54 Messrs. Ryland and Lang. On Measuring [Jan. 9, 



the instrument is held in front of the face with the shaped end against the 

 forehead. One eye, say the left, is covered, and the patient is instructed, 

 the first index being at D, to move the scale index along the plate B until 

 it apparently lies just behind the first index at a. Without altering the 

 position of the instrument, a similar observation is made with the other 

 eye, the scale index being moved to b. The first index is now moved to E, 

 and similar observations taken for each eye, giving the readings c and d 

 respectively for the scale index. 



Then (in fig. 1) join LE, and produce DE to F and to N. Let the distance 

 ab = y, cd = y', EF = x, ED = d, ND = z. 



Let E be the position of the right eye and L that of the left, and let 

 EL = V be the distance between the centres of rotation. Then V may 

 be determined graphically by a simple construction, or, assuming the base 

 line EL to be parallel to SS, may be calculated as follows : — 



From fig. 1 we have 



mpL) = z and Y*= z+d , 



y y 



from which V = d, or V = , d W} . 



\y y I ^y -y{d+x) 



In practice, as only two variables occur in this equation, namely y and y', 

 a table may be computed and used with the instrument. 



In the second form (fig. 2) the instrument has three fixed vertical indices, 

 K, L', and M. The vulcanite plate and sliding index are similar to those 



Fig. 2. 



employed in the first form. With the left eye covered, the white index is 

 moved till it is apparently behind L' at p, and M at n. Similar observations 

 are taken with the left eye, the scale index being moved till it is apparently 

 behind the indices K and L' at q and s respectively. As with the first 

 instrument described, the distance EL = V may be obtained from a simple 



