6 Mr Barlow On the Practical Construction 
Let the angle in the first of the columns be denoted by 
Q 
in the second by 
in the third, or the half difference, by 
P 
d 
And that in the fourth, or angle of prism, by 
a 
Then the rule for computing the index may be stated in 
words at length as follow : 
7. Rule for computing the Index of R fraction. 
1. To the angle P add the angle d, and subtract 4 a from the 
sum, and call the remainder = A. 
% Add l a and d together, and call the sum t= B. 
S. Add together cotangent \ «*, tan A and tan B ; subtract SO 
from the sum, and find the angle of which the remainder 
is the tangent, and call it — D. 
4. From D subtract \ a , and call the remainder = E *f*. 
5. From cos Q subtract cos E, and find the natural number an- 
swering to the remainder as a logarithm, and it will be 
the index sought J. 
* In all these cases the log tan, &c. is to be understood. 
•f If? in any instance, the angle A should be less than 90°, then, instead of the 
angle D, as found above, we must take its supplement, or what it wants of 180 p , 
in order to find E. 
t The algebraical expression for this rule, which will be more intelligible than 
the above to those acquainted with analytical subjects, may be expressed as below., 
Operation. Flint Prism. First Observation. 
To P = 104° 10' To | a = 12° 24'J 
Add d = 7 55 Add d = 7 55 
From sum = 112 5 Sum B = 20 19 
Subtract | a = 12 24| 
A= 99 41 
Cot | a - 12° 24' - 10-6578454 
Tan B =20 19 - 9-5684856 
Tan 84° 13' = D 
10-9942660 
tan D = cot \ a tan (P + d — . | a) tan (d -f k a) 
See Biot, Traite de Physique . 
