ab, figure 20, crossing the central meridian at 90°, just midway between N" and S. The line ab is the stereographic projection of the parallel 39° S., which in this case is a straight line because P is at 39° S.; compare the projection of the parallel 40° S., figure 16, page 269. Since angles are preserved in the stereographic projection, the meridian must make equal angles with one another (5°, figure 20) at N" and S"; hence N" and S" may be considered as the poles of a projection on the plane of a meridian having a diameter N"S", and the construction of the meridians is the same as described on page 256. In drawing a map, such as that of the United States, on a large scale, the location of the meridians and their curvature must be determined by calculation, and one example will illustrate how this may be done: On the diameter ew, passing through the center of the map at right angles to the line "S", it is desired to find the point where that meridian intersects it, which is 35° from the center of the large circle II. Knowing the radius of the large circle II, the radius r, for describing the meridian which intersects the diameter ab at 35° from the center, may be found from a table described at the close of this article. A right triangle Aux may then be constructed, in which the hypothenuse and the perpendicular p (equal to the distance from e to the center of the map) are known; hence from sine. Р the value of A may be found. Construct the chord vx,

A=

r

and from its center m draw a line to A; the line mA bisects the angle A. Also it follows from the construction that in the triangle xvy the angle at v is equal to A; hence tangent

=

xy

" p

A from which the value xy may be calculated. The distance cv being known, and equal to the distance from the center of the map to y, the distance from the center of the map to x is readily determined.

A method like the foregoing was used in plotting the meridians of a large stereographic map of the United States. In addition to a construction line drawn through the center of the map, corresponding to ew, figure 20, two other lines were drawn parallel to ew at measured distances, one crossing near the top, the other near the bottom of the map. The points of intersection of the several meridians with the three construction. lines were then calculated, and each meridian was drawn through the three points thus determined, making use of a large circular arc ruler. The calculation was not especially laborious, since only simple formulas were used, and the same quantities were repeated several times, so that to a certain extent the work becoines almost mechanical.

[To be continued.]

ART. XXII.-On the Hind Limb of Protostega; by S. W. WILLISTON.

ALTHOUGH the structure of those huge Cretaceous turtles, Protostega and Archelon, has been, for the most part, determined in recent years through the researches of Baur, Hay, Case and Wieland, little has hitherto been discovered concerning the limbs, aside from the humerus and femur. In examining the material of Protostega in the University of Kansas museum recently, I found a nearly complete hind limb collected by Mr. Charles Sternberg in the Kansas chalk two years ago. This is of so much interest that I give herewith a brief description and outline figure of it. The species is, I

1

O

Hind Limb of Protostega.

suppose, P. gigas, though I do not feel certain. Among the various specimens of this genus I have examined there is a great difference in size, a character of doubtful value for specific separation, as well as distinct differences in the shape of the limb bones. The present specimen, for instance, is among the largest discovered in the Kansas chalk, and has the femur much more slender than in the specimen figured by Case (Journal of Morphology, June, 1897, pl. vi, f. 18).

The specimen had been, for the most part, washed from its matrix, and the original relation of the different bones lost, but since only the posterior part of the skeleton is present they all clearly belong to the hind limb. The bones of the fore limb, moreover, are all much larger than those of the hind. Some of the phalanges were lost and probably one of the tarsals. In the figure I have arranged the bones as they would seem to belong, though very likely some of the metatarsals and phalanges had different positions in the living skeleton.

For a review of the discussion as to the systematic position of Protostega, the reader is referred to the paper by Professor

Case cited above. The relationships to Chelone and Thalassochelys pointed out by Baur, Hay and Case receive additional confirmation from the structure of the limb, as will be seen in the accompanying figure. The leg, while broader and more powerful, is not essentially different in structure from that of Thalassochelys, and it would seem that there could hardly be longer a question as to the relationship of these forms,Protostega and Archelon, at least,-to the Cheloniidae.

The characters separating Archelon Wieland from Protostega Cope, while not very important, would seem sufficient. Nevertheless, one can derive little justification from the difrent geological horizons in which the forms are found. The relations between the Niobrara and Fort Pierre vertebrates are for the most part very close. I have recognized in both horizons Tylosaurus, Platecarpus and Mosasaurus (Clidastes), as well as Pteranodon and Hesperornis, all very typical of the Niobrara deposits, and the existence of Claosaurus has been recently affirmed in the Fort Pierre. On lithological grounds, there is nothing separating the two groups of deposits, and I protest against the names Colorado and Montana, as perpetuating a wrong impression. On paleontological and lithological grounds there would be much better reasons for uniting the Niobrara with the Fort Pierre than with the Fort Benton. Description. The head of the femur is large, and, in life, evidently nearly hemispherical. The neck is very stout, placed at nearly right angles to the axis of the shaft and is but slightly constricted. The trochanter is large, and stout, with a large, triangular, roughened area on the posterior side for muscular attachment. The smaller trochanter is indicated by a small tuberosity. The shaft is much constricted and curved, with its convexity dorsal; it is nearly cylindrical at its middle part. The condyles are large and stout, the inner more massive than the outer one; their articular surface looks nearly backward. The tibia is much expanded superiorly, and has its articular surface at an angle of about 45° with the axis of the shaft. On its posterior surface, and margin, a little below the angle there is a strong muscular rugosity. The shaft is much narrowed below, and is again moderately expanded for the distal articulation.

