We select from the list of answers quoted by Dr. Raymond in his "Law of the Apex":

"The highest point at which the ore or rock is found "'in place' or between the walls of the vein, and not a "'blow out,' or part of the ledge broken down outside "the walls."

"The croppings, or the exposed surface of the vein, " or lode."

"The highest point at which it approaches or reaches "the natural surface of the ground."

"The highest point of its outcrop in rock in place." "That point at which the vein enters or emerges from "rock in place."

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"The top, or apex, is generally understood to be that part of the lode that is first discovered. A vertical "lode has its apex at the surface."

"Where the mineral-bearing crevice-matter is first "met, either on the surface, or, as in blind lodes, under"ground; but wherever it is met, there begins the 66 apex."

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"The croppings, or highest point of the ledge appearing above or discovered beneath the surface."

"The highest point of the center of the ledge."

"The outcrop in the highest geological level, whether "this is accidentally higher or lower than some outcrop "caused by denudation, or slip."

"Where it comes through or to the surface of the rock "in which it is incased, though it may be covered, and "sometimes is, with twenty or thirty feet of loose "earth."

"That portion of the lode along its course which outcrops to the surface, or, if 'blind,' which comes near"est to the surface."

"The line such vein would make in its intersection "with the surface, calculated from its true dip at each

"The uppermost part of the ledge between the two 66 walls, although these may be missing."

"In case the vein outcrops at the surface, I would "call any portion of such outcrop the top, or apex. If "the vein does not reach the surface, then the highest "point to which the vein, or lode, can be traced is the apex-not necessarily the nearest point to the surface, "but the absolute highest point.

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"The summit, comb, crest, or highest point on the "ridge of a vein, or lode."

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"The upper edge; that part which is first reached or passed, in developing a mine."

"The outcrop, or, in case of a blind ledge, that line "of the vein, or lode, which approaches the surface the "nearest."

"That portion of the vein that is visible in the 66 country rock when the loose dirt or earth has been 66 removed. Some veins stand up above the country "rock like a wall. The top of such veins would be the highest part of such wall above the ground or bed"rock."

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"Its highest point at any given place."

"The outcrop."

"The point at surface where the ore is met with; "either superficially seen in the croppings, or just "beneath the surface."

"Either the outcrop or crevice between walls at the top of bed-rock."

"The vein at the surface."

"Outcrops generally."

"The width of the vein, or lode, on the surface; but "the United States mining law means the top, or apex, "to be the width of the claim, six hundred by fifteen "hundred feet."

"The outcropping of the vein."

"Where it has been projected through the country "rock by an acting subterranean agency or force."

Judge Beatty, then chief justice of Nevada, gave the clearest and most comprehensive of all the definitions. It is as follows:

"The top, or apex, of any part of a vein is found by "following the line of its dip up to the highest point "at which vein-matter exists in the fissure. According "to this definition, the top, or apex, of a vein is the "highest part of the vein along its entire course. If "the vein is supposed to be divided into sections "by vertical planes at right angles to its strike, the "top, or apex, of each section is the highest part "of the vein between the planes that bound that sec"tion."

"Of course, there are irregular mineral deposits departing widely in their characteristics from the 66 typical or ideal vein which seems to have been in "the mind of the framer of the act of 1872. To "such deposits the foregoing definitions will not "apply; and, in my opinion, great difficulty will be experienced in any attempt to apply the existing law "to them."1

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2308. Definition by Dr. Raymond.-Dr. Raymond, in his "Law of the Apex," with reference to these terms and their use in the act of May 10, 1872, says:—

"I have reason to believe that they were used instead "of the word 'outcrop,' in order to cover 'blind lodes,' "which do not crop out. The conception of an apex, "which is properly a point, was probably taken from "the appearance of a blind lode in a cross-section, "where the walls appear as lines and the upper edge as "a point. The term may also have been intended to "cover the imaginary case of an ore deposit which ter"minates upwards in a point. We may, however, dis"miss from consideration the case of a simple point, "and safely assume that the apex is the same as a top, " and is either a line or a surface."

1Report of Public Land Commission, p. 399; Dr. Raymond on Law of the Apex, p. 28.

The definition crystallized by him and found in his Glossary of Mining and Metallurgical Terms," is, "the end or edge of a vein nearest the surface."

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We think this definition should be qualified to some extent. Our views will be found in the next section.

309. The ideal lode and its apex.- For the purpose of elementary consideration of the subject, we present in figure 10, a vertical cross-section, showing two veins, or lodes, of the simplest type, two steeply inclined fissures filled with

ore-bearing materi

al, the one outcrop

FIGURE 10.

ping on the surface, the other terminating on its upward course before reaching the surface.

APEX OF VEIN

SOUTH

These are doubtless the veins which the miner had in mind when he furnished the descriptions which served as guides in the enactment of the law. There appears no room for doubt concerning the meaning of the word "apex" as used in the statutes, when applied to these veins. It referred to the upper terminal edge of the sheet-like vein, whether reaching the surface or not.

NORTH

An ideal location

FIGURE 11.

covering one such apex is represented in figure 11, and the rights flowing from it are unquestioned.

1 Trans. Am. Inst. M. E., vol. ix, p. 102.

How should this apex be defined? It is evidently a surface, bounded by the walls of the vein. It has both length and breadth, and cannot be described as a point or a line.

The apex of the ideal vein within the location is a surface bounded by the walls of the vein and the endlines of the location. This surface is, of course, irregular. It may be higher at one place within the boundaries than it is in another; but mere elevation of the upper edge of the vein at different points within the location is of no moment. If the top of the mountain were ground down to a horizontal plane, the vein as exposed would be a plane surface; but, nevertheless, it would be an apex. The fact that the exposed edge of the vein is ragged, or that the surface of the outcrop is higher in one place above a given datum plane than it is in another, makes no difference in the principle.

If this upper edge does not outcrop so as to be visibly traceable on the surface, but is "blind," covered with detritus or a capping of country rock, it is still a surface bounded by the walls of the vein and vertical planes drawn downward through the end-lines. The plane of contact of the upper edge of the vein with the detritus or capping, intersected by the walls of the vein, would be the apex surface. We cannot conceive that an apex of a lode, within the meaning of the act of congress, can be anything but a surface, although we are aware that the supreme court of the United States has said that an apex is often a line of great length.1 But it undoubtedly meant a surface, because in another portion of the same case it speaks of the "apex in its full "width." Mathematically speaking, there is no width to a line. As was said by the supreme court of Montana, a lead, or lode, is not an imaginary line without dimensions; it is not a thing without shape or form.

'Larkin v. Upton, 144 U. S. 19, 23, 12 Sup. Ct. Rep. 614.