The specimens of _Triarthrus becki_ from Rome are pseudomorphs composed of iron pyrites, as has been said, and are buried in a gray-black carbonaceous shale. A little rubbing of the specimens soon makes of them bronze images of the former trilobite and while under preparation they are therefore easily seen. However, as the average individual is under an inch in length and as all the limbs other than the antennæ are double or biramous, one lying over the other, and the outer one fringed with a filamentous beard, the parts to be revealed by the preparator are so small and delicate that the final touch often obliterates them. These inherent difficulties in the material were finally overcome by endless trials on several thousand specimens, each one of which revealed something of the ventral anatomy. Finally some 500 specimens worthy of detailed preparation were left, and on about 50 of these Beecher's descriptions of _Triarthrus_ and _Cryptolithus_ were based. The black shale in which the specimens are buried is softer than the pseudomorphous trilobites, a condition that is of the greatest value in preparation. With chisel and mallet the trilobites are sought in the slabs of shale and then with sharp chisels of the dental type they are revealed in the rough. At first Beecher sought to clean them further by chemical methods, and together with his friends, the chemist Horace L. Wells, and the petrologist Louis V. Pirsson, several solutions were tried, but in all cases the fossils were so much decomposed as to make them useless in study. Therefore Beecher had to depend wholly oh abrasives applied to the specimens with pieces of rubber. Much of this delicate work was done on a dental lathe, but in the final cleaning most of it was done with patient work by hand. Rubber has the great advantage of being tough and yet much softer than either specimen or shale. As the shale is softer than the iron pyrites, the abrasives (carborundum, emery, or pumice) took away the matrix more quickly than the trilobite itself. When a part was fully developed, the rubbers were cut to smaller and smaller dimensions and the abrading reduced to minute areas. So the work went on and on, helped along from time to time by the dental chisels. Finally Beecher became so expert with these fossils that after one side was developed he would embed the specimen in Canada balsam and fix it on a glass slide, thus enabling him to cut down from the opposite side. This was done especially with _Cryptolithus_ because of the great scarcity of material preserving the limbs, and two of these revealed both sides of the individuals, though they were then hardly thicker than writing paper.