13 



2. Determination of the Projection Error. 



For thc detenniiiatioii of the projection error wc hâve followed the inethod 

 used by Donner. The two scales were compared together in juxtaposition, 

 and then again by projection, scale B being phaced in the position ordinarily 

 occupied by the réseau. A series of observations was also made with scale 

 B reversed, thougli in this case the coniparison in juxtaposition could not be 

 made, and the division errors fornierly deterrained by Gill bad to be used in 

 reducing the observations. For the sake of coniparison^ we have also com- 

 puted the observations for which wc made a direct coniparison in juxtaposition 

 by means of Gill's division errors formerly determincd. In each series of 

 coniparisons betwcen the two scalcS; both direct and by projection, we have 

 always applied to the observations a correction of thc form 



a + hx, 



where x is the distance of the point under observation from the middle of 

 the scalc, and « and h are determincd by Icast squares from équations of 

 the form: 



a-\-hx — (observed quantity) = O 



This correction is intended to remove the eftect of any différence betvveen 

 the racan millimètres of the two scales, as well as the constant difterence of 

 the two initial lines. Wc now let: 



P ~ quantity which must be added to micrometer readings on scale A to 

 reduce them to what they would have bcen if scale A bad bcen placed 

 in the position of the réseau, instead of being up on its bridge. 



Table 3 gives the value of P derived in various ways. 



