232 J. MATTHEWS ON A NEW AND 



The basis of nearly all micrometrical measurements has been the 

 comparison of the graduations of the eye-piece micrometer with 

 those of one on the stage having a known value, and the abso- 

 lute value of those of the eye-piece cannot be known mitil then, 

 because their indications necessarily vary, with the power of every 

 objective with which it is used, and, if more than one eye-piece be 

 adapted to the use of the micrometer, of every eye-piece also. A 

 calculation thus becomes necessary for every separate objective, 

 and as no two, even from the same maker, or of the same nominal 

 focus from different makers, are exactly alike, the table which has 

 been made for one instrument and one set of powers cannot be em- 

 ployed for another set. It is evident, then, that every measure- 

 ment is relative or indirect, not absolute. Surely this is likely to 

 be a source of error, therefore a defect. I will not deny that the 

 needful comparison between the two scales once made and tabulated, 

 this method may be absolutely correct, if the graduation of the 

 stage micrometer be true. But I venture to think that it would be 

 far better to dispense with that in the eye-piece, and measure only 

 from or by that on the stage — as I propose to do — and thus 

 eliminate at least one possible and probable source of error. 



The next defect of the present methods is, that, depending as 

 they do on the use of a properly ruled slip of glass inserted into 

 the eye-piece at the focus of the eye-glass, and that slip having a 

 sensible thickness, the definition of all powers to which it may be 

 applied is impaired, — of the highest most, and therefore precisely 

 in those cases where micrometry is most useful, and accuracy 

 most desirable. Hogg observes (p. 54) that the Micrometer 

 should not be applied to too deep an eye-piece, ** for it is essential 

 to preserve clear definition." Are not, then, those means inhe- 

 rently defective in practice which will not admit of application to 

 all cases with equal accuracy and facility ? Another possible 

 source of inaccuracy may lie in the vagueness of the starting point 

 (if I may fairly use such a phrase), for measurement by tico scales. 



All the rulings, on even the finest and best instruments, have a 

 very sensible dimension, which of course seems to increase with 

 the magnifying power. The exact apposition, then, or collimation 

 of lines in each of the micrometers is not a very easy matter. It 

 is, besides, well known that there often exists a curious optical 

 illusion in the transit of one of two bodies having sharp edges, 

 over another, under ^vhich it does not seem to move for a small 



