Standard Measures of Le7igth. 97 



single measurement from the mean of the whole ; from which 

 it will be seen that the probable error of a single measurement 

 would have to the probable difference of a pair the ratio of 

 unity to the square root of two. The probable error, there- 

 fore, of a measurement made with the inch object-glass, of a 

 space easily contained in its field, is twenty-eight ten-millionths 

 of an inch; and the probable error of a measurement made with 

 the quarter-inch object-glass is twenty-two ten-millionths of 

 an inch. 



Hudson, Ohio. 



»«»« 



STANDARD MEASURES OF LENGTH. 



BY PROF. W. A. ROGERS. 



[Received December loth^ i8yS.) 



The statement on page 10 of the last number of the Journal 

 i^Transaciions) gives me a larger share of credit in the produc- 

 tion of a standard micrometer than is my due. It may be true 

 that I have attacked the problem of a standard inch and a 

 standard centimeter in a way somewhat different from that 

 usually pursued, but others have precisely the same means of 

 solving the problem as I have. First of all. Dr. Edward Clark, 

 of the U. S. Coast Survey, has access to the originals from 

 which my yard and meter-bars were constructed ; he has had 

 long experience in measures of precision, and has abundant 

 facilities for executing the work. 



What is needed in the determination of an aliquot part of a 

 true standard, is a good comparator, suitable both for long and 

 for short measures of length. Instruments of this character 

 are to be found at Johns Hopkins University, at the University 

 of Pennsylvania, at Princeton College, at Stevens Institute, 

 Hoboken, and Mr. Chapman of New York has recently con- 

 structed one to facilitate the pendulum researches of Mr. C. S. 

 Pierce, of the U. S. Coast Survey. There is also a well-mounted 

 instrument at West Point, by Grunow, but it is for end measures 

 only. 



It may be that others besides myself have given attention to 

 the important problem of obtaining a centimeter which is ex- 

 actly one one-hundreth part of a true meter at a given tempera- 

 ture. It would certainly be very desirable if several inves- 

 tigators could take up this problem independently. But 



