680 Lord Rayleigh on Hamilton'' s Principle and 
direct or inclined rays, from a near or distant object, at 
either side of the instrument (but not too far from the axis), 
depend on the six other coefficients, Q Q 1 Q' Q u Q/ Q", 
in the expression of the term T (4) . Here, then, we have 
already a new and remarkable property of object-glasses, 
and eye-glasses, and other optical instruments of revolution ; 
namely, that all the circumstances of their spherical aber- 
rations, however varied by distance and inclination, depend 
(usually) on the values of six radical constants of aber- 
ration, and may be deduced from these six numbers by 
uniform and general processes. And as, by employing 
general symbols to denote the constant coefficients or elements 
of an elliptic orbit, it is possible to deduce results extending 
to all such orbits, which can afterwards be particularized for 
each ; so,b}~ employing general symbols for the six constants 
of aberration, suggested by the foregoing theory, it is possible 
to deduce general results respecting the aberrational properties 
of optical instruments of revolution, and to combine these 
results afterwards with the peculiarities of each particular 
instrument by substituting the numerical values of its own 
particular constants." 
Equations (7) are easily deduced. So far as it depends 
upon the unaccented letters, the total variation of T is 
dT — I dx + m dy + ndz + x dl + y dm + z dn 
dY , dV 7 dY . 
=— ax T"dy j-az, 
dx dy J dz ' 
or regard being paid to (1), 
dT = so dl + y dm + z dn, 
in which 
so that 
Idl+m dm + n dn=0, 
C E- >- l l — = - — 
dl ~ n ' dm J n 
and in like manner by varying the accented letters the second 
pair of equations (7) follows. 
If we agree to neglect the cubes of the inclinations, we 
may identify n, n' with unity, and (7) becomes 
x = (z + 2P) I + P/, y = (z + 2P)m + P^n', 
<r ' = _p 1 / + (^_2P')/ / , y=-P 1 m + (^-2P / V, 
determining x, x' in terms of z, z\ /, V supposed known, or 
conversely I, I' in terms of 2, z', «r, x' supposed known. The 
