THE FORMATION OF MICROSCOPIC IMAGES 43 



opticians in the world, Professor Abbe of Jena ; and, as a result, 

 some of the judgments and opinions, as well as what were supposed 

 to be established truths, depending apparently upon the simplest 

 principles, and not believed to be open to change, have been shown 

 to be absolutely without foundation ; while principles hitherto quite 

 unknown and unsuspected have been shown to operate and to rest 

 on clearly demonstrable mathematical and physical bases. The 

 result has been a complete revolution of what were held to be 

 fundamental principles of microscopic optics and the theory of 

 vision with microscopic object-gl;i- 



Professor Abbe contends that one of the foremost errors relates 

 to the mode in which microscopic images are formed. It was 

 assumed that their formation took place on ordinary dioptric 

 principles. As the camera or the telescope formed images, so it 

 was assumed that the image in the compound microscope was 

 brought about. The delicate and complex structure of an insect's 

 scale or of a diatom were believed to form their images according to 

 the same precise dioptric law^s by which the image of the moon or 

 Mars is formed in the telescope. Hence it was taken for granted 

 that every function of the microscope was determined by the geo- 

 metrically traceable relations of the refracted rays of light. We 

 would nevertheless remark that visibility of detail in, for example, 

 the moon depends on the aperture of the telescope ; of course, what 

 is known as its ' aperture ' is simply estimated by the diameter of 

 the object-glass, but accuracy appears to require that n sin u = a 

 ought to be applied to the telescope. In practice the diameter is 

 taken conventionally for the sake of simplicity, as it makes no 

 numerical difference, because the sines of small angles such as are 

 dealt with in the telescope are proportional to the angles themselves. 

 The microscope, on the other hand, deals with large angles ; con- 

 sequently the sine cannot be dispensed with. 



But Professor Abbe argues that a close examination in theory 

 and practice of the conditions of vision with microscopic objectives 

 shows that such an estimate of aperture is wholly wrong in prin- 

 ciple. The front lens of a -^g-in. objective may be no more than the 

 sVth of an inch in diameter, while a 3-in. objective may have a 

 diameter of half an inch. Yet it is the smaller lens that has by far 

 the larger ' aperture.' 



Light is dispersed from every point on the surface of an object 

 in all directions up to 180. Only an extremely narrow pencil of 

 this can be received by the human eye, a large pencil of light 

 emanating from the object being lost on each side of what the eye 

 receives. The apparent problem of practical optics is to be able, 

 by means of lenses, to gather up and bring to a focus as many of the 

 unadmitted rays as possible. The general manner in which lenses 

 act in doing this we have endeavoured in an elementary manner to 

 show. 



Soon after achromatic object-glasses were first made, Dr. Goring 

 found that the markings on special objects such as the scales of 

 the wings of insects could be seen by some object-glasses, while 

 with others, although the magnifying power was equal, it was im- 



