Limit to Defining -power. By J. J. Lister. 53 



to such an aperture seems evidently impracticable, yet up to au 

 angle of 77° it is shown by the table that the definition on tlie 

 image of the patterns has been very nearly in accordance with the 

 rule. It is observable also that the limit has been ])assed that 

 was inferred by Fraunhofer to the powers of the Microscope* 

 for at the above angle of 77° separation was seen as far as to 

 0' 000017 in. (see table), and the effective rays producing the image 

 were doubtless those of the brightest part of the spectrum whei-e, 

 by his estimate, the length of an undulation \ is about • 000022 

 English inch, \ being for each ray, the space within which he 

 inclined to conclude that an object could never be seen to consist 

 of parts. 



I have not, indeed, met with any object in nature quite so 

 minute in detail as 0*000017 in., but the appearance of parallel 

 lines is abundant in the structure of the scales of some insects as 

 the Lepidoptera and Thysanura, and on the shells of animalcules 

 of the family of Navicula, some of which vanish in the same 

 gradation as the images of the patterns, and as nearly at the same 

 size when seen with pencils of the same angle as their character 

 and the management of light necessary for viewing them would 

 lead us to expect. 



Thus delicate transverse markings on Navicida hippocampus 

 0*000028 in. apart (as measured by the number of markings 

 contained between two divisions of a micrometer in the eye-piece) 

 were just visible with an object-glass of ^q in. focus having a 

 pencil of 47°, some on N. phasmceRteron 0*000024 in. were well 

 seen with a | in. of 61°, and on a Navicida resembling N. gracilis 

 or N. acus • 000023 in. faintly with the same ; similar lines on 

 another of the same species separated * 0000215 in., invisible with 

 that glass, were made out by \ in. of 66°, which again could not 

 show those on a specimen measuring 0*00002 in. that were clearl}'' 

 seen with a ^^ in. of 77°. The last lines were the closest I have 

 found, and did not tax that glass to the utmost. 



The above object-glasses were some of those in the table, and 

 by referring to the column s their performance on the two kinds 

 of object may be compared. The observations together appear to 

 prove that, when well corrected, these focal lengths and pencils 

 are adequate to define respectively whatever could be seen with 

 glasses of shorter focus having the same angles of aperture ; prob- 

 ably the ,^0 and | in. glasses have the full extent of opening for 

 this condition, and it is one that should always be kept in view 

 if high power is required, for while there is convenience in having 

 the glass no deeper than is needed for its work, and very short 

 focus may bring besides difficulty and faults to the manufacture, 

 on the other hand it produces less secondary spectrum, and the 



* Herschel, " Light," Art. 758. 



