192 



THE AMERICAN MONTHLY 



[October, 



begin with some explanations with 

 which many here present are familiar. 



Probably every observer of expe- 

 rience has a more or less clear recol- 

 lection of the long and bitterly fought 

 battle raged among microscopists not 

 many years ago about angular aper- 

 ture. There were advocates of wide 

 or high angles, who believed the value 

 of an objective increased for all pur- 

 poses as the angular aperture was 

 increased, independently of other con- 

 siderations, and this view was advo- 

 cated with all the steadfastness and 

 vigor of such faith as would move 

 mountains, had it been properly direct- 

 ed to that end. On the other hand, 

 there was a more conservative but 

 none the less vigorous party totally 

 opposed to these views. The bitter- 

 ness with which this^ controversy w^as 

 carried on at times, year after year, 

 is a blot upon the literature of the 

 subject. But the differences of opin- 

 ion arose, partly no doubt from stub- 

 bornness and erroneous observation, 

 but mainly from want of knowledge 

 concerning the subject. There was no 

 recognition of a standard by which 

 the value of an objective could be 

 determined. It was a controversy, 

 in fact, between those who believed 

 in tests by resolving fine markings on 

 diatoms, etc., and those who belicA^ed 

 in clear definition of such objects as 

 the podura scale. To be sure, other 

 elements entered into the controversy, 

 as, for instance, the question of the 

 proper ineasurement of the angle of 

 aperture, but the great question of in- 

 terest to workers with the microscope 

 was, what is the best objective for 

 use — a wide or medium angle.? 



At the present time this question 

 can be answered ; but a fev\^ years ago it 

 was purely a matter of opinion. The 

 theory of the microscope then gener- 

 ally accepted was erroneous. The 

 functions of angular aperture were in 

 theory entirely misunderstood. 



Let us endeavor to understand the 

 subject in the light of recent investi- 

 gations, for which we are mainly in- 

 debted to Prof. Dr. E. Abbe, of Jena, 



who has established a theory of the 

 microscope, based upon experimental 

 and mathematical investigations, 

 which, in its essential features, if not 

 throughout, seems as firmly estab- 

 lished as any theory in optical science. 



When an object marked with fine 

 striae, such as a diatom-shell, for ex- 

 ample, or a glass plate ruled with 

 lines and having the markings sepa- 

 rated by spaces as minute as the wave- 

 length of light, is illuminated in the 

 ordinary way under the microscope, 

 it is obvious that the light will be de- 

 composed and a diffraction spectrum 

 formed, precisely as in the case of. 

 Prof. Rowland's beautiful ruled 

 plates. Considering any single ray 

 from the mirror, when it reaches such 

 an object it will be turned from its 

 direct course and pass off" at an angle, 

 forming a microscopic diffraction 

 spectrum. This spectrum may be 

 seen and examined in a manner to be 

 described further on. First I must 

 ask you to recall some old experiments 

 given in text-books on physics. I re- 

 fer to the interference bands of diffrac- 

 tion spectra. You will remember 

 how the waves of light, when their 

 vibrations come together in a certain 

 manner, interfere with each other and 

 produce lines of darkness due to over- 

 lapping spectra. I cannot go further 

 into this subject here. The principle 

 has been brought before 3'ou, and that 

 is sufficient for the purpose in view. 

 It must be clear to any one that if the 

 light is thus turned from its course 

 and decomposed, it cannot go on to 

 form an image in the microscope as 

 it was supposed to do according to 

 the old theory of the microscope. It 

 was then supposed that the microscope 

 formed an image precisely as figured 

 in works on physics in use at the 

 present day, and in the same manner 

 as the telescope. Large objects, and 

 outlines of objects generally, are im- 

 aged in this way ; but obviously this 

 cannot be true of the fine markings 

 closer than a wave-length of light. 



Let us see what becomes of the 

 diai'acted rays forming the spectrum. 



