364 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
1/45,000 in., 8 being tbe value of one line and interspace. Then 
• * o 
will be tbe angle tbe bole subtends at tbe distance of tbe scale. By tbe 
Fraunhofer law u, tbe divergence of tbe diffraction beams is sucb that 
sin u = - but, in order that two diffracted beams may just pass through 
tbe bole, which is tbe condition of tbe limit of visibility of tbe grating, 
sin u must also = =— K ; therefore ^ , and 8 = ^ - = 1/66 in. 
7*5 6 7*5 *011 
The scale actually bad 64 lines per inch. 
(2) Tbe converse problem may be treated in a similar way. Looking 
through a bole in a diaphragm placed close to tbe eye, a scale of 50 lines 
to tbe inch can be just perceived at a distance of 9 in. What is tbe 
diameter of tbe bole ? 
Tbe bole here subtends an angle of ^ at tbe scale ; this angle must 
be equal to sin u if tbe grating is just resolved. Therefore sin u 
=-%, = j - ; a — = *01 in. Tbe actual size of tbe bole by micro- 
o y * u^J 
metric measurement was *011 in. 
These experiments show that tbe diffraction limit is at least fifty 
times greater than that assumed, and tbe line of demarcation between 
fine and coarse must be altered to 1/50 in., from which it follows that 
tbe only Microscope images to be accepted as truthful are those of 
objects larger than the 1/50 in., a conclusion which is known to be 
absurd. 
Another dangerous conclusion from tbe diffraction theory was that, 
because tbe image of fine structure depends upon spectra, therefore make 
spectra. This meant that the spectra should be made as bright as 
possible by reducing tbe aperture of tbe illuminating cone. Reducing 
the aperture of tbe illuminating cone is analogous in its effect to re- 
ducing tbe slit of a spectroscope. Narrow tbe illuminating beam to a 
mere point, and tbe spectra from any diatomic structure will become 
brightly coloured. (So much is this tbe case that if a spectroscope is 
not at band, a coarse diatom, such as a Pinnularia, illuminated by a 
narrow cone when a suitable objective is employed, makes a very good 
substitute ; and a light-filter of any kind can be tested by examining tbe 
spectra at tbe back of tbe objective.) Prof. Abbe, unfortunately, says 
that there is not tbe least ground for supposing that a broad illumi- 
nating beam can be expected to give a truer image than a narrow axial 
illuminating pencil. Apart from tbe question of tbe manufacture of 
false images, this statement renders unnecessary any improvement in 
tbe objective— a statement most damaging to tbe interests of micro- 
scopy. 
In discussing these questions Mr. Nelson carefully defines bis 
nomenclature. The central white beam, sometimes called tbe “ Central 
Maximum,” will be called tbe dioptric beam (D) ; tbe first coloured 
spectrum next tbe dioptric beam the spectrum of the first order (1) ; 
tbe one next to that a spectrum of tbe second order (2) ; and so on ; see 
fig. 48. 
