548 Transactions of the Society. 



comparing observations made by different observers. Constant 

 errors have been eliminated as far as possible, and every measure- 

 ment was made independently and without any knowledge of the 

 results reached by the other observer. Indeed, the substantial 

 agreement of the results was not established until the preparation 

 of this paper. 



Writing in 1878 upon this subject, the late Professor William 

 A. Rogers used the following language : — " A simple and direct way 

 to determine the degree of precision with which measures under the 

 microscope may be made, is to compare measurements of the same 

 space made by different observers and under different conditions. 

 I may get results which show an agreement inter se quite within 

 the limits of the accuracy required, but which are yet wide of the 

 truth. But if another equally skilful observer obtains substantially 

 the same results from a series of measurements made under entirely 

 different conditions, the inference of their general correctness may 

 be drawn with tolerable safety." (See Proceedings American 

 Academy of Arts and Sciences, 1878, p. 178.) 



The powers used in the series of measurements recorded in the 

 paper just referred to were 194, 290, 560, and 870 ; but the relative 

 accuracy of measurements of the same space with different powers 

 is not discussed in the paper above referred to, though reference is 

 made to the accuracy attained by the use of other different measur- 

 ing appliances. 



In order, if possible, to throw further light upon this topic, the 

 writer has measured the same space, the first T ^y mm. of " Powell 

 and Lealand, No. VIII.," with the Spencer stand and Gaertner filar 

 micrometer already described, using in succession the following 

 objectives : an 8 mm. Bausch and Lomb objective, N.A. • 50 ; a 

 No. 5 Leitz objective of 5 '8 mm. focal length and 0*77 N.A. ; a 

 Spencer 4 mm. objective of 0*66 N.A. ; a 2 mm. Himmler homo- 

 geneous immersion objective of 1 ■ 30 N.A. ; and a Zeiss -j^-in. 

 homogeneous immersion objective of 1 ■ 27 N.A. 



The only change made in the apparatus from beginning to end 

 of these measurements, except as noted below, was in the objectives, 

 which were used in the order mentioned. The surrounding con- 

 ditions were maintained unchanged as nearly as possible, so that 

 the variation in the degree of accuracy developed, should there be 

 such variation, might be attributed solely to the change of objec- 

 tives. Of course the personal factor enters into the result, but there 

 was no conscious change in this respect. The readings are given 

 in detail and are as follows : — 



Instruments : Spencer new stand, No. 22, with mechanical stage 

 and achromatic condenser ; Gaertner filar micrometer, with an invar 

 screw having a pitch of \ mm. and two movable parallel spider 

 lines, as before described ; and the Bausch and Lomb 8 mm. objec- 

 tive above described. 



