ZOOLOGY AND BOTANY, MICEOSCOPY, ETC. 815 



has inequalities, or is not perpendicular to the screw, or if the screw- 

 point is out of centre, the errors in the readings are functions of corre- 

 sponding fractions of a single turn, or are " periodic." 



(3) Imperfections in the other parts may introduce numerous irregu- 

 lar errors, capable of entirely destroying the advantantages of micro- 

 metric reading. 



The errors may therefore be either progressive, periodic, or irregular; 

 the first may practically be neglected since only one or two or at the 

 most five turns are employed in theodolite readings ; the irregular 

 errors must be determined and eliminated by repeated readjustment to 

 the same graduation mark, the vernier being clamped, and by observing 

 the mean errors of adjustment and reading ; if these are subject to 

 occasional large variation they indicate imperfections in the mechanism, 

 lubricant, &c. 



It remains to determine the periodic errors ; i. e. to compare the 

 different values found for the same interval on the scale as measured at 

 different parts of the drum. The most convenient interval to use is the 

 distance on the scale between some graduation and a supplementary 

 mark which corresponds to 1/10, 1/8, or 1/5 of a complete turn. The 

 drum is set to 0, one end of the interval is brought on to the cross wires 

 by the vernier screw, and then the other end by a movement of the 

 drum ; the first position is then recovered by a movement of the vernier- 

 screw ; and in this way a series of measurements are made by alternate 

 use of the vernier-screw and drum until the zero-reading upon the latter 

 is again reached; the readings are then reversed. A series of such 

 double sets of observations will give a mean value of the interval which 

 may be regarded as the true value, and the differences between this and 

 the values obtained at different parts of the drum will be the corrections 

 to be applied. An example quoted by Prof. Eeinhertz shows how the 

 periodic error was determined on a micrometer screw, so that by 

 applying the correction the mean error of a single measurement could be 

 reduced from 8 "5 in. to 4*4 in. ; and was finally removed altogether by 

 correcting the eccentricity of the hollow cone in which the screw point 

 was made to work. 



If the periodic errors do not lie within the mean errors of adjustment 

 and reading the screw should be rejected, and in any case the periodic 

 errors should be eliminated by repeated readings at different parts of 

 the drum. 



Araclinoidiscus as a new Test for High-power Objectives.* — Mr. 

 T. F. Smith says that there are two great objections to using the 

 Podura scale as a test object for an oil-immersion. The first is that the 

 conventional markings can only be seen when the scale is a little 

 way off the cover-glass, and, consequently, the objective not working 

 at its full aperture ; and, secondly, it is impossible to tell the best 

 point. 



A dry glass, on the Podura scale, is exceeding sensitive, and a little 

 turn of the correction-collar, or a little difference in the length of the 

 draw-tube, will make all the difference between fine definition and no 

 definition at all. With the oil-immersion, however, you can go through 

 the whole range of the correction-collar without making any difference 

 in the markings, beyond changing them from red to blue. Of course, 



* Journ. Quek. Micr. Club, iii. (1888) pp. 247-53. 



