372 
CAPTAIN KATER ON THE ERROR IN 
I shall now state the results which have been obtained from the comparisons 
I have detailed. 
It has been already shown that a correction must be applied to the observed 
length of the scale, to reduce it to the chord of the given curvature. This, if 
the scale is only 36 inches long, may be applied at once ; but with Sir George 
Shuckburgh’s scale, the length of which is 60 inches, it becomes necessary first 
to find the difference betiveen an arc of 60 inches and its chord, and then to 
take the proportional part of this difference for 36 inches. The same must be 
done with Mr. Dollond’s scale, which is 41 inches long, and with my own, 
the length of which is 45.2 inches. 
The following Table gives the difference between the arc and its chord, and 
the proportional part where necessary for 36 inches. 
Versed Sine. 
Difference of the Arc 
and its Chord on 
36 inches. 
Proportional part for 
36 inches. 
Equivalent 
Divisions of 
Micrometer. 
inches. 
inches. 
inches. 
.012 
.00001 
.02 
.00002 
.03 
.00006 
.04 
.00009. 
2.1 
.05 
.00014 
Difference of the Arc 
Versed Sine. 
and its Chord on 
60 inches. 
.012 
.000005 
.000003 
0.0 
.02 
.000013 
.000008 
0.2 
.03 
.000030 
.000018 
0.4 
.04 
.000054 
.000032 
0.8 
.05 
.000084 
.000050 
1.2 
.10 
.000400 
.000240 
5.0 
Difference of the Arc 
Versed Sine. 
and its Chord on 
41 inches. 
.05 
.000122 
.000107 
2.5 
Difference of the Arc 
Versed Sine. 
and its Chord on 
45.2 inches. 
.05 
.000112 
.000089 
2.0 
Having applied the reduction to the chord, we obtain the error occasioned 
