between fecundity and the fading of the yellow pigmentation of the shanks, ear lobes, etc. The fact that the carotinoid-free hens exhibited normal fecundity enhanced greatly their value for the investigation.

The question was attacked in two ways, first, by observing the histological changes in the shank skin when carotinoid-free food was fed to non-laying pigmented birds, and second, by observing the effects on the tissue and skin pigmentation of feeding carotinoid-rich food to laying carotinoid-free hens. The birds used for the histological studies comprise several yellow shanked White Leghorn cockerels, the specific source of whose pigmentation was not known, and one cockerel from the carotinoid-free flock whose feed was changed from the carotinoidfree ration to one composed principally of yellow corn. The visible skin parts of the latter bird took on a yellow color very rapidly after the introduction of the yellow corn until at the end of 42 days his plumage had a rich creamy appearance and the shanks, beak, ear lobes and vent a deep yellow color. Each of the pigmented birds was placed on a carotinoid-free ration and histological studies made on vertical frozen sections of the shank skin of individuals from time to time as the pigment gradually faded.

As the result of these studies the observation of Barrows 12 was confirmed that the yellow pigment of the shank skin is confined chiefly to the Malphigian layer of the epidermis, with some pigment in the corium. Especially instructive were the sections after staining with Nile blue. The sample of this dye which was used was found to be dichromatic with respect to fat and pigment, fat staining red and carotinoid pigment deep blue. By this means it was determined that carotinoid pigment exists free in granular condition in the shank epidermis, which is contrary to the results reported by Barrows, who concluded that the lipochrome of the shank skin is dissolved in fat. The failure of Sudan III to color the visible skin parts of fowls, as observed by Blakeslee,13 and confirmed by me, is explained readily by the observation that the Malphigian layer of both the pigmented and non-pigmented skin lacks appreciable amounts of stainable fat.

The histological studies of the shank skin as the xanthophyll gradually faded on the carotinoid-free ration showed first a disappearance of pigment from the corium, then a disappearance from the outer layer of the corium which gradually extended to the rete of Malphigi, the last pigment to disappear being the xanthophyll at the base of the Malphigian layer. These observations are interpreted to mean that when

the supply of xanthophyll for the skin is cut off by reason of its removal from the food, or for any other reason, any xanthophyll present in the corium layer of the skin of the shank, ear lobes, etc., is deposited in the rete of Malphigi. At the same time the xanthophyll deposits in the outer layer of the epidermis either wear off by reason of the normal replacement of the outer cells by those lower down, or are oxidized because of closer contact with the air. The xanthophyll deposits in the rete of Malphigi in time become a part of the outer layers of epidermis and are lost also. The skin thus finally becomes free from visible yellow pigment.

The significance of this interpretation at once becomes apparent in the light of the results secured when xanthophyll-rich rations were fed to the laying carotinoid-free hens. After a month on rations containing an abundance of green feed or yellow corn not a trace of xanthophyll had appeared in the ear lobes, shank or vent, and the adipose tissue had taken up such a small amount of yellow color that a very careful examination of the rendered, melted, body fat was necessary to detect the increase in color in comparison with the fat from birds which had received no carotinoids in their ration from birth. The blood serum. and the yolks of the eggs laid during the feeding of the xanthophyllrich rations, however, contained an abundance of yellow pigment.

As the result of the histological studies and feeding trials the author believes that the correct explanation of the physiological relation between egg laying and the fading of visible yellow pigmentation from the bodies of fowls of certain breeds is that in cockerels and non-laying females the visible skin parts represent a normal path of excretion of the xanthophyll pigment derived from the food. Egg laying deflects the excretion entirely to the ovaries, and even prevents the incorporation of xanthophyll with the tissue fat, and this continues as long as the ovaries function with regularity, whether the egg production be at the rate of one egg a day or one egg a week. The result is that the pigment found in the skin at the onset of fecundity is gradually excreted toward the epidermis where it either wears away as the result of the normal structural changes in the epidermis, or becomes oxidized, and thereby decolorized. The movement of yellow skin pigment during fecundity is thus outward and not inward toward the ovaries.

Influence of various feeds and certain dyes on the color of the egg yolk and body fat.-A critical study was made of the effect of certain coloring matters on the pigmentation of adipose tissue, egg yolk and visible skin parts, and also of the relative xanthophyll content of various

materials commonly used as chicken feed, using the carotinoid-free flock.

Carotin alone, fed as naturally highly colored butter fat, and the orange-yellow pigment of the annatto seed, were found to be without influence on the color of the adipose tissue or visible skin parts. Sudan III colored only the adipose tissue of non-laying birds, the visible skin parts being unaffected by this dye. With laying birds, the egg yolk as well as the adipose tissue was colored by Sudan III, but not the visible skin parts.

