LOCATION OF THE SPECTRUM, ETC.

Another advantage of the linear filament lies in the simple structureof its beam, which should make it possible to design much more efficientheadlight lenses than those in use with the V-shaped filament.

I hope that this article will draw attention to a phase of the headlightquestion which appears to have been neglected-the effect of the shape ofthe light source on the shape of the beam, and also hope that it will assistin a small way in bringing the linear filament back into the popularityit deserves.Scientific BureauBAUSCH & LOMB OPTICAL CO.Rochester, N. Y.February, 1918

NOTE ON THE LOCATION OF THE SPECTRUMFORMED BY A PLANE TRANSMISSION

GRATINGBy HERBERT E. IvES

The simplest type of diffraction spectroscope is that which involvesmerely a line of light or slit, and a plane transmission grating held over theeye, through which both the slit and the spectra of the several orders areobserved. Pocket spectroscopes of this type have been put on the market,and are to be found in many laboratories.

The utility of such a spectroscope is increased for many purposes if itbe provided with a scale, whereby wave lengths may be determined. Ascale on glass, consisting of transparent lines on an opaque ground, backedby an opal glass illuminated by any appropriate means, meets this need.In designing a simple spectrometer of this kind, it becomes necessary toknow where to place the scale in order to avoid any parallax between itand the spectrum. This scale position is not, as might be supposed at firstthought, on the circle of which the line joining the slit and the eye is aradius, nor in the plane of the slit. It is found to be located very definitely,as judged by the parallax test, along a curve whose position varies withextreme rapidity with the angle made by the grating with the eye-to-slitline.

172 H. E. Ives

LOCATION OF THE SPECTRUM, ETC.

This focus is evidently a property of the grating alone, since the onlyeffect of a lens placed over the eye is to improve or impair the definition ofthe spectrum without affecting its location. The calculation of this focus

U

I

Fig. 1

proves to be merely a matter of the application of the elementary gratingequation, connecting angle of incidence, grating spacing, wave length andangle of deviation. The derivation of the formula to be used is immediatefrom the diagram, Figure . Here u is the distance from slit to eye, isthe length of grating at the two ends of which the direction of the deviatedray is noted, is the angle through which the grating is rotated, HI and 2 are

H. E. Ives 173

LOCATION OF THE SPECTRUM, ETC.

angles of incidence, e and e2 are angles of diffraction, and u' is the distancefrom the grating to the intersection of the extreme rays. By combiningthe ordinary grating formula

sin e + sin ?Y = ddwith the usual formulae for the solution of oblique trianglesformula for the determination of u' is obtained as follows:

the complete

f, acos sin-

f sin sin-

(d - sin cos~'

X(- -sin Cos'(d

Cos a S

4 i +a' - 2a sin q5cos q sin-

-/I+a2-2a sin 40 - -sin )1

where a = ' and d is the grating spacing.U

In Figure 2, the values of rae calculated for values of a of 0.5, 0.4,

0.3, etc., for 0 = 0, X = 0.5, and grating spacing = inch. The im-20,000

portant point to note is that as a becomes small - approaches a definiteu

0./ 0.2 0.3 0.4 0.5

0.9

0.8

0.7

o.6

0.5s

A=

A - o. st

0.3

0.2

0.1

a = 2Fig. 2

limiting value from which itdiffers but little for a gratingwidth ( = o.iu) as great aswould ordinarily be used formaking parallax tests. Thismeans, as observation con-firms, that the spectrum isquite definitely located at acertain point in space whichremains fixed for compara-tively large movements of theeye to either side of thegrating center.

In Figure 3 are shown thecalculated positions of thespectrum for the grating spac-ing already assumed, the valueof a used in calculation beingchosen small enough (o.oiu)to give practically the limit-

-1 'Is_ __ __^

N,

N

-

174 H. . Ives

LOCATION OF THE SPECTRUM, ETC.

