have the two fields of view differing so much in appear- 

 ance ; and this error never amounts in practice to the prescribed limit. 



