298 PROCEEDINGS OF THE AMERICAN ACADEMY 



It is apparent, therefore, that, though the radius of curvature exceeds 

 a distance of three miles, a correction of 3.8 divisions must be applied 

 to the reading of microscope A, and of 21.4 divisions to the reading 

 of microscope B, for each centimeter of the distance between the 

 two bars. 



The radius of curvature can also be found in the following way. If 

 a tracing apparatus is attached to the microscopo plate, a line traced 

 upon the plane surface of a bar, by the motion of. the jDlate from one end 

 of the bed-plate to the other, will have the curvature due to the dis- 

 tance of the ruling diamond from the centre of the slide. If the bar 

 is reversed, and a second line is drawn upon the same surface as nearly 

 parallel to the first line as possible, then the ver-sin of the curva- 

 ture will be equal to one half the difference between the distance of 

 the lines at the middle point and the half sum of the distances at the 

 two ends. 



Finally, the deviation of the microscope plate both from a horizon- 

 tal and from a vertical plane can be detected by means of a telescope 

 mounted upon the sliding plate. If the telescope is pointed either at 

 the cross wires of a collimator, or at a distant object, and the point re- 

 mains fixed with respect to the cross wires of the telescope during the 

 motion of the slide from one end of the comparator to the other, it may 

 be assumed that it moves in an invariable plane. The longitudinal 

 comparator at the Conservatory is provided with an attachment of this 

 kind. 



( f. ) The relative advantages of comparisons in air and comparisons 

 in a liquid. 



Air temperatures are employed both at the Conservatory and at the 

 International Bureau. At the Conservatory, the bars to be compared 

 remain at a constant air temperature for forty-eight hours before the 

 comparisons are made. The arrangements for maintaining a constant 

 temperature are most admirable and effective. The means of con- 

 trolling the temperature employed at the International Bureau are some- 

 what different, but they give most excellent results. Nevertheless, it 

 is yet an an open question whether the absolute relation between two 

 bars compared in air at a given temperature can be made to agree with 

 the absolute relation determined by submerging them in a liquid at 

 the same temperature. The writer has met with many difficulties in 

 this direction. 



(g.) The variation of the absolute length of a bar by a change in, its 

 molecular structure or otherwise. 



There are some evidences that certain standards have undergone a 



