OF ARTS AND SCIENCES. 325 



also. After contact has been made between the free and the fixed 

 stops, the micrometer line of the microscope is brought into coinci- 

 dence with the defining line at one end of the bar attached to the free 

 stop-plate. The end gauge is then placed between the stops, the free 

 slide being moved back the required distance in order to allow the in- 

 sertion. During this operation the microscope remains undisturbed, 

 and the graduated bar passes under it without disturbance of the focal 

 plane. The difference in the readings, therefore, for the two positions 

 of the free stop-plate, i. e. before and after the insertion of the end 

 gauge, measures its deviation in length from the line standard. If 

 three microscopes are mounted upon plate K, and one of the stop- 

 plates is attached to the front face of the carriage in such a manner 

 that the two stops are parallel with the cylindrical ways, the method 

 of compari.'^on already described is applicable, and conditions (1) and 

 (2) are both fulfilled. 



The sixth condition is met in two ways. 



(1.) By the use of the two stops, H, H^ Fig. 4. 



The stops are first set approximately at the distance apart indicated 

 by the subdivisions to be compared. The method of comparing each 

 space with the constant distance between the stops is tlie same in every 

 respect as that described already. The following example is given in 

 illustration. 



COMPARISON OF INCH SUBDIVISIONS OF (?/=. 



{R — i) m»i!ts Constant. 2 



— 2.7cliv. =— 1.4;n —lAfj. 



-(-2.2 div. = +11 II —0.3 iJL 



— l.Odiv. = — 0.5;u —0.8/1 



-i-0.5 div. = +0.3 IX —0.5 ^ 



-f-2.6div. = +1.3;u +0.8 /t 



—1.7 div. = —0.8 IX +0.0 IX 



In this comparison the distance between the stops was 6.1 div. less 

 than the average value for one inch. When this constant is subtracted 

 from the separate values of ^ — Z, the residuals represent the relative 

 values of the separate subdivisions. With the microscope of Com- 

 parator No. 1 a positive residual indicates that the measured space is 

 too short. In this case the first space is 1.4 /x relatively too long, and 

 the second 1.1 /a relatively too short. In order to obtain the error of 

 any line reckoned from the first line, we must sum the residuals alge- 

 braically. Here the first five inches are 0.8 ya too short. 



