On the Probable Error of Micrometric Measurements. 95 



tween the wires and the images of the lines, were reduced to 

 the least distinguishable quantity, and were as nearly as pos- 

 sible equal. With some of the sets of lines, contacts made in 

 this way could be reproduced almost identically. But the mar- 

 gins of some lines, especially with the higher power, appeared 

 of a character which did not permit the same degree of 

 accuracy to be obtained in this way. 



In most cases, therefore, especially with the higher power, 

 another method was employed for making contact between 

 the wires and the images of the lines. The image of a fur- 

 row cut in a glass plate shows two dark bands with a lio-hter 

 intermediate- band. These bands present various appearances 

 according to the depth of the furrow in the glass, and ac- 

 cording to the different optical circumstances under which 

 they are examined. The wires of the micrometer were placed 

 on the lighter central bands of the two lines in hand, and then 

 brought nearer to the left-hand darker bands until the least 

 visible strip of light remained between the wires and the dark 

 bands. 



In case of the intervals measured with the inch object-glass, 

 the micrometer screw-heads were, in all cases, read to the 

 fourth part of a division. Each interval was measured twice. 

 The following table gives, in the first column, the difference 

 between the two readings of each pair in ten-millionths of an 

 inch; and in the second, the number of cases in which each 

 value of column first occurred: 



Taking the square root of the mean square of these differ- 

 ences, and multiplying by the proper factor, we obtain the 

 probable difference of a pair of measurements, which is thirty- 

 nine ten-millionths of an inch. It may be said that these were 

 the first measurements of precisely this kind made by the 

 writer, and that this probable difference of two measurements 

 of the same interval was larger for him then than now. 



In case of the measurements with the quarter-inch object- 

 glass, twenty measurements were made for a purpose which 



