54 W. A. Rogers—New Diffraction Ruling Engine. 
one, the peduncular groove being in the conical valve. As it 
is evidently new, I propose for it the name D. conica, and 
reserve a full description of it, and further remarks on the 
locality, for another paper. 
These developments establish this beyond doubt as a stratum 
of the Trenton limestone. | 
ART. IX.—On the first Results from a new Diffraction Ruling 
ngine ; by WILLIAM A. ROGERS. 
THE best diffraction gratings are subject to three classes of 
errors :— 
First, The accidental errors of single subdivisions, which are, 
for the mos e irregular motion of the ruling 
diamond upon a non-homogeneous meta 
econd. ‘The periodic or systematic errors, which are a func- 
tion of one revolution of the ruling-screw. 
Third. Errors which depend upon the position of the nut 
upon the screw, and which are equivalent to a varying pitch of 
the screw. 
The errors of this class may be due either to the form of the 
screw itself, to a variation in its diameter, or to an imperfect 
mounting of the screw. The pitch of even a perfect screw 
practically undergoes a slight change with every variation of 
the amount of the friction between the moving parts of the 
ruling-engine. 
et us take as a type, the magnificent rulings of Mr. L. M. 
Rutherfurd, executed by Mr. D. C. Chapman. These gratings 
easily surpass all others in their resolution of the lines of the 
solar spectrum. Here, the first class of errors is so far wanting 
that it is safe to say of a given space, that it is so nearly equal 
to its neighbor that the most rigid investigation with the micro- 
scope will fail to reveal any difference. 
_ For separate, narrow and adjacent spaces then, a well-made, 
and well-mounted screw is subject to less liability to error than 
the microscopic observation with which the comparison is made, 
even under the manipulation of the most skillful observer. 
ith regard to the second class of errors, viz: those which 
are a function of one revolution of the ruling screw, it is to be 
said that the danger of their occurrence is far greater. Indeed, 
I am not aware that they have ever been entirely overcome. 
In the measures of single narrow spaces they easily escape de- 
tection. For example, suppose we have a screw having a pitch 
of one-twentieth of an inch, in which the first half of one revo- 
lution differs from the second half by one ten-thousandth of 