Yellow corn and green feed only were found to be rich in xanthophyll when various plant and animal materials were tested for their xanthophyll content by their effect on the color of the egg yolks when fed to hens laying carotinoid-free eggs. A little of the pigment was found in hempseed, barley, gluten feed and red corn. Wheat, wheat bran, oats, cottonseed meal, rape seed, meat scraps, blood meal, skim-milk and butter-milk were found to contain negligible quantities of xanthophyll.

The experiments here reviewed were conducted at the Missouri Agricultural Experiment Station with the coöperation of Prof. H. L. Kempster of the Department of Poultry Husbandry. The complete data appeared in a recent issue of the Journal of Biological Chemistry.

1 Palmer, L. S. and Eckles, C. H., J. Biol. Chem., 17, 1914, (191–249); Missouri Agric. Exp. Sta. Bull., Nos. 9, 10, 11, 12, 1914, (313-450). Palmer, L. S., J. Biol. Chem., 23, 1915, (261-279); 27, 1916, (27–32).

2 Osborne, T. B. and Mendel, L. B., J. Biol. Chem., 32, 1917, (309–323); 34, 1918, (17-27). Palmer, L. S., Ibid., 27, 1916, (27–32).

Osborne, T. B. and Mendel, L. B., Ibid., 33, 1918, (433–438).

' Palmer, L. S. and Thrun, W. E., J. Ind. Eng. Chem., 8, 1916, (614-618).

"Barbieri, N. A., Paris, C. R. Acad. Sci., 154, 1912, (1726–1730).

7 Blakeslee, A. F. and Warner, D. E., Science, 41, 1915, (432-434); Amer. Nat., 49, 1915, (360-368).

Blakeslee, A. F., Harris, J. A., Warner, D. E. and Kirkpatrick, W. F., Storrs Agric. Exp. Sta. Bull. No. 92, 1917, (95–194).

10

Harris, J. A., .Blakeslee, A. F. and Warner, D. E., These PROCEEDINGS, 3, 1917, (237). Warner, D. E. and Edmond, H. D., J. Biol. Chem., 31, 1917, (281–294).

"Riddle, O. and Harris, J. A., Ibid., 34, 1918, (161–174).

12 Barrows, H. R., Maine Agric. Exp. Sta. Bull., No. 232, 1914, (237–252).

13 Blakeslee, A. F., Storrs Agric. Exp. Sta. Bull., No. 92, 1917, (152).

RADIATIONLESS ORBITS

BY EDWIN BIDWELL WILSON

DEPARTMENT OF PHYSICS, MASSACHUSETTS INSTITUTE OF TECHNOLOGY

Read before the Academy, November 10, 1919

The reaction on an electric charge due to non-uniform motion has been calculated (by Lorentz, for example) and found to be

this term F is merely the first of a series which converges with extreme rapidity provided the dimensions of the charge are small compared with the distance light would travel in the time required for a sensible charge in the velocity. The activity of the force F determines the rate R of radiation of mechanical energy as

What plane orbits are such as to make the radiation as determined by (2) identically zero? The answer to this question is contained in the general integral of the quadratic differential equation of the third order

The integration may be obtained easily by considering v as the radius vector in the hydrograph. Then d2v/dť2 is the acceleration of the moving point in the hydrograph and its radial and tangential components are

of be the inclination of v to a fixed direction. The condition of perpendicularity (3) may thus be written

are the parametric equations of the path, v being any function of the time. The equations contain three constants of integration, which allow an arbitrary choice of axes, and one arbitrary function v. The accelerations along and perpendicular to the path are ' and √v"; the total acceleration is √2+vo", and its inclination to the path, tan-1 (√vʊ"/v').

A simple case may be had by taking v=e-a, which represents a particle combing to rest. Equations (4) may be written

is the polar equation of the locus-showing an equiangular spiral with 45° between radius and tangent. If z = x + iy,

The vector velocity dz/dt is 135° ahead of the radius z, and the acceleration is 270° ahead, which means a retarding acceleration decreasing the areal velocity and perpendicular to the radius. This type of acceleration is found in the straight-bore centrifugal gun.

-at

In (5) the magnitudes of the radius r, velocity v, acceleration v', and its rate v" are in geometric progression with the ratios √2 a, the value of v' being √2 ae-at. If this acceleration be resolved along the radius and along the normal to the path, the respective components are 2√2ae-" outward and 2 ae at inward. A constant magnetic field perpendicular to the plane of motion is competent to furnish a component acceleration along the normal to the path and proportional to the velocity. The electric field in a plane perpendicular to the line joining two like charges at its middle point will act radially from the point of equilibrium upon a like charge with a force proportional to the distance. A proper slight adjustment of the intensity of the magnetic field will take care of the force (1). It is therefore possible easily to set up an electrical problem which is satisfied by the path (5). The general dynamical equation for the motion thus adjusted is