a fmple Micrometer. 291 
3. If the angle be exprefled in minutes and feconds, turn 
it all into feconds, and proceed as above. 1 
Example. At wh&t diftance is a globe of one foot in diame- 
ter when it fubtends an angle of two feconds ? 
2 : 3600 :: 687,55 : 3 6 oox ^ 68 .7vSj _ lz ^^ 0 inches, oi‘ 
103132! feet, which is the anfwer required. 
This calculation may be Ihortened ; for fince two of the 
three proportionals are fixed, their product in the firft cafe is 
41253, and in the other two cafes is 2475180 ; fo that in the 
firft cafe, viz. when the angle is exprefled in minutes, you 
need only divide 41253 by the given angle; and in the other 
two cafes, viz. when the angle is exprefled in feconds, divide 
247 5 1 80 by the given angle, and the quotient in either cafe is 
the anfwer in inches. 
Problem II. The angle, not exceeding one degree, which is 
fubtended by any known extenfion, being given, to find its 
diftance from the place of obfervation. 
Rule. Proceed as if the extenfion were of one foot by Pro- 
blem I. and call the anfwer B; then, if the extenfion in 
queftion be exprefled in inches, fay, as 12 inches are to that 
extenfion, fo is B to a fourth proportional, which is the anfwer 
in inches ; but if the extenfion in queftion be exprefled in feet, 
then you need only multiply it by B, and the product is the 
anfwer in inches. 
Example. At what diftance is a man, fix feet high, when 
he appears to fubtend an angle of 30". 
By Problem I. if the man were one foot high, the diftance 
would be 8 2506 inches ; but as he is fix feet high, therefore mul- 
tiply 82506 by 6, and the produft gives the required diftance, 
which is 495036 inches, or 4 I2 53 
Q ft 2 
For 