--

The fibula is elongated and narrow, of nearly uniform width, except at the upper extremity. This portion of the bone is wanting in the specimen but that portion preserved indicates a moderate expansion superiorly. On the posterior surface, opposite the roughening of the tibia, there is a strong rugosity, produced into an angular tubercle, for muscular attachment.

Three tarsal bones are preserved, and there was probably

AM. JOUR. SCI.-FOURTH SERIES, VOL. XIII, No. 76.-— APRIL, 1902.

one more not recovered. They are all rounded and flattened. The largest, apparently the tibiale, shows a thickened cartilaginous border on three sides, elsewhere thinned. The next larger tarsal, probably the fibulare, is somewhat thicker, and has the thickened cartilaginous surface encompassing nearly the border. The third bone, the smallest, and probably belonging in the distal row, is a more thickened nodular bone, oval in shape with one side much thickened for cartilage.

The metatarsal of the first toe is a thin, broad, hatchetshaped bone, with a proximal thickened articular border for union with the tarsus, a smaller distal surface for phalangeal articulation, a thickened, concave inner border and a strongly convex, thin, outer border.

The three metatarsals belonging to the second, third and fourth toes are moderately slender, with the extremities moderately expanded. Their relative positions I cannot give positively, but I have arranged them in the figure as they would seem to belong. They differ only a little in length; two of them have one border nearly straight, the other concave, while the shortest and stoutest has both borders markedly concave. The fifth metatarsal bears no phalanges. It is a slender, triangular bone flattened proximally, where it articulates with the tarsus; curved, cylindrical and pointed distally. It evidently was much divaricated in life.

The phalanges of the first toe were three in number, the first two short, thickened, with a concave proximal and convex distal extremity. The ungual phalanx I believe to be the slender pointed one of the three preserved. The other ungual phalanges preserved, two in number, were less slender, one much smaller than the other. One other phalanx is known, a rather short and but little constricted bone, apparently belonging in the second row.

Lengths second, third and fourth metatarsals.. 140, 155, 170

University of Kansas,

Lawrence, Kansas.

ART. XXIII.-The Physical Effects of Contact Metamorphism; by JOSEPH BARRELL, Ph.D.

Introduction.-Although much has been developed in past years concerning the physical, chemical and mineralogical effects of the metamorphism produced in sedimentary beds by the contact of igneous masses, but little has been said concerning the wholesale liberation of gases from the sediments so affected, attended by shrinkages of volume and the possible results in the formation of vein fissures, impregnation deposits and new intrusion of igneous matter, owing to these causes and the changes in pressure which accompany them. Certain of these questions were suggested to the writer in 1899 while studying the geology of the Elkhorn District in Montana as a field assistant for the U. S. Geological Survey, and the following article was written in the petrographic laboratory of the Sheffield Scientific School of Yale University under the supervision of Prof. L. V. Pirsson as one chapter in a thesis on the Geology of the Elkhorn District, prepared in partial fulfillment of the requirements for the degree of doctor of philosophy.

Excluding for the moment the possible impregnation and metasomatic effects of mineralizing vapors and heated waters carrying dissolved materials into the contact rocks, the chemical effects consist in the more or less complete expulsion of carbon dioxide and combined water and the formation of the remaining constituents into new minerals. In addition, there are physical effects of considerable magnitude; the strata not only assume a greater hardness and density, but in beds of certain compositions it will be shown that there may be a shrinkage of from 25 to 50 per cent. in volume, attended with the evolution of great quantities of gases which at surface pressures and temperatures would amount to several hundred times the volume of the original sediments.

The reasons why such changes in volume have not been noted in the field probably lies in the special compositions necessary to produce the most striking effects and the fact that intrusions have often greatly disturbed the adjacent

strata.

The kinds of rocks which will be least affected are those of igneous origin. In the presence of later intrusives and disregarding the temporary expansions due to the high temperatures, these will naturally suffer no appreciable change in volume and none at all in mass. The most that would be expected to occur would be the acquisition of certain characteristics due to the minerals having been exposed to long and intense reheating. On the other hand, those subject to the