4l 
First Sur- 
Aperture. T=1. Uncovered. | Covered. | face curved 
0 =75°. 
‘, 20° 1-74 1:62 1°53 1:52 
40° 6°91 6:47 6:07 6:06 
60° 15°35 14:37 13°47 13°46 
80° 26°81 25:07 23°45 23°46 
100° 40:93 38°12 35°52 35°60 
120° 57°30 52:90 48°86 49°21 
130° 66°16 60°38 55°33 56°14 
140° 75°40 67:93 61:89 63.05 
145° 80°13 71.25 64:70 66°39 
150° 84°93 75°23 67-26 69°69 
155° 89°79 78:09 69°70 72°83 
160° 94-69 81-68 71:54 75°89 
165° 99°63 84:77 73°11 78°73 
170° 104:60 86:56 73°97 81:52 
175° 10959 88°43 74°33 84°17 
180° 114°59 88°60 74:52 86°84 
‘These numbers (which, from neglecting the remaining 
reflexions, must give rather too much weight to the larger 
apertures) show clearly that, especially for covered objects, 
nothing is gained above 150° at all commensurate to the dif- 
ficulty of constructing such objectives. But in addition to 
this, I wish to call attention to the fact, that the whole of 
these great apertures is not in every case thoroughly effective. 
«<The mode of measuring them which is commonly used 
is that given by Mr. Lister, in which the microscope is at- 
tached to the alidad of a circular instrument, with its objective 
over the centre, and directed towards a luminary at some dis- 
tance. Looking into it, the field is filled with light, which, 
on turning the alidad, is seen to have a circular boundary: if 
this be brought from each side to the middle of the field, the 
intercepted arc is the aperture.* For objectives of considerable 
* When the aperture is very large, there is a sluggishness in the appa- 
rent movement of the boundary, which makes me have some doubt of the 
accuracy of the process ; it seems almost stationary in No. 6. 
