ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
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indulgence, as the only other avenue for such a purpose has been closed 
to those who do not accept Prof. Abbe’s theory in its entirety. 
The diffraction theory has been likened, as you are aware, to tlio 
theory of gravitation. Let us, therefore, compare them. The theory of 
gravitation may be said to rest on three points — viz. mathematical 
proof, physical law, and experimental proof ; — moreover, it is not afraid 
of criticism. 
The diffraction theory rests on no mathematical proof — in the main 
it accepts the physical law of diffraction ; but on experiment it utterly 
breaks down, all criticism is stopped, and everything connected with it 
has to be treated in a diplomatic kind of way. 
Both theories may be said to resemble an arch, being built up on 
theory and experiment, and held in equipoise by a keystone at the top. 
The diffraction arch, after being built up on theory and experiment, 
culminates with the calculation of the Eichorn intercostals as its key- 
stone. The discovery of these intercostals on the P. angulatum (which 
has been likened to the discovery of the planet Neptune) was arrived at 
by “ a mathematical student, who had never seen a diatom, and who 
worked the purely mathematical result of the interference of the six 
spectra.” 
In the same way the discovery of Neptune may be called a key- 
stone of the gravitation theory. It would be incorrect in this connection 
to say the keystone, because the gravitation theory has many keystones, 
while the diffraction theory has only the one, viz. the Eichorn inter- 
costals. If, for instance, one could prove that the planet Neptune had 
no objective reality, but was a mere optical ghost, the gravitation theory 
would be seriously compromised. If, this evening, I can prove that 
the Eichorn intercostals are ghosts, then I maintain that I have taken 
the only keystone from the diffraction theory arch, and the conclu- 
sions which Prof. Abbe has arrived at in consequence of that theory, 
with regard to illumination by means of the wide-angled cone, are 
fallacious. 
Let me at this place state that I wish it to be distinctly understood 
that I am not, in this paper, attacking Prof. Abbe’s brilliant dis- 
covery that the image in the Microscope is caused by the reunion of rays 
which have been scattered by diffraction, neither do I question what I 
venture to think is his far more brilliant experiment, which exhibits the 
duplication of structure, when the spectra of the second order are 
admitted, while those of the first are stopped out. I regard these facts 
as fundamental truths of microscopy. The thanks of all true micro- 
scopists are due to Prof. Abbe for giving them to us. It will be then 
asked, how can you disagree with that which you admit ? The point 
is, that it is in the meaning of the word “ diffraction image ” that tho 
difficulty lies. Let me explain. There are in reality three kinds 
of diffraction images, for which I will now substitute the following 
names, “ true diffraction image,” “ true diffraction ghost,” and “ false 
diffraction ghost,” in place of those I used in my previous paper.* 
Now I maintain that both Prof. Abbe and his exponents at the R.M.S. 
have fallen into the grievous error of not distinguishing between these 
* Q.M.J., Ser. II., vol. iv., No. 25, p. 17, “true, true false, and false. 3 
1891. H 
