full heat of five small Bunsen's burners, in about four minutes the needles were rather suddenly deflected 24° with irregular action at a particular temperature not even approaching that of the lowest visible redness in the dark; and by heating to a much higher temperature, but still below redness, faint signs of a second similar molecular disturbance in the same direction were manifested. The heat being now stopped and the bar allowed to cool gradually, the same phenomena, and to the same extent, took place, but in an exactly reverse order. On repeating the experiment with this bar, but cooling the bar rapidly by continuous application of cold water, a sudden deflection of 8° occurred when the bar acquired the proper temperature. direction of all the deflections with this bar (as with nearly all the previous bars) during heating agreed with those producible by a decrease of magnetism, and during cooling with an increase of magnetism. By substituting for the fine-wire coil another, containing 3600 turns of size "No. 29" (=0.28 millim. thick) copper wire, very feeble results only were obtained, the coil itself offering too great a degree of conduction-resistance.

The

In these experiments with wrought iron, steel, cast iron, and nickel there is a very gradual magnetic change, in addition to the several sudden or irregular molecular movements and changes of magnetism; this gradual change is manifested by a very faint deflection of the needles in the same direction as those produced by most of the sudden movements.

By substituting a bar of zinc 3 feet (=91 centims.) long and 1 inch (254 millims.) thick, or one of antimony 30 inches (=762 centims.) long and 1 inch thick, for those of the other metals, and heating their middle parts to incipient fusion, I obtained no definite movements of the galvanometer-needles. With a bar of bismuth 15 inches (=38.1 centims.) long and about an inch (=12.7 millims.) thick, and heating its middle part, also no movements of the needles took place.

With a bar 9 inches (=23 centims.) long and 2 inches (=63 centims.) thick, composed of commercial antimony containing a small amount of iron, and with suitable coils about 1 inch (3.8 centims.) in length upon its ends, an irregular succession of ten distinct internal changes in the bar, corresponding to decreases of magnetism, were observed during the heating. The bar was then so hot as to char the wooden wheels containing the wire, and had to be cooled ; during its cooling a continued succession of changes of an opposite kind took place. With a second bar 13 inches (=33 centims.) long and 1 inch (=3·8 centims.) thick, containing more iron, the effects were very feeble, chiefly owing to the wire coils being much further asunder. The method I have adopted admits of the detection of minute

magnetic changes in bars of iron, steel, nickel, &c., especially if a powerful battery and a delicate galvanometer are employed, and might probably be used to throw a light upon the influence which the presence of foreign substances have upon iron &c.

The foregoing phenomena may be employed as an illustration of a very general (I may say, universal) property of matter which has not, that I am aware, been specially recognized as ch. Every substance, even those of the simplest constitution (as the elementary bodies, and even those of them which are in the seous state), when acted upon by a single external force, possesses the power of dividing the influence of that force in such a way that, instead of producing only one force or one effect, it produces s、veral; or, stated more briefly, matter has a universal property of dividing and multiplying forces and effects. For V in heating a bar of iron to redness a whole series of changes occur in its molecular structure, its magnetism, ite dencastous, and its cohesive power, in addition to the changes in 1 cific heat, its thermoelectric capacity, and its electric conducting-power. The changes produced by heat in even so simple a substance as iron were so numerous in some of these experiments as to produce the impression that the metal was endowed with vitality.

i starice,

XXI. On the Measurement of Wave-lengths by means of Indices of Refraction. By WOLCOTT GIBBS, M.D., Rumford Professor in Harvard University*.

IN

N a brief notice + communicated to the British Association for the Advancement of Science at its Meeting in 1849, Professor Stokes has given a method for measuring wave-lengths, which depends upon the fact that, in substances of medium refractive power, the increment of the index of refraction in passing from one point of the spectrum to another is nearly proportional to the increment of the square of the reciprocal of the wavelength. The author showed that even when the intervals were taken much longer than necessary, the error in the wave-length was usually only in the eighth place of decimals. At the date of the publication of this notice the subject of wave-lengths possessed but little interest. The recent development of the spectral analysis of light has given a new impulse to this branch of optics, and has rendered necessary the construction of a normal map of the entire solar spectrum. This has been most

* From Silliman's American Journal for July 1870. Read before the National Academy of Sciences, April 12, 1870.