\ \r

I

I

I

I

I

I

--/-, kb

H. E. Ives 175

ABSTRACTS

ing position, or what may be termed the focus of the grating for an infin-itesimal length. The interesting feature is the rapid shooting away of thespectrum as f increases. By interpolation it is found that for the spacingassumed, the spectrum is most nearly in the plane of the slit for 4 = 24°,although it lies across that plane at a considerable angle. It lies mostnearly on the circle of which GS is a diameter for + =20°.

Physical LaboratoryTHE UNITED GAS IMPROVEMENT CO.PhiladelphiaJuly, 1917

ABSTRACTSTHE MINIMUM RADIATION VISUALLY

PERCEPTIBLE. Prentice Reeves, AstrophysicalJournal, p. 167, September, 1917. CommunicationNo. 5 from the Research Laboratory of the East-man Kodak Company. The previous investiga-tions of the least perceptible radiation havein most cases used stellar light sources and havetaken various uncertain values for the area of thepupil. In the present paper, the writer used adirect laboratory method where all physical stimuliwere under accurate control and there were notroublesome atmospheric conditions as in stellarobservations. Another advantage was the use ofthe observers' pupillary measurements obtainedfrom instantaneous flashlight photographs.

To approximate conditions of stellar observa-tions a stimulus one millimeter in diameter wasviewed from a distance of three meters. Thebrightness of the "star" could be varied by theobserver and the threshold determined. The ob-server remained in total darkness for at least fifteenminutes to assure dark adaptations and used a fixedhead rest for constant visual fixation. The resultstaken under the same conditions from day to dayvary through wide ranges and are explained byvariations of the pupil, factors of attention andfatigue, ideo-retinal light (caused by retinal circula-tion), after images, involuntary eye movements andthe general physiological condition of the observer.As these variable factors are largely beyond ex-perimental control, the only method is to take asmany observations as possible over a wide range oftime and accept the general average as the thresholdvalue. The writer's threshold is the average ofnumerous observations and results were also ob-tained from two other observers and averaged withthe writer's luesva for those days.

If the let B = normal candle power per sq. cm.of source, and assuming the inverse square law and apoint source, the flux through 1 sq. cm. on the axisat the eye will be

SB/R2 lumensand the flux through the pupil of area A will be

Fp = SBA/R 2 lumensNow B = Lumens/n and A = nr 2 so

Fp = SL -r2/R 2

where Fp is the flux through the pupil; S, the area ofthe star; L, the star brightness in lamberts; r, theradius of the pupil; R, is the distance of the eyefrom the star. If the equation is then multipliedby the mechanical equivalent of light M we get

Least perceptible radiation = SLM r 2 /Rergs per sec.

Using the 1 mm star at a distance of 3 meters,the writer's values for L and r were 0.0072 milli-lamberts and 4.65 mm, which gives a result of17.1X 10-lo ergs per sec. The average result forthree observers was L = 0.0088 ml., r = 4 mm.and least perceptible radiation = 19.5X 1010ergs per sec.

PHOTOMICROGRAPHS IN COLOR. C. E. K.Mees, Amer. Phot., August, 1917, p. 448. Coloredlantern slides representing photomicrographs ofstained sections can be obtained by making theprints from the negatives in stained gelatine insteadof by the usual photographic process. The methodis as follows: Lantern slides are sensitized by bath-ing in bichromate solution and after rinsing anddraining are dried in the dark as uniformly as pos-sible. The sensitized plates are then exposedthrough the glass under the negative to the light ofan arc lamp, an average exposure being about threeminutes at eighteen inches distance. The exposedplates are washed in warm water until all solublegelatine is removed. The plates are then washedin plain water, fixed in hypo and washed. They arethen ready for staining. The staining is done witha 1 per cent. solution of dye containing 1 per cent.of acetic acid, the dye being selected to imitate mostclosely the original stain of the section.

When sections stained with two different colorsare being photographed, negatives are made throughsuitable color filters. The prints are stained a colorcomplementary to that of the filter through whichthe negative was taken and are placed face to faceso that a two-color slide is obtained. The choice ofthe filter is decided by visual trial under the micro-scope, the filters chosen being those which mostcompletely absorb one color and transmit the other.Thus, photographing a section stained with Dela-field's hematoxylin and precipitated eosine the A

176