224 Mr. J. F. W. Herschel on the aberrations of 
trials, and which, therefore, have probably some analogy to 
what would be the final results of theory, if presented in a 
tangible shape, and accommodated to the peculiarities of their 
constructions. 
The object of the following investigations is to remove or 
lighten these objections, by presenting first of all, under a 
general and uniform analysis, the whole theory of the aber- 
rations of spherical surfaces ; and in the next place, by fur- 
nishing practical results of easy computation to the artist, 
disentangled from all algebraical complexity, and applicable, 
by interpolations of the simplest possible kind, to all the ordi- 
nary varieties of the materials on which he has to work. In 
the execution of the former part of this plan, symmetry and 
simplicity in the disposal of the symbols, is the object chiefly 
consulted. To attain this, and at the same time avoid circum- 
locution in the descriptive part of the processes, I have found 
it necessary to adopt a language somewhat different from 
that usually employed by optical writers. Instead of speaking 
of the foe al lengths of lenses or the radii of their surfaces, I 
speak of their powers and curvatures , always designating by 
the former expression, the quotient of unity by the number of 
parts of any scale which the focal length is equal to ; and by 
the latter, the quotient similarly derived from the radius in 
question. This mode of expression does no violence to pro- 
priety, as the magnifying power of a lens is really inversely 
proportional to its focal length, and the curvature of a surface 
is always understood to be reciprocally as its radius ; while it 
gives us the advantage of expressing concisely and naturally, 
all the most useful propositions in optics. It is certainly 
simpler (for example) to say, that “ the power of any com- 
