By HENRY PHELPS GAGE A THESIS RESENTED To THE FACULTY OF THE GRADUATE SCHOOL * , - of CoRNELL UNIVERSITY FOR THE DEGREE OF . DocTOR OF PHILOSOPHY REPRINTED FROM THE PHYSICAL REVIEw. Vol. 33, No. 2. August, 1911 . . . . . PREss or THE NEW ERA PRINTing company Lancast ER, PA. - 1911 THE RADIANT EFFICIENCY OF ARC LAMPS BY HENRY PHELPS GAGE A THESIS PRESENTED TO THE FACULTY OF THE GRADUATE SCHOOL OF CORNELL UNIVERSITY FOR THE DEGREE OF DOCTOR OF PHILOSOPHY REPRINTED FROM THE PHYSICAL REVIEw. Vol. 33, No. 2. August, 1911 PRESS OF THE NEW ERA PRINTING Com PANY LAN CASTER PA I9 II f [Reprinted from the PHYSICAL REview, Vol. XXXIII., No. 2, August, 1911.] THE RADIANT EFFICIENCY OF ARC LAMPS. BY HENRY PHELPS GAGE. HE object of the present investigation was to determine the radiant efficiency and the mechanical equivalent of the light from the right angle carbon arc and the Bremer flaming arcs. The symbols used in this paper are: R = total watts radiated. L = light energy; watts of radiant energy of wave-lengths visible to the eye. W = radiant energy of wave-lengths to which water is transparent. The ratios here determined are called: L/R = radiant efficiency. W/R = “water-bath” efficiency. DISCUSSION OF THE LIMITS OF VISIBILITY. When determining radiant efficiency by an integration method such as that of Langley" or of Ångström,” certain arbitrary limits are chosen to divide the visible from the invisible parts of the spectrum. These methods are based on the following definition of radiant efficiency. A2 Eff. = L . _ energy visible part of spectrum R Tax * -º-º-º: total energy radiated 7 eZ 0 where I is the intensity of the light and A2 and A1 are the upper and lower limits of visibility respectively. For most light sources the energy in the ultra-violet is so small that the lower limit XI can be taken as zero with no appreciable error, the energy of the infra-red is however so great that a slight change in the position of the limit in the red causes a great change in the value of L. Langley,” the first to use the integration method, chose the limit .700. Later workers moved the limit of integration far beyond this point to the A line, .76p. 1 Science, June 1, 1883. ? PHYS. REV., I'7, 302, Igo3. 8 Phil. Mag., 30, 260, I890. : tº te : . & º: : 227321 : º : : I I 2 HENRY PHELPS GAGE. [VOL. XXXIII. P. G. Nutting criticizes this as being too far from the natural physio- logical limit, but suggests no other. While the human eye will respond to radiation of wave-length .769. and under favorable conditions to even as great wave-lengths as .82ſ,” this response is very slight. Hence it was thought advisable to choose a new limit which, while arbitrary, would correspond reasonably well with the physiological limit of the human eye. } The principle adopted was that the limit should be so chosen that all light beyond the limiting wave-length should be so small as to be negligible in comparison with the total light. König and Brodhun" have shown that if a white surface is illuminated by two patches of light side by side whose intensities differ by I.6 per cent. the difference can only just be detected. Therefore in choosing the limit it would appear that the rejected light may be as great but should not be greater than I.6 per cent. of the total. In the spectrum of the positive crater of the carbon arc, for exam- ple, there is almost no visible light beyond .700, but in this region the energy is very intense. The result is that changing the limit from .70ſ, to .76p, increases the energy enor- mously while hardly changing the visual effect at all; conversely, mov- ing the limit from .769 to .684, results in a decrease in energy out of all proportion to the decrease in light. The choice of a new limit was made by integrating luminosity curves. The total area of such a curve was taken as the total luminosity and the area beyond different wave-lengths was measured with a planimeter. The ratio of the small area beyond the given wave-length to the total area would be the amount of light lost if all radiation of greater wave- length were removed. Such measurements were made on a luminosity curve of Abney and Festing” (Fig. I), on the red sensation curve of König" and on some curves of my own. The results expressed in curve form (Fig. 2) indicate the percentage of the total light lost if the red end of the spectrum were removed to the given wave-length. Fig. 1. Luminosity curve from Abney and Festing. 1 Electrical World, Vol. 5I, p. I37.I. 2 The strong infra-red line of the sodium arc, see Becquerel, Comptes Rendus, Vol. 97, p. 73. 3 Sitzungsberichte der Königlichen Baierische Academie der Wissenschaft, Berlin, pp. 917–931, 1888, II. Also table in Bulletin of the Bureau of Standards, Vol. 5, p. 286. 