554 Transactions of the Society. 



Objective Prob. Error (r) of Prob. Error (r ) of Average Devia- Greatest Devia- 



single observation Arith. -Mean tion from Mean tion from Mean 



div. jx div. fx div. /x div. /j. 



8 mm. B. & L. 



ldiv. = 0-10175^ ±0-4 = ± 0-04 ±0'13 = ±0-013 0-46 = 0*05 1-2 = 0-12 

 No. 5 Leitz. 



ldiv. = 0-067/x ±044 = ±0-03 ±0-14 = ±0-009 0-51 = 0-03 1-3 = 0-09 

 4 mm. Spencer 



ldiv. =0-047/* ±0-43 = ±0-02 ±0-14 = ±0-007 0-47 = 0-02 1-0 = 0-05 

 2 mm. Himmler. 



ldiv. = 0-02154 M ± 0-87 = ±0-02 ±0-27 = ±0-000 1*1 = 0"02 2-1 = 0-05 

 1/18 Zeiss; Gaert- 

 ner filar, 

 ldiv. = 0-015,u 



Series A.. ..±1-2 = ± 0-02 ±0-38 = ±0-006 1-38 = 0-02 3-06 = 0-05 

 „ B .. .. ±2-63 = ±0-04 ±0-83 = ±0-012 3-18 = 0-05 6-83 = 0-10 

 1/18 Zeiss ; Zeiss 

 filar, 

 ldiv. = -01247^ 



Series C.. .. ± 1-63 = ± 0-02 ±0-51 = ±0-006 1-72 = 0-02 4-64 = 006 

 „ D. .. ± 1-87 = ±0-02 ±0-58 = ±0-007 1-82 = 0-02 5-88 = 0-07 

 „ E .. .. ±1-21 = ±0-02 ±0-38 = ±0-005 1-29 = 0-02 3-55 = 0-04 

 „ F .. .. ±0-98 = ±0-01 ±0-30= ±0-004 1-21 = 0-02 2-35 = 0-03 



The conclusions fairly justified by the work recorded in this 

 paper seern to be as follows : — 



1. That with experienced observers, measurements of micro- 

 metric spaces from y^- mm. up to -^ mm. may, when made in a 

 series sufficiently large, be relied upon as accurate within limits 

 considerably less than 0-1 /-i, probably under favourable conditions 

 to about • 05 //,, though as to the correctness of this last statement 

 the writer is not so confident as to the first. 



2. That there is no advantage in the use of high powers or 

 large numerical apertures, but in the writer's opinion a positive 

 disadvantage if the power used is very high. In the comparison of 

 standards from 1 millimetre up to 1 metre, the experience of the 

 writer is that, in a series, a 1-in. objective, and in the measurements 

 of small units, as mentioned in this paper, a 4 mm. objective, afford 

 ample initial amplification. 



Of course, if the unit measured is very small, and in a band of 

 spaces of similar dimensions, the numerical aperture employed 

 must be sufficient for its resolution, and the amplification sufficient 

 to enable the setting of the wires to be accurately made, nothing 

 further seems necessary ; but such measurements do not come 

 within the scope of this paper. 



Personally the writer is of the opinion that the lowest power 

 that will suffice to accomplish the desired result is the best ; and 

 this is believed to be the better practice. 



