OF ARTS AND SCIENCES. 889 



the surfaces of TFand Q^^ are slightly convex between centimeters 15 

 and 45, while ^3 is convex to a less degree between centimeters 70 

 and 85. The surface of Q^ is nearly plane when the cathetometer is 

 supported at its neutral points. 



EELATIVE ERRORS OF THE SUBDIVISIONS. 

 A plus sign indicates that the measured space is too short. 



The relative errors of the 10 centimeters of the first decimeters of 

 Q3 and Q^ were found to be as follows. The centimeter subdivisions 

 of W and Q^^ were not investigated. 



The errors of the one-tenth millimeter subdivisions seem to be 

 inappreciable, indicating that the screw employed has no sensible 

 periodic error which is a function of a single revolution. 



With regard to the decimeter subdivisions, it shotild be said that the 

 graduation was done in three operations, the second zero being at about 

 the thirty-third centimeter, and the third at about the sixty-sixth 

 centimeter. 



