116 A. A. Michelson — Measurement by Light-waves. 



It is especially with a view of testing whether it is not pos- 

 sible to utilize these light- waves to even greater advantage that 

 I desire to institute a comparison between the telescope and 

 microscope on the one hand, and the refractometer on the 

 other ; to point out some remarkable analogies in their funda- 

 mental properties ; and to illustrate a few cases in which the 

 last-named instrument appears to possess a very important 

 advantage over the others. 



In the microscope (and the same remarks can be modified to 

 apply equally well to the telescope) the performance depends 

 largely on the quality of the objective. Let this be supposed 

 a single perfect lens. Very elementary considerations will 



sin ol 



show that the magnifying power of the lens is - — - , where a 



and /9 are the apparent semi-diameters of the lens viewed from 

 the object and image respectively; and this is greatest when 



a = 90° and then M=- — -. But it is well known that the image 



sin ft ° 



of a luminous point consists of a series of small concentric rings 

 of light ; and it is easy to show that the radius of the first ring 



is the wave-length divided by 2 sin j3, or JiM. This means that 

 the indistinctness of the image grows in exactly the same pro- 

 portion as the magnifying power. 



Now a microscope is commonly used : 1st, to separate into 

 their elements closely packed groups of minute objects ; 2d, to 

 recognize the forms of minute objects ; 3d, to locate the posi- 

 tions of minute objects. In the first case and also the second, 

 it is manifestly useless to increase the magnification beyond the 

 limit where interference fringes are just perceptible. In the 

 third case, however — were it not for the attendant decrease in 

 the illumination — it would be advantageous to go beyond this 

 point — so far in fact that the apparent width of the fringes is 

 about a hundred times that of the cross-hairs in the eye piece. 

 But long before this stage is reached the illumination is much 

 too feeble for distinct vision. (If the lens is in any way im- 

 perfect, the imperfections are of course much magnified.) 



With the first-named requisites of telescopes and microscopes, 

 namely, " resolution " and " definition," we have no further 

 concern. It is especially with regard to the third requisite — 

 which may be termed "accuracy" — that I wish to institute a 

 comparison between these instruments and the refractometer. 



As there appears to be a slight confusion in regard to these terms, it may not 

 be amiss to propose the following: 



Confining the attention to the objective alone, 

 Let B = diameter of objective. 

 F = focal length of objective. 



a = apparent semi-diameter of objective viewed from the object. 

 p — ■ u (i it » ii image. 



