THE NEW NATIONAL STAND AED OF LENGTH, AND ITS PEINCIPAL COPIES. 685 
Section VIII . — Formation of Fnd-measure Bars. 
The form given to the end-bars depended in some degree upon the process adopted for 
comparing end-measure bars with line-measure bars, which originated, I believe, in a 
suggestion from myself. Suppose that we have two end-bars, each nearly equal in length 
(as measured between its extreme ends) to the length of the line-bars (as measured from 
line to line). Suppose also that each of the end-bars has a well sunk to the middle of 
its depth, with a transverse line cut upon a pin (as in the line-measures); the line being 
not necessarily at the middle of the length of the bar, though it is essential that its 
distance from the centre of the bar’s length be nearly the same in both end-bars. As, 
generally, one segment of the bar, from the transverse line to the end, will be longer 
than the other segment, let the longer segment be denoted by -|- and the shorter by — . 
And suppose that the two bars are placed end to end, the -}- end of one being opposed 
to the. — end of the other, as shown in Figime II. The distance between their trans- 
verse lines will evidently be the sum of the + segment of the first bar and the — seg- 
ment of the second bar ; and the conditions that I have stated, as to the similar division 
of the lengths of the two bars, will make that sum so nearly equal to the length of the 
line-measm’e, that the difference may be measured by the micrometer-apparatus. Then 
interchanging the positions of the end-bars, so that their other ends shall be in contact, 
the distance under observation will be the sum of the — segment of the first bar and 
the -f- segment of the second bar. Adding together the two measured distances, we have 
a comparison of the sum of the two end-bars with double the length of the Ime-bar. 
In order to make this determination available, it is necessary further to determine the 
difference between the whole lengths of the two end-bars. A felicitous suggestion by 
Mr. W. Simms, jun. gave the means of doing this. Mr. W. Simms’s proposal was, to 
apply the process above described to three end-bars, determining the measure of the sum 
of each pau- of end-bars in reference to double the length of the line-bar ; then there 
are given three equations to find three unknown quantities. The length of each of the 
three end-bars is thus found without difficulty. 
The general principle of determining the lengths of the end-bars by the contact of 
their ends (without the use of supplementary pieces, such as had been employed in all 
pre-vious determinations) being adopted, it was important to decide on the form of those 
ends. In the opinion of the Committee, the use of plane ends could not be sanctioned. 
One difficulty attending them is, the uncertainty as to the removal of particles of dust, 
&c. from every part, and the certainty that if any such particles remain they will disturb 
the measure of the bar ; while at the same time the act of pressing two bars together, 
either with or without a slight movement, does not tend to remove the particles. An- 
other difficulty is that, even though we were assured that the ends are perfectly clean, 
yet we cannot be assured that the bars, when laid in a horizontal position end-to-end, 
will touch in the whole breadth of their ends ; inasmuch as, if the position of one of the 
bars is slightly erroneous in azimuth, or slightly erroneous in inclination to the horizon, 
MDCCCLVII. 4 u 