4 Phil. Trans., I 77, 423, 1886. * Zeit. Psy. Phys. des Sinnesorgane, 4, 312, 1893. Also Gesammelte Abhandlung, p. 286. : . : : : No. 2.] THE RADIANT EFFICIENCY OF ARC LAMPS. II 3 From these data and from the general appearance of the spectrum it was decided to use as the limit in the red .684,. The curves show that with this limit the light removed is less than I.6 per cent. of the total. sº \ | | \ Illumihation due to | light of wave length. greater than 2. Fig. 2. The limit is easily located in the arc spectrum of a mixture of lithium and potassium, being nearly half way between the lithium line .67IM and the potassium doublet .691 u. Also the absorption spectrum of neo- dymium shows a dark line at .68p. The limit in the violet could be determined in the same way but is of no great importance, as the energy of the ultra-violet part of the spectrum with most sources is so small that it can safely be neglected. In the study of the arc however it seemed advisable to arrange the apparatus to remove all radiation less than .44, thus allowing the cyanogen band of the carbon arc at .42p to pass but excluding that at .388p. Between these two bands there is practically no light. APPARATUS. In the work to be described a modification of the method of Ångström was used. The apparatus was similar to his, the main difference being l– C. S. T, \% ŽS Fig. 3. Arrangement of apparatus to measure L'/R. : : Jº I I4 w HENRY PHELPS GAGE. tvol xxxiii. that Ångström used two separate sources of light, one being dispersed into a spectrum, the energy of the other being measured direct; while in the present apparatus both the direct A H.0 /\ 4\ * s :*-*. and the modified light come from the same source. - Energy from the source L (Fig. 3) can reach the thermo-junction of the radiomicrometer Ra by either of two paths, (a) direct, no absorption ex- cept by air, (b) through the prism train P. Light from the source is focused by the condenser C. on the adjustable slit S, is rendered parallel by the lens Cº, dispersed by the prism P and focused as a spectrum at R-V by the mirror M1. The screen S2 is placed in the red end of the spectrum so that it cuts off all of the infra-red to .68A. The mirror M2 reassembles the spectrum to a patch of white light at the radiomicrometer. - - The intensity of the patch of direct light is fixed by the brightness and distance of the source L, but that of the other patch W can be varied by widening or narrowing the slit SI until it is of the same brightness as the direct light. The prism consists in a 60° hollow prism of carbon bisulfide immersed in a square glass cell filled with distilled water. It gives a good dispersion with a deviation of but 20° from a straight line (Fig. 4). The lenses are of glass. The mirrors are plano-concave lenses, silvered on the concave side. The focal length of M1 is 50 cm. and of M2 is 25 cm. Fig. 4. Compound prism. THE RADIOMICROMETER (Fig. 5). The suspension of the radiomicrometer was of no. 36 copper wire free from iron, to the bottom of which was soldered a small thermo-junction of bismuth and antimony. To the top of the loop was fastened a piece of silvered cover glass and the whole was suspended by a quartz fiber. The radiomicrometer was provided with two windows. The one which faced the light had no glass in it in order not to absorb any energy, the one which faced the other way was so placed that the light source could be seen through the instrument. This window was covered with a plane glass. The junction (Fig. 6) was made by cementing a rod of bismuth and one of antimony to a piece of mica with sealing wax and making connection between them at one end with fusible metal. The free ends were soldered No. 2.] THE RADIANT EFFICIENCY OF ARC LAMPS. II 5 to the copper loop with fusible metal and the junction dipped into dead black japalac. To get the small rods or wires of bismuth and antimony the metal was melted in a glass tube and the tube drawn down to capillary size. When cold this left the bore of the tube filled with a fine rod of the brittle metal. The ends of the metal were tinned with ordi- nary solder and then with Woods' fusible metal. It was then an easy matter to solder these rods which were left within the glass together and to the tinned ends of the cop- per loop. CALIBRATION. The radiomicrometer used in | this work did not need to be very sensitive as the energy to || be measured was comparatively large. The ballistic method was used: the farthest point reached on the first swing being recorded in all cases. To determine whether there was selective absorption by the black japalac surface of the junction, the ratio of W/R was determined for the positive crater of the carbon N Fig. 5. The radiomicrometer. arc using a Sullivan galvanometer and a lecture room thermopile whose surfaces were covered with different substances: (1) camphor soot, (2) black japalac, (3) dull yellow shellac. The value of W/R came out nearly the same in all cases showing the proportion of energy absorbed to be nearly the same in the visible as in the invisible parts of the Fig. 6 spectrum. rig. o. The scale of the radiomicrometer was calibrated by an Radiomicrometer - * º te junction. acetylene flame moved to different distances. This showed that the “kick” and the steady deflection were proportional to the incident energy. Merritt has shown that the ballis- 3. : II 6 HENRY PHELPS GAGE. (vol. XXXIII. tic throw is proportional to the steady deflection both by experiment! and by theory.” * The radiomicrometer was also calibrated roughly in absolute units by a Hefner lamp and by a Nernst glower. The radiation of the Hefner lamp was taken from Ångström' as II.3 Watts. Example: Distance Hefner. Kick. Kick X d”. For 1 Watt : Kick X &2. # 35 cm. 7.42 9,100 808 50 3.75 9,400 832 - 820 This value was checked by a Nernst lamp. Input filament. 