628 
ME. AIEY’S ACCOrXT OF THE COXSTEUCTIOX OF 
Avork), but Avere knoAvn (by the friendly communication of the Director and Officers of 
the Survey) to the persons engaged on the National Standards. Secondly, a tubular 
scale 5 feet long, Avas prepared in the year 1833 for the Eoyal Astronomical Society, and 
Avas compared Avith numerous standards in the year 1834. 1 must refer to Daily’s 
account of the comparisons in the Memohs of the Eoyal Astronomical Society, vol. ix. : 
but 1 may extract the folloAving points. After experimental proof of the mjmious 
effects of resting the tube upon tAVO fixed supports, it Avas placed upon tAvo rollers, at 
the quarter-length distance from each end. A frame caiT}ing tAvo microscopes Avas pre- 
pared, for observing the divisions of the tubular scale and those of other bars or scales 
AAliich might be brought for comparison. A AieAV of this is gNen in page 75 of the 
accouirt to Avhich I refer : its structure Avas A^ery Aveak. The scale in question Avas com- 
pared Avith several similar tubular scales, aird AAith the Imperial Standard. MoreoA'er. 
lines for obserAation Avere cut at the distarrce 60 inches on foru- sides of the tube, 
and their iirtervals Avere compared. It is impossible by extracts to do justice to this 
paper ; I can orrly remark that any persorr who Avishes to become acquainted AAith the 
state of the Imperial Standard and the impossibility of observing it accurately, AAith the 
errors of conrparisorrs before 1800 and the inaccuracies after that tirrre, must strrdy this 
merrroir. At the same time I remark, that, as aaIII appear hr the course of the present 
conrmunicatiorr, on some importarrt poirrts there Avas still roorrr for additional exactness. 
The lerrgth of the seconds’ perrdulum Avas measured by Bessel hr 1835 (I shall allude 
shortly to an important correctiorr previously made by him hr the theory of the pendu- 
lum). The method which he used Avas that of observing the Aibrations of two pendu- 
lurrrs Avliose differeirce of lerrgth is exactly equal to the starrdard (oire toise). This is, so 
far as I arrr aAvare, the only instance irr AAirich air end-standard has been used for a 
physical measure Avithout the essential aid of optical apparatus. 
In the same year, Bessel constructed the ireAV Prussian Standard of three Prussian 
feet. This is an end-standard ; the bar being of steel, and the ends being of sapphire. 
A line-standard had been made in 1816, but Bessel’s confidence in hne-measru'es 
appears to have been shaken, partly by Katek’s discovery of the effects of tri fli ng flexure, 
mentioned above (though he acknoAvledges that the means of obA’iatmg the injrmous 
effect is extremely simple), and partly by Daily’s remark on the “ personal equation ” or 
difference in the Avay in Avhich different persons observed the large and distorted point 
on Graham’s 1760 bar. Moreover, the laAv of Prussia defined the Prussian Foot hr terms 
of the French Toise, Avhich is represented by an end-standard. This chcrrnrstance, in 
combination Avith the application of the toise to the indirect measure of the pendulum 
mentioned above, appears sufficient justification of the introduction of an end-standard. 
These are the principal points in the history of standards bearing upon the accuracy 
of comparison and application of standards. But a discoA'ery had been made in a related 
subject, Avhich bears importantly upon the legal provision for the restoration of the 
British Standard in case of its loss. Bessel discovered that the correction Avliich had 
been usually applied, and Avhich Avas applied by Katee, for reducing the vibrations of a 
