Mr. Troughton, to the account he has given of this pendulum in Nicholson’s Journal, for December, 1804, has added the lengths of the different parts of which it was composed, and the expansions of brass and steel from which these lengths were computed. The length of the interior tube was 31·9 inches, and that of the exterior one 32·8 inches, to which must be added 0·4, the quantity by which in this pendulum the centre of oscillation is higher than the centre of the bob. These are all of brass. The parts which are of steel are,--the middle wire, which, including 0·6, the length of the suspension spring, is 39·3 inches. The first pair of wires 32·5 inches; and the second pair, 33·2 inches. The expansions used were, for brass ·00001666, and for steel ·00000661, in parts of their length for one degree of temperature. _Benzenberg’s Pendulum._ This pendulum is mentioned in Nicholson’s Journal for April, 1804, and is taken from Voigt’s Magazin für den Neuesten Zustande der Naturkunde, vol. iv. p. 787. The compensation appears to have been effected by a single rod of lead in the centre, of about half an inch thick; the descending rods were made of the best thick iron wire. As this pendulum deserves attention from the ease with which it may be made, and as others which have since been produced resemble it in principle, we have given a representation of it at _fig. 215._, where A B C D are two rods of iron wire riveted into the cross pieces A C B D. E F is a rod of lead pinned to the middle of the piece B D, and also at its upper extremity to the cross piece G H, into which the second pair of iron wires are fixed, which pass downwards freely through holes made in the cross piece B D. The lower extremities of these last iron wires are fastened into the piece K L, which carries the bob of the pendulum. To determine the length of lead necessary for the compensation, we must recollect, as before, that the distance from the point of suspension to the centre of the bob (speaking always of a pendulum intended to vibrate seconds) must be 39 inches. Let us suppose the total length of the iron wire to be 60 inches; then, from the table which we have given, we have ·4308 for the length of a rod of lead, the expansion of which is equivalent to that of an iron rod whose length is unity. Multiplying 60 inches by ·4308, we have 25·84 inches of lead, which would compensate 60 inches of iron; but this, taken from 60 inches, leaves only 34·16 instead of 39 inches. Trying again, in like manner, 68·5 inches of iron, we find 29·5 inches of lead for the length, affording an equivalent compensation, and which, taken from 68·5 inches, leaves 39 inches. The length of the rod of lead then required as a compensation in this pendulum is about 29-1/2 inches. The writer of this article would suggest another form for this pendulum, which has the advantage of greater simplicity of construction.