Transactions of the Cambridge Philosophical Society, المجلد 23

a₁ aberration approximation arbitrary asymptotic expansion b₁ b₂ bitangent C₁ C₂ coefficients condition congruence consider const constant contains correlation corresponding cos² cosh curve of contact cylinder denote determinant double curve equal equation exit-pupil expression finite formula Fourier series g₁ given gives h₁ h₂ Hence holomorphic homoscedastic I₁ independent integral intersection Jacobian k₁ linear lines Mathieu functions N₁ notation obtain p₁ partition periodic functions permutation phase-space plane positive quadric quasi-periodic regression of X3 residual curve S₁ satisfied scroll second-type single-valued singular points solution spherical spherical aberration suffix suppose surface symmetric functions T₁ tensor theorem theory trajectory-domain transformation u₁ v₁ values vanish variables wave X₁ X3 on X1 XXIII Y₁ Z₁ zero