148 



APPENDICES 



But now let the magnification be, say, 4 diameters (m = 4), then we get the N". A. at v;hich the 

 lens works h orn (IV.). 



Actual N. A. = ~ — ^= — = 025. 



4+1 2 X 16 40 



It may be added that it is largely due to the very low N, A. of photographic lenses that they are 

 superior to proper microscopic-objectives for the lowest forms of photo-micrography, as owing to 

 that very low N. A. the correction of the axial pencils are not carried to any great degree of 

 refinement ; the computer then has a chance, not otherwise afforded him, to utilise the available 

 radii and distances for the correction of astigmatism and coma of the oblique pencils, and for 

 the obtaining of a fairly large plane of field free from objectionable distortion. 



APPENDIX II 



TO OBTAIN THE NUMBER OF LINES TO THE INCH IN A SPECIMEN 



To obtain the number of lines to the inch ; say, for example, in one of Amphipleura pellucida : 

 Place on the stage a ruled micrometer, using the lines separated by an interval of -0001 inch. Place 

 one of the webs of a movable parallel wire micrometer used in place of the eye-piece on one line, and 

 the other, say, on the 6th, so that 5 spaces of •0001 inch are thus included between them. Take 

 5 readings off the head of the micrometer. 



Eevolutions. 

 Say they are as follows : 4*589 



4-670 

 4-642 

 4-680 



4-699 

 5/2^280 



4-656 mean. 



Divide this mean by 5 and -931 of a revolution of the head of the micrometer = "oooi inch (I.). 



"Without touching the draw tube of the microscope, place the Amphipleura pellucida in situ, and 

 set the wires a distance apart so as to contain a given number of lines ; say, a separation sufficient 

 to enclose 5 lines. Eead the interval on the head of the micrometer. In a specimen of our own it 

 was -551 of a revolution. To ascertain the value in terms of an inch : — 



as Eev. -931 = -0001 by (I.), so -931 : -551 : : 'OOOI inch. 



, '551 X -OOOI ^ . , 



hence = say -00006 inch. 



•931 ^ 



Pive lines, then, are in every -00006 inch : how many in i inch. 



•00006 : I : : 5 = — ^ = 83,300. 



-00006 



If the answer be required in mm. then, as i inch = 25-4 mm., the 83,300 must be divided by 25-4. 



The great difficulty with this method is to be quite certain that the threads of the micrometer 

 really coincide with the minute lines of the specimen. To enable this to be as accurately done as 