100 volts, 1.07 amps. = 107 watts; Radiation, mean spherical, IO7 watts; Equatorial, I36 watts (: times mean sph) ; Distance kick X d” I36 that obtained with the Hefner but is slightly greater as might be expected owing to the reflection from the heater just back of the glower. In a similar way the more sensitive suspension no. 2 was found to have a constant of 3,540. IOO cm.; Kick I2.5; = 920. This is in general argeement with SOURCES. The Right Angle Carbon Arc.—A simple hand feed arc lamp was used, either carbon of which could be moved separately. The carbons were held in the position shown in Fig. 7. The current was kept constant by feeding the carbons forward whenever the current showed signs of dropping. Soft-cored “Columbia Projector” carbons were used. Tests were made using alternating and direct cur- rent. With the latter both the positive and negative craters were tried. In some cases the lower carbon was shaded from the radiomicrometer so only the upper carbon could be seen. This Was especially necessary when making measurements on the negative crater. The energy from the cyanogen arc between the electrodes was measured by shading both carbon tips. Both the light and energy from the arc is negligible in comparison with that from the hot tips. - - With alternating current an inductor (choke coil) was used instead of a resistor because it furnished a much steadier current. Fig. 7. Right angle arc. 1 American Journal of Science, 37, I67, 1889. * American Journal of Science, 41, 422, 1891. * L. c. : : No. 2.] THE RADIANT EFFICIENCY OF ARC LAMPS. I 17 The Bremer Flaming Arcs.-A lamp was kindly furnished by the late C. J. Toerring. It was made for alternating current and burns 8-mm carbons. An economizer and set of blow magnets caused the arc to take the position shown in Fig. 8. The electrodes used were 8-mm. “Excello” carbons known as “yellow” and { { & ºn ºf G º y 9 brilliant white. *::::: t METHOD. Ps Photometric Match.-The apparatus was so arranged * that light from the source could strike the radiomicrometer † after having traversed either of two paths, i. e., either Fig. 8. Flame arc. straight or through the prism train. In front of the suspension was an aluminum shutter covered with a piece of white paper. By using screens with suitable holes the direct light was made to fall at the sides of the reassembled light (Fig. 9). The brightness of the reassembled light could be varied by opening or closing the slit SI until it was photometrically equal to the direct light. In making a photometric match the screen was º viewed either through a red or a green glass. This was necessary on account of the great brightness of the patches and on account of the slight yellowish Color of the mirrors which rendered a photometric match difficult. The energy of the spectrum being Fig. 9. White shutter used e tº as photometer. greater in the red than in the blue, the match was made through a red glass rather than through a blue glass. This method gives visual equality at the shutter. The thermo-junc- tion, however, is some distance behind the shutter necessitating a cor- rection. Call the light falling on the shutter L and R, that striking the thermo- junction L’ and R'. The radiomicrometer will then give the ratio of L'/R', not L/R. R/R' = D”/D*, where D is the distance from the source to the shutter and D' that to the junction. The value of L/L' is ob- tained by this reasoning: Fig. 10 Suppose I (Fig. IO) to Image formation of an extended source. be the image of an ex- tended source of light of uniform brightness with sharply defined edges and d to be a diaphragm. If the radiomicrometer be placed at I or in : * II 8 *HENRY PHELPS GAGE. IVol. XXXIII. the shaded area in the neighborhood of I it will receive light from the entire area of the diaphragm. An eye placed at this point will see the entire opening of the diaphragm lighted with the intrinsic brilliancy of the image I of the source. In this case as far as illumination is con- cerned the behavior is just the same as though there were an extended source of light at the diaphragm with the intrinsic brilliancy of I. Within the shaded area the energy will follow the inverse square law the distance being measured from the diaphragm. Outside the shaded area but within the dotted area the energy SJ will follow the inverse square law but 25% — ...:”; the distance must be measured from CAN. the image I, for now the radiomicro- £.25 meter will receive light which has Fig.11. either passed through all parts of I or Position of diaphragm (R—V) for correct- which would pass through all parts ing L'/R. of I just as it would if I were the - original source. In the case of the experiment the radiomicrometer was placed in the shaded area (light struck it from all parts of the diaphragm) and the position of the diaphragm was at the focus of the spectrum where the cut off screen was located. The apparent distance of the diaphragm was used. Apparent distance of diaphragm (R—V, Fig. 11) to mirror. . . . . . . . . . . . . . . . . . . . . . 