Proceedings of the British Association. 163 



succession of intermediate tints, which the Daltonians see in con- 

 trast. The Dahonians see exactly as we do, the mixed rays dis- 

 covered in the spectrum by Fraunhofer, at least in all that portion 

 which appears to them illuminated. 



Prof. Whewell, after mentioning some cases of persons affected 

 with this peculiarity, remarked that he doubted the propriety of 

 the name now given to this defect : few persons would desire to 

 be immortalized through the medium of their defects ; and Dal- 

 ton, least of all, requires such a means of handing down his name 

 to posterity. 



Mr. Dent presented a paper on ihe preservation of steel chronom- 

 eter balance springs, by forming upon them a thin coat of pure 

 gold, by means of the electrotype process. Prof. Christie read a 

 pa]Der on the preservation o£ mag7ietic needles and bars from oxi- 

 dation, by the same process. 



On the relation of Sturtn's Auxiliary Functions to the Roots 

 of an Algebraic Equation, by Prof. Sylvester. The author wish- 

 ed to bring to the more general notice of mathematicians, his 

 discovery of the real nature and condition of the auxiliary func- 

 tions, so called, which Sturm makes use of in locating the roots 

 of an equation: these are obtained by proceeding with the left 

 hand side of the equation, and its first differential co-efficient, as 

 if it were our object to obtain their greatest common factor ; the 

 successive remainders, with their signs alternately changed and 

 preserved, constitute the functions in question. Each of these 

 may be put under the form of a fraction, the denominator of 

 which is a perfect square, or in fact the product of many ; like- 

 wise the numerator contains a huge heap of fractions of a similar 

 form. These, therefore, as well as the denominator, since they 

 cannot influence the series of sigtis, may be rejected ; and fur- 

 thermore, we may, if we please, again make every other function, 

 beginning from the last but one, change its sign, if we consent 

 to use changes, wherever Sturm speaks of calculations of sign, 

 and vice versa. The functions of Sturm thus modified and 

 purged of irrelevancy, the author, by way of distinction, and 

 still to attribute honor where it is really most due, proposes to 

 call " Sturm's Determinators," and proceeded to lay bare the in- 

 ternal anatomy of these remarkable forms. 



Prof. Moseley gave an account and drawing of a machine for 

 calculating the 7iumerical values of Definite Integrals. The 



