178 Mr. M. Ponton on certain Laws 
temperatures, in order that these might operate as a check on 
each other. 
It will be particularly noted that in each medium the con- 
stants e and a are independent of the absolute magnitudes of the 
extrusions, and are affected only by the relations which these in- 
dividually bear to each other. Hence, provided those relations 
be preserved, the constants ¢ and a will remain unaffected by any 
alteration in the adsolute magnitudes of the extrusions, which 
may accordingly be multiplied by any multiple m, mtegral or 
fractional, without altering ¢ or a. These two quantities are 
thus consistent with an indefinite number of sets of indices of 
refraction, so that these last may always be altered in a certain 
manner without affecting those constants. 
This point being kept in view, the followimg general formula 
will be found applicable to all media whatever, namely, 
deli tse cilia al aad, a 
(B—eb) ty | (C—ec)ty | D—ed) ty | Bee) eq 
i eae cored sanda 
+ Gi f)tn* Ga) tn | Hay en S =” 
the quantities ea and 7 being each constant for the same medium 
and temperature, and S being the sum of the normal wave- 
lengths, or the total amount of vis viva involved, the conserva- 
tion of which thus depends on these three constants. To find 
B C 
R B—eb C—ee 
+ &c. =%, and call > =ea', then 7 is the difference between ea 
the constant », if we call the sum of the series 
and ea’. Ifa>a’, then the sign of 7 is +; if a'><a, the sign 
of 7 is —, and in either case is constant for the medium and 
temperature. 
Now the value of 7 depends on the relation of X (the sum of 
the positive or negative extrusions) to a; and there may always 
be found for each medium and temperature such a positive value 
of X as shall make 7=0. ‘This it is proposed to call the limiting 
value of X, and to denote it by X’. In some media this limiting 
value nearly coincides with the actual value of X, as given by 
observation ; in others the actual value is several times greater 
than the limit; while in a few it falls somewhat below it. Call- 
. , 
ing = =o, it will be found that, making a small allowance for 
the effects of errors of observation, this quantity » is constant 
for all media whatever ; so that in every instance we have aw=X’, 
the limiting value of the extrusions. This constant w may be 
