dence of the practical end of dephosphorization. When there is, so to speak, no more phosphorus, the oxygen of the air exerts itself entirely on the iron and manganese, and there are then seen abundant fumes of a very peculiar intensity, proceeding from the oxides of iron and manganese. There were no projections during the operation, which is surprising for nearly white iron. It is necessary, from this point of view, to believe that the phosphorus acts in the same protective way as the silicon, and prevents the reaction of the oxide of iron on the carbon from becoming tooviolent.

The operation is terminated by the addition of spiegel. Neither explosions nor rephosphorization of the dephosphorized metal are noticed. There is something here which demands an explanation, for the engineers of Hörde do not seem to have recourse to silicious additions, and one cannot well see how the carbon of the spiegel would react less tumultuously here, on the oxide of iron of the bath, because the pig iron was less silicious and contained more phosphorus.

The lining, of which we have not yet spoken, for it presents no new character, is made with dolomitic bricks, having the following composition:

Silica,

Iron and alumina,

Carbonate of lime,

Carbonate of magnesia,

Before baking.

After baking..

These bricks, like those which they used at Eston, are long and difficult to bake. 36 hours for kindling, an excessively quick fire during 100 hours, and slow cooling of 100 hours, are necessary. The dolomite of Rühr, which they employ, is neither rare nor costly, but 5 tons of coal are necessary to bake 1 ton of bricks.

These basic linings resist for a hundred operations; this is already a splendid result; but the convert rs, with ordinary silicious lining, support a thousand operations before requiring renewal, which is generally caused more by accumulations than by corrosion.

The bottoms are made (en pisé) with the débris of basic bricks, agglomerated with mineral pitch. They employ no tuyeres, but pierce holes in the mass, which are necessary for the introduction of the air.. These bottoms will resist fifteen operations, about half the life of ordinary silicious bottoms. Their deterioration would seem to be due more to a physical action than to a chemical decomposition.. Perhaps,

in increasing the blast pressure, the shocks from the liquid mass would be diminished and agitations quieted, as has been observed in Sweden.

The loss, according to the engineers of Hörde, is not greater than in their ordinary operations with pig iron from hematites, 10 to 11 per cent.; whereas with the silicious iron of Luxemburg, in the same basic converters, the loss reached 15 per cent. M. Massenez gives the following explanation: 1 part of silicon requires at least 2 parts of iron to form a silicate; the less silicon there is to scorify, the less will be the loss of iron.

This seems probable, for it has been long noticed that silicious iron leads to a greater loss in puddling. Further, the phosphoric acid, the state of which in the slag is a subject of much dispute, combines, in part at least, with the lime and magnesia, and is not so greedy for iron as the silica.

The sulphur of the iron seems to be eliminated to two-thirds. What becomes of it? It is held that the manganese facilitates desulphurization. It is necessary to admit, then, that it forms some sulphuret of manganese or of calcium in solution in the slag, a point which is not yet elucidated, and which presents great importance in the future of the process; for, if it is easier and more economical to produce "white" iron, it is to be feared, also, that it is much less sulphurous than grey and silicious iron obtained from the same burden.

The fact that phosphorus is sought for in the iron, or added during the operation, as the case may be, in order to facilitate its after elimimation, is certainly very interesting, and seems even paradoxical.

(To be continued.)

American Laureates of the French Academy.--At the last public annual session of the French Academy the Lalande prize was awarded to Prof. C. F. H. Peters, of Clinton, N. Y., for his planetary discoveries. The total number of asteroids discovered by him is 43, eight of which were added to the list during the past year. At the the same sitting, the Valz prize was awarded to M. Trouvelot, of Cambridge, Mass., whose magnificent drawings of the planets Mars, Jupiter and Saturn represent the telescopic appearances with remarkable accuracy and furnish an excellent basis for the minute study of the superficial phenomena of these planets.- Comptes Rendus. C.

THE INVOLUTE OF THE CIRCUMFERENCE OF A CIRCLE.

By L. D'AURIA.

Professor of Applied Mechanics, former Engineer of the Military Topographic Institute in Italy, etc.

The relation between the circumference of a circle and its involute,. as well as the relation between the area of a circle and the area generated by the tangent line in describing the involute of the same circle once occurred to the writer in a problem of mechanics, and fruitlessly he searched in many authors of differential and integral calculus in use to find them; so that he was compelled to determine these relations by himself. The following is the method he used:

Let L be the length of the involute of an arc of circle of radius. R, and degrees. If we imagine the circular are divided in a certain number, n, of equal parts, each part will evidently contain £ degrees;

n

and if we imagine drawn the tangent lines at the extremities of these n arcs of circle, the angle formed by two consecutive tangents will be

Now, the length of one of the n circular arcs is

and the length of the successive tangent lines drawn at the extremities of the n circular arcs, and confined between the involute and the evolute, are evidently

When n is a very great number, the sum of the n successive arcs of involute confined between the n+1 tangents (1), will be equal with approximation to the sum of n circular arcs, each containing

described successively by radii equal to the tangents (1). The sum of these n circular arcs is

n

degrees

This formula, with the supposition of n = ∞, becomes exact, and will be

L ==0.

(2)

or denoting by C the circumference of the circle (evolute)

(3)

The formula (2) holds good, also, when the involute of the whole circumference being described by a thread developing from it, this operation is continued, so that the rotation of the tangent line will exceed 360°.

Substituting in equation (2) successively

= 360, y = 2 × 369, y = 3 × 360, . . . = N × 360, 9 the corresponding values of L will be

πС, зπС, 5π С, 7πС, . . . . (2N-1)π С.

.

These values form a series proportional to the series of the odd natural numbers 1, 3, 5, 7, 9, 11,

Denoting by A the area generated by the tangent line in describing the involute of a circular arc of radius R and degrees, conserving the other denotations (n being a very great number) the area A will be, with approximation, equal to the sum of n circular sectors, each degrees, described successively by radii equal to the tan

containing

This formula, with supposition of n = becomes exact, and will be

This last formula and formula (3) can easily be memorized, and although they are not in use in ordinary problems of mechanics, it would be not superfluous to introduce them in some manual of engineering.

A NEW PENDULUM SUSPENSION.

By LOUIS H. SPELLIER.

The time-keeping qualities of a clock are almost entirely dependent upon the correctness of the pendulum, and ever since its introduction as a medium to divide time into equal intervals, it has received the very greatest attention accordingly.

As it is the object of the compensation of the pendulum to keep its centre of gravity regardless of change of temperature, at an equal distance from its centre of oscillation, so its suspension should allow only its re-occurring oscillations to follow the track of a straight line and to move in a straight plane only.

The chief if not the only condition to arrive at this result is to give the suspending spring an even tension. Unless this condition is complied with the oscillating pendulum will be accompanied by the well known wabbling side motions which so greatly interfere with its cor

rectness.

Pendulums have been suspended on one as well as on two springs, the latter of which is almost entirely abandoned. None of the suspensions so far had a contrivance which would automatically adjust the tension of the suspending spring, and so with mathematical certainty avoid the wabbling motion alluded to. The author claims to have succeeded in constructing such a suspension. It solves the problem perfectly.