[Illustration 79b (Rectangle with lengths and area): Shape of a Long Meer or Double Measure.]
The sides of a long meer are of equal length, and similarly its ends are equal; therefore, if the number of fathoms in one of the long sides be multiplied by the number of fathoms in one of the ends, the total produced by the multiplication is the total number of square fathoms in the long meer. For example, the double measure is fourteen fathoms long and seven broad, which two numbers multiplied together make ninety-eight square fathoms.
[Illustration 79c (Rectangle with lengths and area): Shape of a Head Meer.]
Since meers vary in shape according to the different varieties of veins it is necessary for me to go more into detail concerning them and their measurements. If the vein is a _vena profunda_, the head meer is composed of three double measures, therefore it is forty-two fathoms in length and seven in width, which numbers multiplied together give two hundred and ninety-four square fathoms, and by these limits the _Bergmeister_ bounds the owner's rights in a head-meer.
[Illustration 80a (Rectangle with lengths and area): Shape of a Meer.]
The area of every other meer consists of two double measures, on whichever side of the head meer it lies, or whatever its number in order may be, that is to say, whether next to the head meer, or second, third, or any later number. Therefore, it is twenty-eight fathoms long and seven wide, so multiplying the length by the width we get one hundred and ninety-six square fathoms, which is the extent of the meer, and by these boundaries the _Bergmeister_ defines the right of the owner or company over each mine.
Now we call that part of the vein which is first discovered and mined, the head-meer, because all the other meers run from it, just as the nerves from the head. The _Bergmeister_ begins his measurements from it, and the reason why he apportions a larger area to the head-meer than to the others, is that he may give a suitable reward to the one who first found the vein and may encourage others to search for veins. Since meers often reach to a torrent, or river, or stream, if the last meer cannot be completed it is called a fraction[3]. If it is the size of a double measure, the _Bergmeister_ grants the right of mining it to him who makes the first application, but if it is the size of a single measure or a little over, he divides it between the nearest meers on either side of it. It is the custom among miners that the first meer beyond a stream on that part of the vein on the opposite side is a new head-meer, and they call it the "opposite,"[4] while the other meers beyond are only ordinary meers. Formerly every head-meer was composed of three double measures and one single one, that is, it was forty-nine fathoms long and seven wide, and so if we multiply these two together we have three hundred and forty-three square fathoms, which total gives us the area of an ancient head-meer.