ceases to be a lode. Mineralization, moreover, may be sporadic and may come in again beyond a greater or less area of unmineralized rock. The court, as does the miner, only gains his knowledge of the facts by developed workings down the dip or along the strike. The unknown is always ahead. If again, we deal with mineralized and replaced quartzites, or other sedimentary rocks, whose mineralization fades almost imperceptibly into the unaltered phases of the rock, perhaps to reassert itself farther on, the same difficulties in establishing boundaries arises. But, on the other hand, if one endeavors to apply the usual geological conceptions of a vein,-as due to circulations along a line of fracture, to replacement bodies, distributed as they habitually are irregularly throughout a greatly disturbed series of sediments, with cross-fractures, faults, joints, bedding planes, and brecciated areas, it is impossible to assign to each of these lines of circulation preferential importance in the introduction of the original ore-bearing solutions. The ore-bodies themselves are of all manner of shapes, sizes and relations. All the nomenclature of the subject would be of necessity called in. Chimneys, pipes, rake-veins, shoots, bonanzas, etc., would here and there find application. An interpretation of the replacement type of ore-body on the lines of typical so-called fissure-veins soon develops greater difficulties than does one on the "broad lode" basis. Both witnesses and court, endeavoring to testify or to reason with accuracy and candor, almost inevitably are face to face with questions which have to be decided on the basis of judgment rather than scientific accuracy. In consequence much superficial and unwarranted criticism is often directed by half-informed persons against both courts and witnesses, whereas the very general nature of the provisions inevitably admits and involves latitude in interpretation. Of course in this respect the so-called apex law is not unique among laws. As one grows older and experience widens, the impression of the great and endlessly variable nature of human society deepens. A professor in a university only needs to be on a committee whose duty it is to decide questions of eligibility for athletic teams, in order to learn how very complex an apparently simple matter may be. If, again we consider disputes arising over veins as defined by geologists instead of replacement bodies, we find ourselves in difficulties scarcely less serious. Branching fractures of greater or less size are often present in areas of extended mineralization. Sericitization, pyritization, or other alteration and impregnation of the wall-rocks incident to vein-formation take place in all shades of intensity and with greater and greater inclusion of unaltered wall-rock in their ramifications. To decide where a vein, lode or ledge, under these circumstances ends, and where country-rock begins, is not a matter of scientific accuracy, but the decision must often of necessity be arbitrarily made by the court. With regard, thus, to titles affecting mining property there is but one logical conclusion, that is, geology is out of place in the law, and ownership should not rest upon it, but upon definite surface monuments and boundaries. The constructive and helpful attitude is one which seeks revision and the establishment of boundaries of ownership capable of exact and not difficult definition. The influence of all well-wishers and friends of the mining industry should be directed to obtaining such revision. As regards present titles under the existing law and the precedents established in the courts, one way out is found in combinations of disputatious holdings into large and comprehensive ownership. Litigious disputes are thus prevented. Many other advantages follow in the way of intelligent and economical development and administration. Butte is an instance in point. As another way out, companies having adjacent properties may of their own accord agree to rights inside vertical planes i.e., to common law rights. Friendly relations then become normal and natural. Experience gained by one company is at the disposal of the other. Bisbee is a case in point. Some years ago the Mining and Metallurgical Society of America conducted an extremely valuable and suggestive discussion of this subject and exercised much influence on Senators and Congressmen specially qualified to take the matter up. It was the desire of the latter to revise all the laws affecting land ownership, coal-lands, lode-claims and placer claims at once. Before, however, the matter crystallized into legislation the European war broke out and matters incident to it have ever since occupied the stage. Sooner or later, however, revision as affecting new locations will inevitably come up again. New laws can easily be passed for new locations, but whether legislation can constitutionally be made in any respect retroactive is a question upon which the writer does not feel capable of expressing an opinion. Thus whether a time limit could be set for the assertion of extralateral rights at say ten years ahead, and that at the expiration of the time only developed ore-bodies could be claimed under it; and whether later than a fixed date common law rights would prevail. Prohibition for instance has come in and rightly or wrongly both by constitutional amendment and by statute has destroyed the value of many millions of investment, previously perfectly legal and deserving the protection of the law. The old customs and the theory of ownership of underground waters as in the cases against the City of Brooklyn and its pumping plants for municipal water supply on Long Island have been modified in recent decisions, which greatly curtail the City's right to draw its water from the ground. To the layman it would seem as if considerations believed to be of great public benefit sometimes find expression and sometimes modify old principles. The quieting of titles to mining property is certainly one. In conclusion, it seems to the writer, that in revision the following principles or practices should prevail for lode-claims. 1. Ownership as in the common law inside of vertical planes passing through surface boundaries, as the legal phrase goes "ab orcu ad cœlum." 2. One claim and only one in each mining district to be located by any one individual and only by him in person, so as to avoid the present abuse of powers of attorney. Claims afterward to be subject to sale like any other property. 3. A claim to be theoretically square in shape, and, in order to conform to the general and well-established practice of the Land Office, to be a quarter mile on a side, i.e., to be one-sixteenth of a section or forty acres, a size not quite twice the full area of a present-day claim. We compensate in this way for the restriction of each individual to a single claim. The sides should be laid out true north and south and east and west. The main feature of location is to be a central point where lines joining the middle points of opposite pairs of sides would intersect. This point being fixed by the discoverer would make the accurate location and revision of sides possible by a surveyor. 4. Seniority of location to have right of way. 5. Fractional claims necessarily permissible. 6. Annual payments in cash, based on acreage, to be necessary to hold claims and so adjusted as to militate against the speculative and undeveloped holding of claims for long periods. In the absence of development the charges could be increasingly heavy as years passed. The introduction thus of a system of governmental leasing rather than patented ownership. 7. Liberal interpretation of mineralization. Proper provisions regarding timber in conformity with present forest reserves. Other not difficult provisions for prompt registration, annual payment, lapsing of title, etc., incidental to administration. COLUMBIA UNIVERSITY, NEW YORK, N. Y. J. F. KEMP. DISCUSSION. This department has been established by the editors in order to afford to those interested in questions relating to economic geology an opportunity for informal discussion. Contributions are cordially invited either in the form of discussion of more formal papers appearing in earlier numbers or bearing upon matters not previously treated. Letters should be directed to the Editor, Sheffield Scientific School of Yale University, New Haven, Conn. The full name of the author should be attached to all communications. Sir: In reconnaissance plane table mapping it is often convenient to use a slide rule for calculating difference in elevation, which is the product of the horizontal distance and the tangent of the vertical angle. The common slide rules give tangents from 45° down to about 5° 45', below which value the graduations fall to the left of the scale. Mostly the vertical angles are less than 5° and one has to use a table of natural tangents together with the graudations on the face of the slide. Dr. John M. Stetson, of the Sheffield Scientific School of Yale University, recently pointed out to me the fact that below 10° or so the value of the tangent of an angle is virtually equal to the radian measure of the angle. Therefore if the horizontal distance is multiplied by the radian measure of the vertical angle, the product is the difference in elevation. The radian measure of an angle may be found by multiplying the number of minutes in the angle by 0.000291. Then E=HXaX 0.000291. where and E the difference in elevation of the two points, H the horizontal distance between them, a the vertical angle in minutes. Thus with a horizontal distance of 1275 feet, a vertical angle of 3° 24', the difference in elevation is found as follows: |