the slider L there are two pins, TT, to prevent its rising high enough to touch the string; and in the bar I there are two wires O O, like staples, to support the slider L in its place.

Fig. 6. is the moveable bar M with the hooks.

Fig. 7. is the hooks at large.

Fig. 8. is the bar I, shewing the notches in which the strings lay, to let the pirns pass over them, (when the tubes are brought over as in Fig. 3).

Fig. 9. is the slider L, with the pins that move the pirns.

Sir,

Mr. John Robertson, stocking weaver here, having lately communicated to the Highland Society of Scotland your letter to him of the 6th April, 1805, together with a model of his machine for weaving fishingnets, I have been desired by the directors to recommend him to the notice of the Society of Arts, &c, and to mention that if his invention can be made practically useful, it will most materially contribute to the extension of the fisheries, by cheapening the expense of outfit.

Although improvements in the mechanic arts do not fall within the plan of their Institution, yet the Highland Society have given Mr. Robertson a few guineas, to enable him to attend personally on the Society of Arts, &c. and to explain his machine. I am, Sir,

Your most obedient Servant,

D. MACLACHLAN, Secretary..

Highland Society Hall, Edinburgh,

March 26, 1806.

To C. TAYLOR, M. D.

**. I

From

From Mr. Robertson's subsequent statement to the Committee of the Society of Arts, &c. it appears that the nets used in the Northern fisheries are of one breadth throughout. He supposes he could make three courses of one hundred meshes each in one minute; that such a loom should be about 3 feet, wide, and would cost about fifteen or sixteen pounds.

. A Certificate from Sir John Sinclair stated that Mr. Robertson's invention was much approved of in Scotland, and that he trusted it would be found entitled to the patronage of the Society of Arts, &c.

New Theory of the Tides.

By M. LAPLACE.

From HIST. DES MATHEMAT. tòme IV.

M. LAPLACE has treated this subject in a very complete manner in the Mem. de l'Académie for 1775, 1789, and 1790, and particularly in his Mécanique céleste.

After having established the conditions of equilibrium for a point acted upon by any given number of forces in any given directions, M. Laplace considers the conditions of the equilibrium of fluids; the property which characterises them being perfect mobility, it follows of course, that for a fluid mass to become in equilibrium, it is necessary that each of the molecules that compose it be in equilibrium by virtue of the forces that influence it. From this principle; therefore, he determines the relation that should exist between the forces acting on the system, in order to the fulfilment of this condition; and he applies it to the equilibrium of a homogeneous

fluid mass surrounding a solid nucleus fixed, and of any given figure.

He afterwards introduces into his differential equa tions the forces which disturb the state of equilibrium These forces are, first, the attraction of the sun and moon; second, the attraction of the aqueous bed, of which the interior radius is that of the spheroid in equilibrium, and the exterior radius that of the perturbed spheroid.

Taking first upon the supposition of the earth being spherical without any rotary motion, and the depth of the sea every where the same, he seeks for the oscillations that in such a case would be excited by the united action of the sun and moon.

The integration of the differential equations presenting many difficulties, the author limits himself to a case of great extent, which is the supposition that the depth of the sea is only a function of the latitude. In this case even the investigation of the radius of the spheroid conducts to a linear differential equation, of which the integration surpasses the forces of analysis; but the author observes, that in order to determine the oscillations of the ocean, it is not necessary to integrate this equation generally, and that it is sufficiently satisfactory, because the parts of these oscillations, depending on the primitive state of the sea, would soon have disappeared, from the effect of the exterior obstacles; so that without the action of the sun and moon, the sea would long since have arrived at a state of permanent equilibrium; whence it follows, that the action of these two luminaries agitates it incessantly, and that it is sufficient to consider thus the oscillations which depend on such action.

As

As he proceeds to develope the terms that produce them, M. Laplace divides them into three classes; the first not at all depending on the rotary motion of the earth, but solely on the motion of the attracting body in its orbit; they vary very slowly, and do not become the samé again until after a long interval. The terms of the second class depend principally on the rotary motion of the earth, and become the same again after an interval of nearly a day; lastly, those of the third class depend on a double angle, and consequently return in like manner after in half a day. Hence result three different kinds of oscillations, the periods of which are the same as those of the terms that produce them; the increase of the radius of the spheroid being given by a linear equation, these oscillations are superposed without being confounded, which permits the author to consider them separately.

He proceeds to examine the first, supposing the earth to be a revolving ellipsoid, which renders the depth of the sea a function of the latitude only; and he demonstrates that if the attracting luminary be at a sufficient distance, these oscillations may be calculated as if the depth of the sea were nearly the same in every part ; the portion of these oscillations which depends on the motion of the nodes of the lunar orbit, may be very considerable; but the author demonstrates that these great oscillations are almost entirely annihilated by the resistance that the sea meets with in its motion, and that they are very nearly the same as if the sea were placed at each instant in equilibrium under the luminary that attracts it: this result becomes the more exact, as the attracting luminary moves more slowly in its orbit; the error is consequently insensible with respect to the sun,

and

and the observations indicating that the oscillations of this class are very small, the same consideration may be applied to the moon, notwithstanding the rapidity of her motion.

M. Laplace next proceeds to develope the terms produced by the second species of oscillations, which depend principally on the rotary motion of the earth.

This observation is here very important, and becomes even indispensable to enable us to deduce from these terms a law of the depth of the sea. It affords the means of expressing in a very simple way the oscillations of this species, when the spheroid is a revolving one. From these oscillations proceed the difference of the tide in one and the same day. This difference is very small, as the observations indicate; whereas in the ordinary hypothesis, the difference would be very great : it is necessary, therefore, that the depth of the sea be nearly constant. The author determines, on this hypothesis, the oscillations that he has examined.

He calculates, on the same supposition, the oscillations of the third species; observing afterwards that the resistance which the sea experiences in its movements, renders those of the first species independent of the law of its depth, he concludes that it is only necessary to consider those laws of the depth of the sea, by which we may determine at once, the oscillations of the second and third species; which reduces it to the supposition that the depth of the sea is nearly uniform. He gives, in this hypothesis, the numerical expression of the oscillations, and of the flux and reflux of the sea according to various suppositions with regard to depth. Having thus determined the oscillations of the sea, supposing the earth to be a spheroid of revolution, the VOL. XII.-SECOND SERIES. lii authot