360 
CAPTAIN KATER ON THE ERROR IN 
losophical Transactions for 1821, not to differ sensibly from the Imperial 
standard yard. 
The bars intended for the Exchequer, &c. were half an inch thick and 
one inch and a quarter wide ; the thickness being nearly the same as that 
of Sir George Shuckburgh’s scale. 
The dots upon the surface of the bars having been adjusted, so that then- 
distance appeared to be equal to the distance from zero to thirty-six inches 
on Sir George Shuckburgh’s scale, further comparisons were made after 
the plugs carrying the dots had been securely fixed ; “ and it was with sur- 
prise and disappointment that I found the whole of them apparently too 
short. They had been adjusted upon a board of mahogany carefully planed ; 
and the table upon which they were now placed was so flat as to occasion 
little alteration in a spirit-level passed along it. The error of the stand- 
ards was, however, far too considerable to be attributed to any curvature 
which on this occasion could take place ; and it was not until after several 
days that I discovered the cause of this perplexing circumstance. I found 
that by placing a card, the thickness of which was accurately one-fiftieth of 
an inch, under the middle of the standard, the distance of the dots was much 
increased ; and by placing a card of the same thickness under each of the 
extremities, and withdrawing that which was under the centre, the distance of 
the dots was considerably diminished. The total difference amounted to no 
less than .0016 of an inch; whilst the double of the error, which would have 
arisen from mere curvature under similar circumstances, would not have been 
one ten-thousandth of an inch. 
“ The cause was now evident : by elevating the middle of the standard, the 
under surface was shortened and the upper surface extended ; and on the 
contrary, when the extremities were elevated, the upper surface was com- 
pressed and the lower surface lengthened ; the quantity of the effect evidently 
depending upon the thickness of the bar. 
“Having thus assured myself of the source of the error, a method of 
obviating it soon presented itself. As the upper and under surfaces of the bar 
are in different states, the one being compressed and the other extended, there 
must be an intermediate plane which suffers neither extension nor compression; 
and this plane must be nearly midway between the two surfaces. I therefore 
