Standard Measures of Length. 99 



archives reduced to that temperature by the known coefficient 

 of expansion, {b) The subdivisions of the centimeter must be 

 sensibly equal. 



As a perfect test of the homogeneous character of the sub- 

 divisions, I offer the following scheme as a check : 



The distance from The distance from 



line I to line 2 = line iot to line 100 



line I to line loi line loi to line i 



It will be seen that this test, with the exception of one par- 

 ticular curve, completely covers the case of periodic or accumu- 

 lated errors, and it is precisely this class of errors which re- 

 quire the most careful investigation. 



The problem of the subdivision of a given unit into exactly 

 equal parts, is an extremely difficult one, as the many failures 

 the writer has made will abundantly testify. 



With the experience which I have had, I can hardly agree 

 with the remark of Mr. Beck on page 310 of the -Proceedings of 

 the Royal Microscopical Society, that there would be no difficulty 

 whatever in obtaining scales ruled according to a uniform 

 standard. I have a large collection of micrometers by different 

 makers, both at home and abroad; I have standards by Froment 

 and Brunner, of Paris, and Merz, of Munich ; I have transfers 

 from every well-known precision-screw in this country, includ- 

 ing such makers as Buff & Berger, of Boston ; Clark, of Cam- 

 bridge ; Brown & Sharpe, of Providence ; Rutherford, of New 

 York ; Clement, of London ; Salleron, Bianchi, Froment, and 

 Perreaux, of Paris. The investigation of these transfers is not 

 yet quite completed, but I feel safe in saying that no two of 

 them agree at a given temperature, and the errors of subdivision 

 are, in many cases, very large, and in all cases easily measura- 

 ble. Of the micrometers made abroad, the best I have seen 

 are by Powell and Leland. They are superbly ruled, and the 

 errors of subdivision are much less than usual, but in the two 

 plates measured the unit was found to be nearly ij^ per cent. 

 too long. 



By the kindness of Professor J. E. Hilgard, Assistant in 

 Charge of the U. S. Coast Survey, I obtained the opportunity 

 of comparing the unit of my own screw with the Brunner 



