252 
angles to their axes, like the cavities adopted by Mr Baily, at 
the writer’s suggestion, near the ends of the standard yards and 
their copies. Let s denote the length of the original standard, 
c that of the copy @ traits. | 
Then, the end D of the bar DE being brought into contact 
with the end B of AB, the distance CF may be compared by 
microscopes with c. Again, A being brought into contact with 
fi, FC can be compared in the same manner with c. And AB, 
DE may be compared with s by touch. From the data thus 
obtained the difference between s and c may be readily found. 
The cavities formed in the middle points of the bars must 
weaken them so as to materially injure their value except for 
the single operation described. 
The same end may however be attained without the neces- 
sity of sinking cavities down to the axes of the bars. The 
object of the Observer is to obtain a visible mark invariably 
fixed for some hours or some days in the axis of each bar near 
its middle point. 
At the middle of each bar let a right-angled prism be at- 
tached with its two smaller faces parallel to the vertical and 
horizontal faces of the bar supposed to be square. Attach also 
a small plate of glass, having a fine line traced upon it, in such 
a position that the line seen by total reflexion in the prism may 
appear to cross the middle point of the axis of the bar at right 
angles to it. 
The marks thus obtained in the axes of the bars may now 
be used instead of the lines C, F traced in cavities sunk in the 
bars, and the operation of comparing c with s will be exactly 
the same as that which has been already described. 
In a Memoir by Steinheil on the construction of a compa- 
rateur for measures d bouts in the 27th Volume of the Denk- 
schriften der Akademie der Wissenschaften of Vienna, pave 
166, it is stated that the probable error of a comparison by 
touch is 000005 millimétres, and that of a single comparison 
