Sept. 1927

This means that for the kth circuit the saturation curve between ik and φ*, used in eq. (42), must be the one which obtains with the currents Ik, J*_ i , 7*_2, . . . . 72, I i at their full values, while the currents ik + i , ik +2, . . · , in, are all equal to zero.

Literature References. Comparatively little has been done on the general theory of mechanical forces in magnetic circuits, especially taking saturation into account. Some recent articles, of applied nature, are listed below. References to earlier contributions will be found in these articles.

Doherty and Park, Mechanical Force between Electric Circuits; Am. Inst. Elec. Engrs., TRANS. , 1 9 2 6 , Vol. 4 5 , p. 2 4 0 .

Lehmann, The Calculation of Magnetic Attraction) Ibid., p. 3 8 3 .

Hague, "Forces Acting on Conductors Near Iron;" World Power, 1 9 2 6 , Vol. 5, pp. 1 2 4 and 2 0 5 .

Hak, "Calculation of Mechanical Stresses in Reac­tance Coils;" Elek. u. Masch., 1 9 2 4 , Vol. 4 2 , p. 1 7 .

Lienard, Revue Gen. de VElec, 1 9 2 3 , Vol. 1 4 . p. 5 6 3 .

Appendix It is shown in connection with eq. ( 1 0 ) that the mag­

netic energy stored in a saturated circuit (Fig. 2 ) is represented by the area C Ν Ο cC. Similarly, the stored magnetic energy, after the displacement, δ s, has taken place, is proportional to the area C Ν Ο mCf. When this displacement occurs at constant linkages Φ, the mechanical work is done entirely at the expense of the stored magnetic energy. Consequently, the curved infinitesimal strip C OC represents the work done, F δ s, so that

F = (area of strip C Ο Cy/δ s (44)

This expression permits the visualization of the relations and also the solution of some special cases. Consider, for example, a saturated electromagnet with a small air-gap (a lifting magnet). Within a certain range of small values of air-gap, the lines of force in the gap may be assumed to be straight lines, normal to the iron surfaces, and the flux in the iron parts may be considered to follow the same paths and to have the same leakage, independent of the magnitude of the gap. In other words, within a certain range of gaps, the same satura­tion curve may be used for the iron, and only the exciting ampere-turns for the air-gap changed. With this limitation, the area of the strip C OC may be obtained from the air characteristic alone. For the air-gap we have

IT = (Φ/Τ) ( 8 e - 8)/(μ A) (45) where I Τ are the exciting ampere-turns; sQ and s are some distances whose difference gives the length of the air-gap; A is the cross-section of the magnetic path in the air-gap, and μ the absolute permeability of the air. Τ being the number of turns, the linkages Φ divided by Τ give the actual flux. From eq. (45)

903

Τ δ I = - (Φ/Τ) δ 8/(μ A) (46) With the foregoing assumptions, the strip COG be­comes a triangle, so that

area Cf 0 C = — 0.5 δ J . Φ . (47)

The minus sign is necessary because δ I is a negative quantity. Substituting this expression in eq. (44), and using for δ I its value from eq. (46), we get

F = 0 .5 Α Β2/μ (48) where Β is the flux density in the air-gap. Expression (48) is the usual formula for the lifting force of an electromagnet.

The same result may be obtained from eq; (14'd). With the limitations stated above, the saturation curve for the whole electromagnet may be written in the form

Ti = φ (φ) + (φ/Τ) (s0 - 8)/(μ A) (49) where the function φ (φ) is the m. m. f. required for the iron parts. At a constant φ,

δι/δ 8 = - (φ/Τ2)/(μ A) (50) Substituting in eq. (14d) and integrating, will give eq. (48).

PORTABLE LAMPS DEMONSTRATE DESIRABILITY OF SHADED LIGHT

It has taken certain branches of the electrical indus­try interested in lighting a long time to learn that more and better lighting involves proper shading and diffusing of light. For example, lighting fixtures have been designed and sold without shades. Even some "mod­ern electrical homes" have been opened to the public without demonstrating the desirability of shades on certain brackets and ceiling fixtures. After years of effort on the part of certain exponents of good lighting the electrical industry is beginning to awaken and bestir itself to the commercial possibilities of better lighting. The homes of this country need more light, but this cannot be sold easily and permanently unless the princi­ples of good lighting are used as a vehicle.

The public is not alone in its ignorance and indiffer­ence. Many persons in companies which are in a posi­tion to aid the better lighting activity in the residential field are not conscious of the value of shaded light. To these the portable lamp conveys a convincing message. Many millions of these are entering the homes yearly. They have combined decorative and utilitarian value. The public has accepted them without much effort on the part of organizations promoting better lighting. Would they be acceptable if they were not equipped with shades?

Every dealer or salesman who is not convinced that shaded light is of primary importance should take the shades off the portable lamps in his home. How un­bearable would he find this condition of glaring light! Then he might try to sell portable lamps without shades. Again he would learn a lesson.—Electrical World.

KARAPETOFF: MECHANICAL FORCES BETWEEN ELECTRIC CURRENTS