166 
PKOCEEDINGS OF THE SOCIETY. 
given by Professor Stokes the object is supposed to be self-luminous, 
emitting a pencil of rays of 180° in glass, which pencil was shown to 
pass by a single refraction, without aberration, from the front lens, and 
to present to the second lens a pencil in air of only just beyond 81°. 
Professor Stokes did not say the whole of this pencil can be made 
available in a practical construction, but he stated that a very con- 
siderable portion of it — largely in excess of what is available in a dry 
lens — could be so used. After this denionstration the question of the 
possibility of immersion lenses having apertures exceeding the 
maximum possible in dry lenses would be settled from the theoretical 
point of view. His opinion on the validity of Professor Keith’s com- 
putation of the aperture of Tolies’ — Mr. Crisp’s lens — must also be 
conclusive. It remained to endeavour to support the computation by 
actually measuring the aperture of the lens before the meeting — which 
he proposed doing, not of course expecting any general agreement at 
this stage of the discussion as to the least objectionable way of 
measuring apertures, especially with this individual lens. He would 
be content to show the measurement by Professor Abbe’s apertometer, 
the results obtained with which he had found to correspond with those 
obtained by a modification of Professor Robinson’s method which was 
submitted to Professor Stokes, and for the accuracy of which he had 
his authority. A method was specially commended by Mr. Charles 
Brooke in one of his Presidential addresses, viz. : to measure the 
working diameter of the front lens, which is taken as the base line 
of an isosceles triangle ; taking the exact focal distance as the per- 
pendicular, the triangle would represent the angle of aperture. The 
objection to this method in practice, was that when it was tried with 
the ^ lens, the data furnished were so various and contradictory that 
no reliance could be placed on the results: in one case the focal 
distance being given as 0*13, then *018; in another *025, — the 
working diameter being given first as • 043, then as • 033. 
Professor Stokes said that of course it would be understood that, as 
stated by Mr. Mayall, he confined himself to the consideration of a 
2 ^oint as if it were self-luminous, and contemplated that the object was 
illuminated by immersion ; if they let in light to the plane surface in 
air they would be limited to twice the critical angle. 
The President announced that they had received a letter from 
Professor Abbe, thanking the Society for the honour done to him by 
his election as an Honorary Fellow of the Society. 
Mr. Charles Stewart (Secretary) read a paper by the Eev. W. H. 
Ballinger, “ On the Measurement of the Diameter of the Flagella of 
Bacterium termo, a contribution to the question of the ultimate 
limits of vision with our present lenses.” 
The President said that what must have struck everyone who had 
listened to this paper was the extreme smallness of the objects 
measured, for if Mr. Ballinger was correct (and there was no reason 
for doubting his correctness), then it was clear that objects of very 
much greater minuteness could be rendered visible than had usually 
been considered possible. These objects were about the smallest 
which the microscope would show, and yet it a 2 ) 2 )cared that they 
