As a preliminary to an investigation of certain diffraction patterns I was led to consider, in some detail, the geometrical aberrations of a symmetrical optical system; and it appeared convenient then to classify the aberrations in orders according as they depend upon various powers of certain small quantities and to exhibit them as coefficients in the expansion of an ‘ Aberration Function.’ If aberrations of the first order only are considered, it becomes evident that one of them stands, in some sense, apart from the rest; I refer to the so-called ‘Petzval’ condition for flatness of field. It is of interest to notice that this condition was known to Coddington and to Airy before the time of Petzval—known at least as far as concerns systems of thin lenses. In the usual notation the condition is ΣΚ/μμ′ = 0; it is therefore independent of the positions of the object and pupil planes and in this respect it stands alone among the first order aberrations. But an increasing number of similar aberrations of higher orders will be found and it is of interest to examine these and to investigate their geometrical meaning. In the following note is given a proof of the Petzval condition, differing from that usually given and falling more into line with the general theory, and indicating also a general method of examining aberrations of this peculiar type.