Some Remarks on the Apertometer. By Prof. E, Ahbe. 23 



auxiliary lens, to a small part of its focal length, or applying a small 

 eye-liole in the case of an observation by the naked eye, the area of 

 entrance of the image-forming pencils may be diminished to an 

 extremely small diameter, owing to the inverse action of the ampli- 

 fication of the objective. With a -j^^-inch objective, for example, there 

 is no lack of light, and no other inconvenience, if this entrance- 

 area is reduced to a diameter of one-thousandth of an inch. The 

 pencils crossing in the apex at the conjugcde focus of the objective 

 may be made in this loay to define the angle of aperture practically 

 like single rays. 



The foregoing remarks should explain all the discrepancies 

 which have appeared to some observers in using the apertometer, 

 and they will be applicable more or less to every method of mea- 

 suring apertures. 



The irregularities observed by Professor H. L. Smith with low- 

 power objectives will disappear at once, as soon as he focusses the 

 objective not by the naked eye but by an eye-piece, and takes care 

 that the position of the diaphragm in this eye-piece corresponds 

 virtually (i. e. the action of the field-lens considered) to the 

 position into which the eye-hole at the end of this tube is brought 

 afterwards. Repeating his measurements in this way with the 

 apparatus figured on p. 775 of his paper, he will find the correct 

 angle of the lowest powers as of the highest, but, of course, the 

 angle corresponding to a length of tube of 4 inches, according to 

 the description of his apparatus. In the case of a low-power 

 objective, this angle may be sometimes considerably less, sometimes 

 considerably larger, than the aperture of tlie same objective on the 

 10-inch tube, both cases being equally possible, though not equally 

 frequent. Professor Smith's own method of observation is subject to 

 exactly the same conditions for obtaining correct results, the posi- 

 tion and the diameter of the illuminating area (tissue-paper or 

 ground glass) at the end of his tube requiring special precautions. 

 Both methods will yield similar results with low or high powers, if 

 both are applied with the same precautions. But for both methods 

 Professor Smith will do well to exclude another source of errors in 

 his apparatus by taking away the magnifying lens at the end of the 

 swinging arm between the centre g and the eye-hole /, applying 

 this lens outside the eye-hole, if he cannot dispense with it. 



A stop with a small circular hole at the centre of Professor 

 Smith's apparatus, as suggested by Dr. Woodward in his paper, 

 will not correct by itself a faulty adjustment of the objective or the 

 dia})hragm, and will bo quite unnecessary if the adjustment is made 

 correctly. But in the case of a coarsely incorrect adjustment the 

 observation would be practically impossible ; the limits of the aper- 

 ture would be invisible as long as the conjugate area to the critical 

 diaj)hragm does not approximately coincide with the circular hole. 



