290 
Transactions of the 
[Monthly Microscopical 
Journal, Dec. 1, 1869. 
It will thus be seen that the new plate not only permits the 
use of objectives of the shortest focal length known, but that it is 
also most favourably constructed for the use of oblique light or of 
an achromatic condenser of extremely short focus. 
This plate was accompanied by an interesting letter from Nobert, 
dated Barth, February 26th, 1869, in which that skilful optician 
acknowledges the receipt of the photographs of the several bands, 
copies of which I had sent him, and, after speaking of them in a 
highly complimentary manner, admits that they exhibit the true lines 
up to the fifteenth band inclusive. He goes on to express his belief 
that the resolution of the higher bands is a physical impossibility, 
an opinion which he bases upon Fraunhofer's formula with regard 
to the spectra produced when Hght is permitted to fall upon closely- 
ruled parallel lines. " The formula sin x = ^ , if by X we designate 
the length of the undulations, by h the distance between two lines 
of the grating, and by x the angle of the refracted rays, gives for 
sin X an impossible value when b becomes less than X." Nobert 
further refers to his paper on gratings in Poggendorff 's ' Annalen ' 
for January, 1852, which those interested in the mathematical 
aspects of this question will find worthy of examination. 
If the view taken by Nobert of the significance of Fraunhofer's 
formula is correct, the shortest wave-length in the visible part of 
the solar spectrum would appear to be the measure of the smallest 
dimension we can ever hope to render visible by means of the micro- 
scope ; and it becomes, therefore, a matter of great interest to know 
whether he has rightly applied the formula, and whether it can be 
shown by actual experiment that the limit he imagines has any real 
existence. Nobert himself would appear to have entertained some 
little uncertainty as to his own deductions, for he writes : — " I am 
therefore very anxious to learn whether in resolving the lines of 
the test-plate we shall be able to progress beyond the fifteenth 
band. It would be a very important step, and one which would 
warrant the hope of the further improvement of the microscope." 
After reading Nobert's letter, I sent it to my friend F. A. P. 
Barnard, President of Columbia College, well known for his studies 
in connection with the apphcation of mathematics to optics, with 
the request that he would give me his opinion as to the application 
of Fraunhofer's formula to the question of the visibility of closely- 
ruled lines when observed under the microscope. Dr. Barnard 
replied in a letter, dated April 3rd, from which I make the fol- 
lowing extract : — 
" You will find a simple statement of all that Fraunhofer ever 
discovered on this subject, in my article in the Smithsonian Keport 
for 1862, pp. 181-18'3. 
