Taking the above value of the absolute wave-length and applying the appropriate corrections to some of the fundamental lines given in Prof. Rowland's paper (this Journal, March, 1886) the wave lengths of the principal Fraunhofer lines in air at 20° and 760mm are,

Comparisons between these wave-lengths and the older ones become somewhat uncertain toward the ends of the spectrum since the appearance of lines like A, B, G and H vary so much with the dispersion employed. The relative wave-lengths above given are certainly exact to within one part in half a million.

It may not be out of place here to discuss the most recent work on this problem. Just before the publication of my first paper the very elaborate paper of Müller and Kempf appeared. Their work is a monument of laborious research and it is unfortunate that so much time should have been spent in experiments conducted with glass gratings of small size and inferior quality. Since the invention of the concave grating, it is a waste of energy to make micrometric measurements with plane ones, and this statement could hardly be corroborated more strongly than by the relative wave-lengths given by Müller and Kempf. The probable error of their wave-lengths is in general not less than one part in two hundred thousand. That the value assigned by them to the absolute wave-length is as near the truth as it probably is, is due to no lack of faults in the gratings. Their results for the line D, were as follows:

A discussion of these errors as exemplified in the paper under consideration would take up too much space to be inserted here, but one or two points are worthy of notice. When a grating gives different results in the different orders, it is evident that there are in it serious errors of ruling, and the maximum amount of the variation will give a rough esti

mate of their size as compared with those of other gratings. Applying this test, the four gratings rank as follows: "5001," 8001 L,""2151," "8001," where the first which gave for the w. l. 5896-14, had no sensible variation in the different orders and the last, which gave 5895 97, varied in the most erratic fashion. It by no means follows, however, that because a grating gives identical results in the various orders, it is therefore free from errors of ruling. Witness Grating III of this paper in which the error was of a kind which could not be detected at all in the spectrometer. Yet it was large enough to give, if neglected, 5896-28 for the wave-length of D,.* Speaking of errors in gratings a case in point is the work of Peirce. On account of the reasons heretofore noted Peirce's standards of length are somewhat uncertain in value so that no definite correction can be as yet applied to his wave-length from this cause. Three of his gratings, however, I have calibrated, and each of them showed an error tending to diminish the wavelength. If the mean result obtained from these had been assumed to be correct it would have been equivalent to the introduction of a constant error. Peirce's preliminary result is for this reason too large by more than one part in a hundred thousand; how much more, it is impossible to say without knowing the results obtained from each grating and so being able to apply the corrections found. Peirce's method was such as should have secured very excellent results and such will undoubtedly follow a further investigation of the standards and gratings. Still another recent determination is that by Kurlbaum, who used two good sized speculum metal gratings and measured them with particular care. Like the previous experimenters he neglected, although he did not ignore, the errors of ruling and consequently the results he obtained are somewhat in doubt. A serious objection, moreover, to his work is the very small spectrometer he used. To undertake a determination of absolute wave length with a spectrometer reading by verniers to 10" only, and furnished with telescopes of only one inch aperture is simply courting constant errors. More especially is this true since it would be hard to devise a method more effective in introducing the errors of ruling, than to use a grating with telescopes too small to utilize its full aperture, and then determine the grating space by measuring the total length of the ruled surface. Kurlbaum's gratings, too, were of an unfortunate size, 42 and 43mm broad respectively, and consequently by no means easy to measure. On the whole his result, 5895.90 is not surprising.

*The results given by the gratings used by the author, neglecting the correc tion A would be as follows:

I. 5896-20; II, 5896-14; III, 5896-28; IV, 5896-12 Curiously enough the mean would be practically unchanged.

The agreement of relative wave-lengths as determined by different experimenters unfortunately gives no measure as to the accuracy of the work. The relative wave-lengths as determined by Müller and Kempf and by Kurlbaum agree in general to within 1 part in 100,000: the absolute wave-lengths assigned by these experimenters vary by more than 1 part in 30,000.

A very ingenious flank movement on the problem of absolute wave-length has been made by Macé de Lépinay. His plan was to use interference fringes in getting the dimensions of a block of quartz in terms of the wave-length, and then to avoid the difficulties of the linear measurement by obtaining the volume through a specific gravity determination. His results do not indicate, however, experimental accuracy as great as can be obtained by the usual method, and the final reduction unfortunately involves a quantity even more uncertain than the average standard of length, i. e., the ratio between the meter (?) and the liter.

It may be interesting here to collect the various values which have been given for the absolute wave-length within recent years. Results are for the line D,.

