Journal of Applied Microscopy. 



179 



A Study of Various Styles of 

 Cross -Wires. 



In making a measurement with a filar 

 micrometer, spectrometer, sextant, and 

 a variety of otlier instruments, the prin- 

 cipal difficulty one encounters is in the 

 setting of the cross-wires. There are 

 several methods employed to make these 

 settings as accurate as possible, and as 

 the purpose of the work described in this 

 paper was to test their relative efficien- 

 cies, I will describe them at once. By re- 

 ference to the figure it will be seen that 

 A consists in setting the point common 

 to two crossed wires over the given 

 fixed line; B is when one wire is super- 

 posed on the line; in C this line bisects 

 two parallel wires, and in D the refer- 

 ence line is at one side of the movable 

 parallel wires and at a distance from one 

 of them equal to their distance apart. 



Styles of Cross-wires. 



The problem of determining the most 

 advantageous form for accurate settings 

 is a psychological one, no less than a 

 physical. Much depends upon the obser- 

 ver, the instrument, and the occasion. I 

 made use of a micrometer microscope 

 whose constant was 15.3: that is, 15.3 

 turns were ea.uivalent to one millimeter. 

 I then selected four observers, three of 

 whom had done more or less work with 

 Instruments of this kind, and the fourth 

 was entirely without experience. Ob- 

 servations were recorded in sets of 

 twelve for each of the four methods, and 

 tests were made in which the time of 

 observation was limited to a definite 

 period, usually two or three seconds. 

 Another set of readings was taken in 

 which settings were made by each 

 method in turn, that is to say, the ob- 

 server would follow methods A, B, C 

 and D, and then go back to A. 



It was attempted to make the external 

 conditions, such as the light, the time of 

 day, the condition of the instrumen'., 

 etc., as nearly uniform as possible. After 

 the settings had been made, the "prob- 

 able error" of each group was computed. 

 The probable error of the mean of a set 

 of observations is a term used in the 

 theory of Least Squares to denote a 

 number of which it can be said that the 

 probability of the true result lying be- 

 tween the mean, plus this number and 

 the mean, minus this number, is just 



equal to the probability that it does not 

 lie between these limits. Thus, if 

 61.8-1-0.6 represents the mean of a set 

 of observations and its probable error, 

 we may say that the true result is just 

 as likely to lie between 62.4 and 61.2 as to 

 lie beyond these limiting numbers. To 

 deduce the probable error the following 

 formula is used: 



'V 



p. E.=o.67. / e; + e: + Ev.-e^ 



n (n — 1) 



when E, E-, etc., represent differences 

 between the mean and the separate ob- 

 servations, and n is the number of obser- 

 vations made. The following tables 

 were made up from data which seemed 

 to be typical of all the observations 

 taken. 



0BSBRVE3R 1. 



Time unlimited. 



Method. 



B. 



C. 



Settings 



P. B 0.42 0.20 0.21 0.23 



Time limited. 

 Method. 



Settings 



P. E. 



0.62 



Method. 



Settings 



P. B. 



D. 



0.46 0.50 0.32 



Each method in alternation. 



