176 An Account of Experiments for determining the Length of 
accuracy truly surprising, when it is considered that all errors of 
observation are included in this minute quantity. 
Comparison of the different Standards. 
The microscopes being placed at the distance of 39:4 inches, 
were advanced by single tenths, from zero of the scale through 
the space of two inches; and the mean of twenty measurements 
thus obtained being compared with the distance from zero to 
39:4 inches, this last was found to be in defect 1-2 divisions of 
the micrometer, or ‘00005 of an inch. And as this is the por- 
tion of the scale employed in ascertaining the distance between 
the knife edges, this difference must ultimately be subtracted to 
obtain the distance of the knife edges, in parts ‘of the mean value 
of the scale*, 
From the high. importance which attaches to General Roy’s 
scale, as having formed the basis of the Trigonometrical Survey 
of the kingdom, I was particularly desirous of comparing it with 
that of Sir G. Shuckburgh, in order that 1 might be enab‘ed to 
give the length of the pendulum in parts of that standard which 
constitutes the foundation of one of the most important scien- 
tific operations ever carried on in this country. Fortunately, 
this scale was purchased at the sale of General Roy’s effects by 
Mr. Browne, who readily confided it to my care. From the mean 
of a number of comparisons, I found the distance from zero to 
39°4 of General Roy’s scale, equal to 39°40144 of Sir G. Shuck- 
‘burgh’s standard f. 
The standard yard made by Bird in 1758, for the House of 
Commons, better known by the name of Bird’s Parliamentary 
standard, is little adapted for measurements where great preci- 
sion is necessary. The yard is determined by two large dots 
made on gold pins which are let into a bar of brass. The mean of 
a num- 
* From an examination of this scale by the late Sir G. Shuckburgh, it 
appears that the greatest liability to error is ‘00033 of an inch, or, as cor- 
ag ys «i Mr. Troughton, -000165 of an inch, the chances against which are 
as oO 
+ The very great difference between this result and that stated by Sir Gea. 
Shuckburgh, in the Philosophical Transactions for 1798, renders it necessary 
for me briefly to detail the manner in which the comparisons were made. 
The two scales were placed in contact, and remained thus for twenty-four 
hours ; after which, sixteen comparisons were taken in the course of the 
day; but these were rejected in consequence of the temperature having in- 
creased six degrees during the operation. When the scales had been to- 
gether forty-eight hours, sixteen other comparisons were made during two 
succeecing days, the thermorheter remaining steadily at 70’. The greatest 
difference between any one of these last and the mean result, did not 
zmount to four divisions of the micrometer. The mean of the first set of 
observations exceeded that of the last by ‘00017 of an inch. Imagining 
that the difference between Sir George Shuckburgh’s result and mine, might 
possibly 
