50 



Journal of the Mitchell Society [September 



The middle ordinate (M) of an are whose central angle is a° and 

 whose chord is c feet, is given by the formula : 



M = R vers i/oa (4). 



c" 

 Also M ^= approx (5). 



8 R 



Formula (5) shows that for any radius, the middle ordinates vary 

 as the square of the chords. The above formulas were used in com- 

 puting Table III. 



Assuming the arc to be parabolic, we ha-ve a convenient relation 

 between ordinates at any point along the chord and the middle ordi- 

 nate. See Fig. 3. For example, an ordinate at 8/10 of the chord- 

 length from one end of the chord is 6/10 of the middle ordinate. 



In practice, the middle ordinate is usually less than 1.0 foot, pro- 

 vided the chords do not exceed the limit where they vary more than 

 .05 ft. from the arc. Table III shows these limits to be as follows : 



middle ordinates uj) to 1.31 ft. 



