296 PROCEEDINGS OF THE AMERICAN ACADEMY 



face of the bed-plate on either side can be brought to a plane which 

 shall be parallel with that through which the microscope moves, by 

 working it down till every part remains in the same focus. The bars 

 to be compared are placed directly upon the surface thus prepared. 



(d.) The form and material of a bar which is best adapted to fulfil 

 all the conditions which are essential to success in comparisons extend- 

 ing over a long period of time. 



In general, the form of a standard bar should be the same as that 

 with which it is to be compared. For example, if one desires a stand- 

 ard yard which is to be compared with "Bronze 1 1," at Washington, 

 the bar should be made of Baily's metal, and should be one inch 

 square and about thirty-eight inches long. Kater preferred a thin bar. 

 A width of one centimeter with a depth of three centimeters will be 

 found to yield good results when the bar is placed upon a fiat surface. 

 Of all the forms proposed, that of M. Tresca, which has been adopted 

 by the International Commission, seems to me the best designed to 

 overcome all the difficulties of the problem. It is convenient to han- 

 dle ; it retains its form under its own weight, and cpiickly answers to a 

 given change of temperature. I have had the pleasure of using a bar 

 of this form for several months with the most satisfactory results. I 

 began with considerable prejudice against it, influenced to some degree 

 by a remark made by Professor Wild concerning it. It is undoubtedly 

 somewhat difficult to manufacture, and will probably be found to be 

 rather costly ; but these are the only serious objections that can be 

 urged against it. I express the opinion that it is well adapted to scien- 

 tific work of the highest order. For use with my own bar, I have had 

 constructed a special objective provided with an interior illuminator. 

 The working distance is just sufficient to allow the passage of the bar 

 under it. 



(e.) Tlie investigation of the error due to the horizontal curvature of 

 the ways of a longitudinal comparator. 



If the microscopes are stationary, and the bars to be compared are 

 brought in succession under them, the curvature of the ways will pro- 

 duce no effect; but when the relation between the separate subdivisions 

 of the given unit are to be investigated, or when a given length is to 

 be transferred from one bar to another, the error arising from the cur- 

 vature of the ways cannot be neglected. The comparisons of Trough- 

 ton, of Hassler, and of Bache are subject to this class of errors, though 

 of course it might have happened that in each case the curvature of the 

 ways was insensible. I cannot find that any observations were made 

 to determine the amount of the curvature. By reversing the position 



