CAPTAIN KATER ON THE ERROR IN 
374 
Versed 
Sine. 
Sum of 
Errors. 
Sum of Errors 
Reduced to a 
Versed Sine of 
.01 of an inch. 
inches. 
.01 
.02 
.03 
.04 
.05 
inches. 
.00061 
.00107 
.00132 
.00179 
.00223 
incites. 
.00062 
.00053 
.00044 
.00045 
.00045 
Mean . . 
.00050 
The errors arising from the thickness of different scales, though nearly in 
proportion to their thickness, do not seem to follow any very regular law, but 
to depend in some measure upon the manufacture of the material employed, 
as well as upon the thickness of the bar : thus if we reduce the error of each 
scale to what it would have been had the scale been half an inch thick, thirty- 
six inches long, and the versed sine equal to .01 of an inch, we have the fol- 
lowing results for comparison. 
Errors resulting from a varied sine of .01 of an inch, the bar being supposed 
thirty-six inches long, and half an inch thick. 
Error when 
curved 
upwards. 
Error when 
curved 
downwards. 
Sum of Errors 
with a Versed 
Sine of .01 of 
an inch. 
Imperial Standard Yard 
inches. 
.00013 
.00017 
.00012 
.00025 
inches. 
.00031 
.00042 
.00056 
.00061 
inches. 
.00044 
.00059 
.00068 
.00086 
Sir George Shuckburgii’s Scale. . 
Mr. Dollond’s Scale 
Captain Kater’s Scale 
Here it may be seen that the sum of the errors of my scale is the greatest, 
and this scale is upon a bar of cast brass not hammered. 
Mr. Dollond’s scale is of plate brass, and Sir George Shuckburgh’s appears 
to be made of cast brass faced with plate brass. 
The Imperial standard yard is upon a bar of brass, which I should judge from 
its apparent hardness to have been well hammered ; but the preceding result 
given from this bar must be too little, as it has been shown that a wire .012 of 
an inch diameter was more than sufficient to produce the greatest errors to 
which the bar is liable. 
