Now the refractive index μ varies inversely as the velocity; hence we I have extracted from the article on Light in the Encyclopædia Metropolitana the values of x for the seven fixed lines, as determined by M. Fraunhofer, and have also taken the values of μ given by the same author for seven kinds of glass and three fluids, water, solution of potash, and spirit of turpentine. For each of these substances we shall have seven equations between p, q and 7, with the known values of μ and x. I have always determined p, q, from the equations given by the lines (B), (E) and (H), and by substituting the values of the last two quantities, q and 7 in the other equations, have determined from them values of p. The verification of our formula consists in the near coincidence of the values of p with each other. The rest will be easily understood from the following tables. Table I. contains the values of X, 100,000 and 1,000,000 for the different fixed lines expressed in parts of a Paris inch: they are multiplied by some power of 10 merely to avoid decimals. The next Table contains the values of μ to four places of decimals. I have not considered the succeeding places determined with sufficient accuracy to admit of our reasoning on them, as will likewise strike any person who examines the Tables wherein the results of two experiments on the same substance are given. 1 Designating the values of by b, c, d, &c. we obtain the following equations: b=p-15488.q+ 23987.7, c=p-17047.q+ 29060.7, d=p-21139.q+ 44685.7, e=p-26434.q+ 69875.1, f=p-31071.q+ 96541.7, g=p-39705. q + 157650 . l, h=p-46657.q+217690.7; .. b-e=10946.q- 45888.l, e-h=20223.q-147815.7; .. 20233 (b-e)-10946 (e-h) = (147815.10946-45888.20223) × l, And four other values of p are to be found from the equations c, d, f, g. The following Table contains the values of q and deduced from equations b, e, h. The following Table contains the values of p deduced in the manner before mentioned. Flint Glass, No. 13. .38624 .38624 .38623 .38624 Flint Glass, No. 23. .38626 .38639 .38624 .38629 .38629 .38626 .38629 .38627 .28637 .38629 .38717 .38726 .38718 .38717 .39755 Flint Glass, No. 30. .38722 .38732 .38717 .39751 .39747 .39755 .39760 .39755 .39755 The principal discrepancy in these results arises from the values of p given by the line G, they being in nearly every case too great. I can only conclude from this, that our approximation ought to have been carried to another term, as for G and H the value which the third term introduces is considerable, and there can be little doubt but that the fourth would produce a sensible effect to the fourth place of decimals. It would, however, diminish the variation which the expression admits of, to proceed to other terms, and for that reason, considering our object merely to test the accuracy of our conclusions, no better plan has suggested itself than to leave the expressions in their present form. If, however, it were requisite to determine accurately the values of p, q... of course the plan to be adopted would be, that of introducing |