228 Mr. Arry on Achromatic Eye-pieces of Telescopes, 
to work almost without rules, in most instances merely copying 
the constructions which more able opticians have found to 
succeed. I flatter myself that an attempt to investigate, on the 
simplest principles and in the most comprehensive manner, an 
optical theory of so great importance, avoiding at the same time 
all unnecessary refinements and useless generalities, will be re- 
ceived with encouragement by the Society, whom I have now 
the honor of addressing. 
The first attempt at improvement on the single eye-glass of 
the first refracting telescopes was made by Huygens. Instead of 
a single eye-glass he used two convex lenses, whose focal lengths 
were in the proportion of 3 to 1, and which were placed at a 
distance equal to twice the shorter; the lens of greater focal length 
being that nearer to the object-glass; and the image being formed 
between the two eye-glasses. His intention was to diminish the 
spherical aberration of the extreme pencils by dividing the re- 
fraction into two parts: for, as he found the spherical aberration 
to vary nearly as the cube of the refracting angle, it was easy 
to see that the aberration would be reduced to 4th of its former 
quantity, if the whole refraction, instead of being effected by one 
refracting angle, were effected by two, each equal ‘to half the 
former. It will easily be seen that in his construction any pencil 
is refracted equally by both lenses, and the improvement which 
he aimed at was therefore completely attamed. But there were 
other advantages of which he was ignorant, and which were not 
discovered until the construction had been many years employed. 
It is smgular, that in his attempt to diminish spherical aberration, 
he should have hit upon a construction which completely removes 
also chromatic aberration. This was discovered when the unequal 
refrangibility of light was established, and the mode of obviating 
the inconveniences thence arising was invented: and the con- 
struction of Huygens, commonly known by the term of the 
