THE MEASUREMENT OF MICROSCOPIC OBJECTS. 289 



compared with those ot the object, then the distance of the 

 divisions required can obviously be determined as is usually done 

 with an ordinary unverified scale by comparing it with a standard 

 one. If, for instance, 10 divisions in the eye-piece micrometer 

 coincide with a space of 25 mic. on the stage-micrometer, we get a 

 value of 2 -5 mic. for one division. 



The errors which are incidental to this method of determination, 

 and the measurements based upon it, are of course proportional to 

 the accuracy of the two micrometer- divisions ; they are not, how- 

 ever, of much importance in view of the perfection of modern 

 dividing machines. In the eye-piece micrometer, where the 

 equality only of the intervals not their absolute magnitude 

 comes into account, they may be regarded as almost infinitely 

 small, as may be easily seen if the micrometer-divisions are slid 

 over the real image of any object, the latter always covers the 

 same number of division-lines. On the other hand, however, 

 as shown by Harting, slight differences occur in the sense that the 

 intervals do not correspond exactly to the values specified by the 

 optician, but appear somewhat too large or too small. In the 

 glass micrometers of Oberhaeuser the difference is said to amount 

 to '041, in those of Plcessl to -009 of the asserted value, so that 

 in order to be exact the results of the measurements must be 

 diminished by these fractions. To what extent these statements 

 hold good for micrometer-divisions of recent date we need not 

 inquire; we recollect, however, having repeatedly measured one 

 and the same object, employing Ploessl's and Oberheuser's gradua- 

 tions, without meeting with essential differences. The differ- 

 ences which occur in the micrometers of the principal makers 

 appear to us of very minor consideration in the determina- 

 tion of the size of microscopic objects (disregarding quite special 

 cases). 



In many investigations where measurements are necessary, it 

 is indeed only a matter of relative accuracy i.e., of the com- 

 parison of the results of the same observer. He is supposed 

 to know what importance the possible error might attain, and 

 of course will try to avoid those sources of error which would 

 impair the accuracy of his conclusions. Generally speaking, he 

 is satisfied by a few rapidly made measurements in more diffi- 

 cult cases, by a greater number of careful measurements and 

 calculation of the arithmetical mean ; the testing of the measuring 



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