82 On a Possible Exjolanation of the Method employed by Nohert 
througli this cylinder, was first set in position. The gravity slide 
having been firmly clamped down upon the ways, the open space 
surrounding the nut was then filled with plaster of Paris. 
In this way the screw is set in perfect adjustment for one 
position of the gravity slide. Practically, it is found to be in good 
adjustment for every position upon the ways. But any slight 
deviation from adjustment in a horizontal direction is corrected by 
means of the adjustable ways, while that in the vertical direction is 
for the most part overcome by leaving one end of the precision 
screw free. 
Good results have also been obtained by using a " free nut." 
In this case nice adjustments are unnecessary, as the nut moves 
freely upon the screw, pushing the gravity slide before it. If this 
arrangement is adopted, care should be taken that the nut, if not 
symmetrical with respect to the screw, should fall freely in the 
direction of gravity, and bear at every point throughout its whole 
length against whatever holds it in position while the screw is in 
action. The most serious objection to this arrangement is a certain 
amount of lost motion, which seems inevitable. 
It is not to be inferred that all periodic errors have been over- 
come by the arrangement described above ; but experience has 
shown that they have been very much diminished. In fact, I have 
never succeeded in ruling but two precisely similar plates, in which 
there was an exact coincidence of every line from beginning *to end, 
when examined under the microscope. In one plate of 100 lines, 
ruled with great care, each interval being y^To inch, there are, 
according to three independent measures made by different persons, 
eighty-four cases in which the errors are less than xooVoo 
inch, and the greatest individual error is -^j^q-q of an inch ; but the 
maximum periodic error varies with the different observers between 
sTnhnrand^^^of aninch. 
Nobert's bands proceed by increments of 5630 lines to the 
English inch. The following table gives the number of lines to the 
inch in each band. 
Band. 
Lines in an inch. 
Band. 
Lines in an inch. 
1 
11259 
11 
67556 
2 
16889 
12 
73186 
3 
22519 
13 
78816 
4 
28148 
14 
84445 
5 
33778 
15 
90075 
6 
39408 
16 
95705 
7 
45037 
17 
101334 
8 
50667 
18 
106964 
9 
56297 
19 
112594 
10 
61926 
