internus), or run in grooves (as the long head of the biceps), or perforate other tendons (as the deep flexor of the fingers), or turn through fibrous pulleys (as the digastric, the extensor of the toes, &c.). By comparing the effect of a known force acting on particular tendons, at first in their natural situations, and afterward detached and free, the influence of friction in each case would be readily determined. This source of error seems to have been very generally overlooked by writers on animal mechanics.

I conclude, for the present, with suggesting that to distinguish the pectoralis major into "portio elevans" or "attollens," and "portio deprimens," might serve to impress the rationale of its peculiar insertion and twofold action, upon the memory of the student.

LXXIX. Researches in the Undulatory Theory of Light, in continuation of former Papers. By JOHN TOVEY, Esq.

To the Editors of the Philosophical Magazine and Journal. GENTLEMEN,

HAVING deduced, (p. 500 of your last volume,) by a new method, the laws of the propagation of plane and spherical waves in elastic media, I will now, with your permission, show how the formulæ may be extended to the most simple cases which are known to occur in the undulatory theory of light, of waves not spherical emanating from a center of agitation.

(1.) It will be remembered that in my paper at p. 270 of the last volume, the sums were considered as comprised in three classes, when it appeared that those of the first class, composed of odd products of the differences, vanish, in consequence of the first supposition there made respecting the arrangement of the molecules. The sums also of the second class, composed of even products involving odd powers of the differences, were neglected; because the terms of these sums must be about half of them positive and half negative, and consequently the sums themselves very small in comparison with those of the third class, which last, being composed of even powers of the differences, have their terms all positive.

(2.) If the radius of the sphere of influence be not very much greater than the intervals between the molecules, the sums may or may not be sensibly the same for different directions of the coordinates, according as the intervals are the same or different for the different directions. Suppose, for example, every eight adjacent molecules to be at the corners of a rectangular parallelopiped; suppose fig. 1 to be a section of the medium, the dots denoting the molecules in their

That the spark and shock obtained from an electro , on breaking battery communication, are not the spark ock of the battery nor of the electro-magnet, but, most ly, the electricity induced on the wire of the helix by ctricity of the battery, or, if it be true that a current along the wire, the electricity intercepted in its passage he copper to the zinc.

1. That the spark and shock do not depend, except 1 certain limits, on the size of the battery.

1. That they confirm what I ventured to assert at the last ing of the British Association (1835) on the nature of mag

m.

h. That the real power of the battery is not increased but nished by the electro-magnetic, or rather, electro-galvanic

X.

st. The spark and shock (the latter of which I do not reect to have seen remarked before,) obtained with an elec -magnet on breaking battery communication, are not the urk or shock of the battery, for neither one nor the other a exist until after battery communication is actually broken. gain, if they arise from the battery, to receive the shock it ould be necessary to form a part of the communication be veen the copper and zinc. This, however, is not required; is necessary only to form a part of the communication beween the extremities of the helix, or between one extremity of the helix and either the copper or zinc of the battery. Neither does the shock or spark arise from the influence of the bar of soft iron inclosed in the helix: on the contrary, the retention of magnetism in the bars, either from the nature of its iron or the action of a keeper, will proportionably diminish the effect; and I have no doubt that if a large portion of magnetism were retained in a powerful electro-magnet by the keeper, and the keeper were torn off with violence from the magnet, a shock and spark would be perceived at the moment of disruption, which, together with those obtained when battery communication was broken, would form a spark and shock exactly eral to what were obtained had there been no retenti ism by the keepers when battery commu

LXXXI. On a new Method of preparing Iodous Acid. By LEWIS THOMPSON, Esq., Member of the Royal College of Surgeons.

To the Editors of the Philosophical Magazine and Journal. GENTLEMEN,

SEND you a new method of preparing iodic acid; it is I cheaper and safer than the process of Sir Humphry Davy, and affords a purer acid than the plan pursued by Gay-Lussac. I say purer, because from some experiments which I have lately made, and intend to repeat more carefully, I am led to conclude with Sir Humphry Davy, that the acid of GayLussac is sulpho-iodic acid.

Process for preparing lodic Acid.

Put one atom or 126 grains of iodine into a proper bottle with 24 ounces of water, and pass chlorine, previously washed in cold water, through the mixture until it shall have become colourless; set the solution aside for an hour; then heat it to 212° Fahr., to disengage the uncombined chlorine, and add 2 atoms or 295 grains of recently precipitated oxide of silver; boil the whole for ten minutes, filter, and evaporate carefully to dryness: the product is pure anhydrous iodic acid.