These figures are discordant enough. When beginning the present work, I had hoped that it would prove possible to make a determination of absolute wave-length commensurate in accuracy with the relative wave-lengths as measured by Prof. Rowland. This hope has proved in a measure illusory, by reason of the small residual errors of the gratings and the greater uncertainty involving the standards of length. I feel convinced, however, that the result reached is quite near the limit of accuracy of the method. It should be remembered that any and every method involves the uncertainty of the standards of length, an uncertainty not to be removed until a normal standard is finally adopted and exact copies of it distributed. And as far as experimental difficulties are concerned, the next order of approximation will involve a large number of small but troublesome corrections, such as the effect

of aqueous vapor on atmospheric refraction, varying barometric height, the minute variations in the grating space, failure of thermometer to give temperature of grating exactly, and countless others which will suggest themselves only too readily.

*

Aside from the use of gratings, decidedly the most hopeful method as yet suggested is that due to Michelson and Morley. Theoretically the plan is particularly simple and beautiful, consisting merely in counting off a definite number of interference fringes by moving one of the interfering mirrors and measuring, or laying off upon a bar, the resulting distance. The mechanical difficulties in the way, are however formidable, and whether or no they can be surmounted, only persistent trial can show. The possible sources of error are of much the same type and magnitude as those involved in the comparison of standards of length, and if these errors are avoided, the uncertainty concerning the standards still remains. Whether or no the practical errors of the method are greater or less than with gratings only experience can prove. Certainly if the method is capable of giving exact results it is in the hands of one able to obtain them from it.

In closing this paper I can only express my sincerest gratitude to the various friends who have done all in their power to facilitate my work, and especially to Professor W. A. Rogers who has been tireless in his endeavors to determine the true value of the standards of length; to Mr. J. S. Ames, Fellow in this University, who has given me invaluable aid in the work with metal gratings; and to Professor Rowland who has furnished all possible facilities and under whose guidance the entire work has been carried out.

Physical Laboratory, Johns Hopkins University, March, 1888.

ART. XXXI.-Three Formations of the Middle Atlantic Slope; by W. J. MCGEE. (With Plates VI and VII.) (Continued from page 330.)

THE COLUMBIA FORMATION.

General Characters.-The Columbia formation exhibits two phases which, although distinct where typically developed, intergraduate. The thicker and more conspicuous phase occurs commonly along the great rivers at and for some miles below the fall line, and may be designated the fluvial phase; while the thinner generally forms the surface over the remainder of the Coastal plain, and may be designated the interfluvial phase.

*This Journal, III, xxxiv, 427.

The first phase is bipartite, the upper division consisting of massive or obscurely stratified brick clay, loam, and fine sand, and the lower of stratified and cross laminated gravel and coarse sand, containing abundant erratic bowlders; while the second consists of an indivisible bed of gravel, sand, clay, etc., chiefly of local origin and thus varying from place to place though tolerably homogeneous in each exposure. The first phase, too, is confined to limited altitudes, approximately constant on each river but rising northward, while the second occurs indiscriminately at the highest and lowest altitudes within the Coastal plain, its thickness culminating at the lower levels and along the coast.

The Fluvial Phase. The bipartite phase of the formation is well developed along all of the larger rivers of the Middle Atlantic slope, but most characteristically and extensively on the Potomac, the Susquehanna, and the Delaware.

The deposits on the Potomac.-Washington lies within a rudely triangular amphitheater opening southward, into which the Potomac falls from the northwest and the Anacostia from the northeast, the former passing from torrential to estuarine condition and turning southward within the limits of the city. The western side of the amphitheater is the Piedmont escarpment, which south of the city is a terraced or irregular slope rising to a somewhat undulating plain 200 to 425 feet in altitude; the eastern side is the line of bluffs overlooking the Anacostia and rising into two broad terrace plains 175 and 275 feet in height respectively; and the northern confine is the deeply ravined margin of a terrace 200 feet in altitude stretching from the breach made by the Potomac in the Piedmont escarpment directly eastward to the broader valley of the Anacostia three or four miles above the confluence. The floor of the amphitheater is a series of low terraces rising from a few feet below to about 100 feet above tide, the most conspicuous two being about 40 and 80 feet in altitude respectively. To the southward the amphitheater opens into a broad valley occupied partly by the Potomac estuary and partly by a low but extended series of terraces, of which the best developed members are about 20 and 40 feet above tide respectively.

Throughout this amphitheater the fluvial phase of the Columbia formation is the prevailing superficial deposit up to 150 feet above tide; except where manifestly eroded or buried beneath modern alluvium, it is everywhere exposed; all of the lower and many of the higher terraces are built of it; and it unquestionably lines the estuaries of both the Potomac and the Anacostia beneath the recent alluvium. The relation between the deposit and the topographic configuration is striking, and