+ Report of the British Association for the Advancement of Science for 1849. Notices and Abstracts, p. 10.

successfully accomplished by Ångström*; but an attentive study of his work, as well as of the elaborate researches of Van der Willigent and Ditscheinert, will show that new measurements will be far from superfluous. The imperfections even of the best ruled glasses are so great that it may be reasonably doubted whether the wave-lengths of very fine lines can be satisfactorily measured directly. Methods of determining such wave-lengths, depending upon the comparison of the refraction- and diffraction-spectra, have been given by myself and by Thalen. As it seems at least desirable to multiply such methods, I will here give first a discussion of the method of Stokes in its original form, and afterwards a simplification of that method, which will also have its uses.

If Cauchy's formula for dispersion,

b с n=a+ + λ2

be reduced to its first two terms, and if we then eliminate the constants a and b from three of the equations of the form

b

n=a+ እዩ”

we shall obtain the three following equations, involving only wave-lengths and indices of refraction :

Of these equations (1) and (3) serve for extrapolation and (2) for interpolation. To test the degree of accuracy attainable in determining wave-lengths by these formulæ, I have selected the measurements made by Van der Willigen ¶. The indices of refraction determined by the Dutch physicist are in fact the only * Recherches sur le Spectre Solaire. Berlin, 1869. † Archives du Musée Teyler, vol. i. p. 1.

Sitzungsberichte der k. k. Akad. der Wissenschaften, vol. i. (1864).
Silliman's American Journal, vol. xlvii. March 1869.

Mémoire sur la détermination des longueurs d'onde des raies métalliques,

1868.
¶ Archives du Musée Teyler, vol. i.
p. 70.

indices which are at once sufficiently exact and sufficiently numerous. In addition they have the great advantage of having been made with reference to lines in the solar spectrum the wavelengths of which had been measured by the same observer. There can therefore be no question of identity. As a first example of the method, I give a determination of the wave-length of C, taking B as one of the lines exterior to C, and taking in succession seven other exterior lines more refrangible than C, to combine with B. Formula (2) was therefore employed, and with e following data and results:

In this Table the first column gives the designation or number of the line, the second its index of refraction as determined by a Steinheil prism of 60°, the third the corresponding wavelength according to Van der Willigen, and the fourth the wavelength as found by formula (2) by combining B with each line after C in succession.

The mean of the seven values of the wave-length of C thus found is 656.70, which is in excess of Van der Willigen's own determination of the value of C by 0.14. From this it appears that the method may be applied with a tolerable degree of approximation, even in the case of a flint-glass prism of high dispersive power, and for indices of refraction which refer to lines at considerable angular distances from each other. The increase in the computed values of C as the intervals between B and the second line of comparison are increased, however, will clearly appear from the Table. The following results were obtained with the indices of a second Steinheil prism, No. 2, of 46° 52′ 25"-8, also of flint glass:

the mean of which is 656-28, the error being —0·28. To determine to what extent the method applies when flint-glass prisms are used and the indices are selected from the more refrangible portion of the spectrum, the following data were assumed :

In this Table line 37 is taken as the middle line in applying formula (2), and the results obtained by combining the other lines in pairs are given in columns 4, 5, and 6. It will be seen that, as in the case of the less refrangible portion of the spectrum, the results obtained are with this prism always too high. For the purpose of comparison, I have computed the same wavelength from the indices of refraction of the second prism. The data and results are as follows:

In the case of the first prism the mean of the errors is +0.21, while for the second the mean of the errors is +0.35. From this it appears that in the more refrangible portion of the spectrum the errors are considerably greater than in the less refrangible portion, even for equal differences of wave-length, and, further, that the advantage in precision is with the prism having the higher dispersive power. As the probable errors of the measurements of the indices of refraction are not given, it is impossible to determine to what extent the errors in the computed wave-lengths are due solely to want of precision in the indices. It is also to be remarked that, while with the second prism the errors in the less refrangible portion of the spectrum are affected with the sign, in the more refrangible portion they are largely positive. The close agreement in the value of the wave-length of 37, as found by Van der Willigen, with the values as found by Ditscheiner and Ångström (438.27 and 438.28), proves that the source of error is not an erroneous determination of this quantity. It seems, therefore, certain that the nearly constant errors noted above are due in part to the fact that the indices of refraction are determined only to five places