., Monthly Mi ical 
(296 . Transactions of the pee ir 
Il.—On Aplanatie Definition and Illumination with Optical 
Illustrations. By G. Royston-Pieorr, M.D., M.A., &e. 
(Read before the Royau Microscopicau Society, October 12, 1870.) 
Puate LXVII. 
Mr. PREsIpDENT AND GENTLEMEN, 
I have in the first place to express my regret that circum- 
stances over which I had no control prevented me from accepting 
the invitation to be present at the discussion of the first paper I 
had the honour of sending for the consideration of the Council. 
I have also to tender the Council my thanks for the present 
opportunity of explaining some views and methods applicable to 
Aplanatic Definition and Illumination. Important as is this subject, 
I fear that I shall fail to do justice to its merits to attention, though 
without doubt it forms the very pith and marrow of accurate instru- 
mental vision. 
At the outset I must ask your kind indulgence for the course 
I am about to pursue. There are many in this room who may 
perhaps think my conclusions turn upon points so elementary as to 
be unworthy of iteration ; whilst many others may think the details, 
on the contrary, too technical or complex. 
But, yet, [ hope no apology is needed for appealing to funda- 
mental truths. It is only by mastering the axioms of science that 
true progress can be made. 
The man who starts on a voyage of discovery must provide him- 
self not with instruments only, but with fundamental principles. 
There are two fundamental cogent truths which have done 
more for exact science than any other par eacellence. 
Thus Astronomy, Navigation, Trigonometry, and Optics are 
built up upon that great property of right-angled triangles—that 
of the squares of their sides. 
And Optics is especially dependent upon their relations to each 
other, or the rule-of-three proportion of their sides. 
If it be desired to form a perfect 
square angle of 90°, we have only to 
form a A whose sides are in the relation 
of 5, 4, and 3.* . 
Again, if a blue ray of light passes 
out of the spectrum, and is transmitted 
through two different media, as water 
and glass, a triangle constructed with 
its sides representing the refractive in- 
dices of the blue ray in each media, and one angle representing 
* The square of 5 or 25 being equal to the sum of the squares of 4 and 3, or 
25 = 164 9. 
