-L. Bell—Absolute Wave-length of Light. 175 
Besides the experimental difficulties of the task, it is far from 
an easy matter to secure proper standards of length. The 
standards used in various former investigations have proved to 
be in error, sometimes by a very considerable amount, and 
indeed very few of the older standards are above suspicion. 
As Peirce has very justly remarked in connection with this 
subject, ‘‘ All exact measures of length made now must wait 
for their final correction until the establishment of the new 
metric prototype.” Short standards of length are in some 
respects peculiarly liable to error, since they must be compared 
with the subdivisions (often not sufficiently well determined) 
of secondary standards, and small sources of uncertainty such 
as poor defining lines, slight changes in the apparatus and the 
like, of course are much more serious as the length is less. 
Fortunately there were available for the measurement of the 
gratings two standard double decimeters which have been de- 
termined with almost unprecedented care by Professor W. A. 
Rogers. ‘l’hey are upon speculum metal; were graduated and 
determined by Professor Rogers early in 1885 and were pur- 
chased by the university late inthe same year. They are desig- 
nated respectively Sf and S§ and are discussed at length in the 
Proceedings of the American Society of Microscopists for 1885. 
The bar S, is 23°" in length. Near one edge is the double 
decimeter S? divided to centimeters, the 5™ lines being triple. 
S, is 27™ in length and graduated in the same way. ‘The 
defining lines in both are fine and sharp and the surfaces are 
accurately plane. ‘hey are standard at 16°°67 C. and from an 
elaborate series of comparisons with four different standards 
the coefficient of expansion was found to be, 
17:946 ju per meter per degree C. 
S¢{ and S% depend for their accuracy on a long series of inde- 
pendent comparisons with Professor Rogers’ bronze yard and 
meter R, and steel standards whose relation to R, was very 
exactly known. R, has been determined by elaborate com- 
parisons with various standard meters and yards, and is de- 
scribed and discussed at length in the Proceedings of the 
American Academy, vol. xviii. The length of the meter was 
determined both directly and through the yard, by comparison 
with the following standards : 
I. The meter designated T, copper with platinum plugs, traced 
and standardized by Tresca in 1880 from the Conservatoire line 
metre No. 19, which bears a very exactly known relation to the 
Metre des Archives. 
IJ. The yard and meter designated C. S., brass with silver 
plugs, belonging to the Stevens Institute. The yard was com- 
pared with the Imperial Yard in 1880 so that it is directly and 
