NOTES AND MEMORANDA. 307 
passage, it will be at once seen, is limited to the “dry lens,” and 
while he says the “smallest object,” the context shows that he means 
the separation of lines, and nota single object, for he at once goes on to 
show that closer lines may be separated by the use of blue light and 
immersion objectives, and also says, “ The size of the smallest bright 
point that can be seen depends on entirely different considerations, 
and might be considerably less.” All these speculations of Sorby 
and Helmholtz (and Abbe may be included) are based on theoretically 
perfect microscopes. (In this case the ‘ microscope” means the 
objective, the all-important part of the instrument.) Now who ever 
saw a “theoretically perfect” microscope? Who can ascertain, that 
one is theoretically perfect? How can it be ascertained that one is 
perfect? The only possible way of measuring the approximation 
towards perfection is by the performance. So long as the per- 
formance of the best microscopes falls short of what a theory says is 
possible, the theory may be accepted as correct; but when the micro- 
scope has done more than theory says is possible, theory must be in 
fault. For years microscopes have been made, and are in use, that 
do more than Helmholtz’s theory will allow. The difficulty with 
Helmholtz and Abbe is that they had not seen and experimented, in 
1872, 1875, and 1874, with all the microscopes that had been made 
at that time, but only with such German instruments as came in their 
way; and that made their theories to agree with the performance of 
those instruments. That the theories are wrong is proved by the fact 
that Nobert’s lines, finer than 112,000 to the English inch, have been 
seen repeatedly by numerous observers, whereas Helmholtz fixes the 
theoretical limit at 110,000. On the other hand, as yet no lines so 
fine as 114,000 to the inch have been seen. Nobert has ruled lines 
that he claims are 224,000 to the inch. Until something finer than 
112,000 is actually seen, it must be an open question whether the 
failure is the fault of the microscope or of the ruling. Nobert him- 
self has not seen his own finer lines, and always pronounced it im- 
possible to see any finer than 80,000 to the inch, until he saw 95,000 
to the inch with a Tolles’ immersion lens. The writer saw 90,000 to 
the inch with a dry lens more than ten years ago. As to the size of 
a single object which may be seen, there is but little known. The 
limit is undoubtedly in the perfection, or rather want of perfection, 
in the microscope. The best experiments in this direction have been 
made by Mr. W. A. Rogers, of the Cambridge observatory. Various 
writers have assigned different values to the angle at which an object 
can be seen, varying from 6” to 120”. This is, of course, a physio- 
logical matter. Mr. Rogers says, “ Even the smallest value named is 
much too large. I will at any time undertake to rule a single line 
one 30,000th of an inch in breadth, which can be seen the distance 
of seven inches from the eye. This corresponds to an angle of about 
1”. Comparing minute particles of matter which can be seen under 
a Tolles’ ,1,th objective with those that can be measured, in the 
way indicated above, there is every reason to suppose that the limit 
of visibility falls beyond one 400,000th of an inch. But that light 
is of ‘too coarse a nature’ to enable us to see particles of matter as 
