Issociati 163 
£ Proceedings 
succession of intermediate tints, which the Dalionians see in con- 
trast. The Daltonians see exactly as we do, the mixed rays dis- 
covered in the spectrum by Fraunhofer, at least in all that arsed 
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 dow tis name 
to posterity. 
~ Mr. Dent sireteuted a paper on the preservation of ea olerchaalee 
eter balance springs, by forming upon them a thin coat of pure 
gold, by means of the electrotype process. Prof. Christie read a 
paper on the preservation of magnetic needles and bars from oxi- 
datien, by the same process. 
On the relation of Sturm’s Ausiliary Functions to the Roots 
ofan 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 
put under the form of a fraction, the denominator of 
which i is @ perfect square, or in fact the product of many ; like- 
wise the numerator contains a huge heap of fractions of a similar 
These, therefore, as well as the denominator, since they 
cannot influence the series of signs, 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- 
ogy anatomy of these remarkable forms. 
~ Prof. Moseley gave an account and drawing of a re for 
ting the numerical values of Diefrrise Integrals. 'The 
