234 
Mr. Barlow on the rules and principles for 
point or stop. A board about two feet square, covered with 
black crape, and having a clean circular piece of card paper, 
with fine cross lines upon it, was placed at a convenient 
measured distance from the lens, and then the draw tube was 
adjusted till we had the focus exactly coincident with the 
cross wires. This is easily ascertained, by moving the eye a 
very little upwards and downwards. Then, when the image 
does not fall exactly on the wires, this motion of the eye will 
produce an apparent motion between the cross wires on the 
telescope and those on the card ; but when they are coinci- 
dent, then, however the eye may be moved, the image and 
the cross wires will be at rest. This being determined, the 
focal length for this distance of the object is read off as above 
described. Let this focal length be/, the distance d, radii r, r', 
and index 1 a ; then, by a simple inversion of the well 
known formula for the focal length of a lens, we have 
a 
r r 
r + r' 
But as for these experimental purposes we made the radii 
equal, or r = r', this formula became simply in this case 
a 
rti+i) 
- - (i). 
The only possible source of error this method involves, is 
in the measurement of the tools ; but this, from repeated 
experiments, we found might always be determined to within 
less than a five hundredth part of the radius, which can only 
affect the result to the amount of about TTooth part of the 
index. 