It will be at once perceived by the above process that there is no such acid as the chloriodic, the acid so called being in fact merely a chloride of iodine, which when dissolved in water is converted into muriatic and iodic acids, with a variable quantity of iodine. How this mistake can have passed so long unnoticed is to me a matter of surprise; at the same time I must observe that I have not been able to unite chlorine and iodine in the proportions necessary to form these acids without the intervention of water; there is always an excess of iodine: but I have no doubt that this may be effected in a sufficiently reduced temperature. In the last experiment which I made on this subject 50 grains of iodine combined with 41.5 cubic inches or about 30 grains of chlorine: the substance thus formed when put into a large quantity of water, and exposed for some days to the sunshine, deposited 8 grains of iodine and became of a pale yellow colour.

That the muriatic and iodic acids exist ready formed in the solution I am confident, not only from the taste and smell, but because I have obtained free muriatic acid from it by distillation, although when this is continued until the solution becomes a good deal concentrated, these acids react upon each other and produce chlorine and iodine.

m

{{ cus3 ô Σ · (÷ (1) + ↓ (7) A =,") ▲ x2 + sino 6 £

.

· (+ (r) + & (r) ▲ z,2) ▲y,

➡m sin 8 cos Σ . († (†) + 4 (r) ▲ z?) ▲ x, ▲y, · The third sum in this equation must be zero in consequence of the supposed arrangement of the molecules round the axis of x,, and therefore, if we denote by c and c, the products

of the first and second sums multiplied by

m

2

V1 = √(c,2 cos2 + c sin2 ).

2

Fig. 2.

we have

(4.)

(7.) Let CD, DE, (fig. 2,) be elementary portions of a wave-surface diverging from the centre of agitation O; let A D, BE, be planes coinciding with CD, DE; and let OA, O B, be perpendiculars to these planes. Then the velocity with which the wave is, at CD, transmitted in the direction perpendicular to CD, must be equal to the velocity of a plane wave moving in the direction of O A; and the velocity with which the wave is, at D E, transmitted

in the direction perpendicular to D E, must be the same as that of a plane wave moving in the direction of O B. Consequently, if we conceive an indefinite number of plane waves, which, at the commencement of the time t, all pass through the centre of agitation O, the wave surface will be that touched by all these plane waves at any instant.

(8.) Now let a number of planes like AD and BE, all perpendicular to the plane of the angle a Oy,, be so drawn. that their perpendicular distances from O, the origin of the coordinates, may be proportional to the values of given by: the equation (4.); where is the angle which the perpendicular drawn from O to any plane wave makes with the axis Ox. Then the curve in the plane of x, Oy, touched by all these planes will, by the property of the equation (4.), be an ellipse, the axes of which are proportional to c, and c.

(9.) The phænomena of chemistry show that molecular attractions and repulsions vary rapidly at particular distances of the molecules from each other. Suppose then the forces. mf(r), of the paper at p. 7, to vary rapidly at particular values df(r) of r. The differential coefficients dr may, in consequence,

become, for these values, so large as to make the parts of the sums Σ which contain them so much greater than the other parts, that the latter may be neglected. Accordingly we will assume this to be the case; and then the first of the equations (3.) becomes

This equation, being symmetrical with respect to x and y, gives for, the same value whether a coincides with Ox, or with Oy, (fig. 2). We shall therefore assume that V is sensibly the same for all values of . And then if we put

m Σ . (¢ (1) + ↓ (r) ▲y2) ▲ x2 = c2

2

(5.)

we have (10.) Now conceive a number of plane waves, perpendicular to the plane of a, Oy,, (fig. 2,) all of which, at the commencement of the time t, pass through the centre O; and, since is the same for all values of 0, conceive the velocities of these waves to be all equal; then their distances from the centre O will constantly be equal, and the curve, in the plane of x, Oy,, touched by all of them at any instant will be a circle.

(11.) If the system of coordinate planes be turned on the axis of x, the circle and ellipse (art. 10 and 8) will describe a sphere and spheroid. And since this turning of the coordinates will not, by the supposition (art. 4), sensibly affect the values of the sums, and consequently not alter those of v, and v, it follows that the agitation at the centre O will in general produce two sets of waves; of which one set will be spheroidal, and the other spherical: the vibrations in the spheroidal waves being perpendicular to the axis of x,, and the vibrations in the spherical waves perpendicular to those in the spheroidal.

(12.) From the supposed arrangement of the molecules round the axis of x, it follows (art. 6 and 9,) that c c1, and consequently that when is zero we have v = v. Hence by limiting our view to a spherical and spheroidal wave, both of which emanate from the centre of agitation at the same instant, we perceive that they will constantly coincide along the axis of r. And when is a right angle we have v1 = C which shows that the spherical wave will include, or be included by, the spheroidal wave, accordingly as c is greater or less than c

By referring to Professor Airy's Mathematical Tracts, p. 346-350, it will be seen that the results obtained in this and the preceding article are sufficient to explain the prin