2.2 cm 1 1 — 1 2 - 25 T 2.2 Apparent distance of diaphragm to screen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26.2 cm. Apparent distance of diaphragm to junction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 28.2 cm. L d” 28.2 Ratio E7 - F T 26.2% = 1.16 Distance of source to screen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 107 cm. Distance of source to junction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 cm. 2 R D'" Io92 = − = — = I.O R! Dº Io?? 3, L I.I6 X L' X L’ — — — ". . = I. I2 — . R 1.03 R' R’ In view of the great amount of work previously done by the method of the water cell it seemed desirable to examine the “water-bath” efficiency of the sources as well as the true radiant efficiency. Moreover, No. 2.] THE RADIANT EFFICIENCY of ARC LAMPS. I IQ the latter is often difficult to measure directly as L is so small compared to R that it cannot be measured accurately. In this case the ratio of L/W was found as an intermediate value and multiplied by W/R to get the value L/R. L/W was determined in exactly the same way as L/R except that an 8-cm. water-bath was put in the path of the direct ray. The “water-bath” efficiency is the ratio of the energy to which water is transparent to the total amount of energy radiated. The observed value W/R is subject to two corrections. I. The non-selective absorption and reflection of the water-bath. Photometric tests show this to be about to per cent. of the incident light. 2. The water-bath makes objects seen through it appear nearer by a distance of one fourth its thickness, 2 cm. In cases where L/R is determined both directly and indirectly the two results may not quite agree. When this occurs the values are adjusted to divide up the error between them. The Location of the Cut-off Screen.—There are two methods of locating the cut-off screen: By looking through the window behind the radiomicrometer the spectrum R-V can be seen. When using a source with a discontinuous spectrum such as the yellow flame arc the screen can be placed in the spectrum till its edge lies just beyond the last visible band, thus allowing all visible but none of the invisible radiation to pass. The spectrum of a white source can be made to appear as if it were discontinuous by placing a solution of a didymium salt before the slit St. A solution of crude “cereum oxide” containing about 20 per cent. didymium oxide was dissolved in hydrochloric acid and showed the following rather sharp absorption bands: .68Ou, 6229, .578u, .5329, .52Op, 4829, .4761, .4444, 427A and trans- mission bands at .837, and .77ou. A spectroscope may be set up to examine the light passing through the radiomicrometer window. With a continuous spectrum the position of the cut-off screen can be followed with the spectroscope, and it can thus be moved to the correct position. With point sources such as the carbon arc the cut off was very sharp, with discontinuous spectra like that of the yellow flame arc there is a wide dark space between the visible red and the infra-red, but with white extended sources such as the white flame arc the cut off is not sharp but may extend from .66p to .7M. This is because of the great slit width necessary, Readings.--The radiomicrometer was used in connection with a lamp and scale. The scale was first set so its zero coincided with the image I 2C) - HENRY PHELPS GAGE. [Vol. XXXIII. of the lamp filament, then by removing a screen the radiomicrometer junction was exposed to the radiation which it was desired to measure. The radiation was allowed to fall upon the junction until the instrument had reached the farthest point on the first swing, which was recorded. The screen was replaced at leisure. This is a much quicker procedure than to wait until the instrument has settled down to the final steady deflection. The radiomicrometer was exposed alternately to the direct and to the modified radiation from the source. After ten readings of each had been made the photometric balance was readjusted and another set was made. In this way the effect of any drift in the radiant energy of the light from the source could be eliminated. Limiting wave-length. Fig. 12. Besides the measurements of efficiency, determinations were made of the distribution of energy in the different parts of the visible spectra of the yellow flame arc, and the positive crater of the carbon arc. In both cases the determinations were made as for the measurement of L except that instead of comparing L with R, L was measured with different positions of the cut off screen. The results for the distribution of energy in the different bands of yellow flame arc are included in Table X. The dis- tribution is such that three fourths of the visible energy is due to the red band and one fifth is due to the green band. The results with the positive crater are shown in Fig. I2, which is a curve between the limiting. No. 2.] THE RADIANT EFFICIENCY OF ARC LAMPS. I 2 I wave-length and the total energy made up of waves whose lengths are less than the limiting value. The Mechanical Equivalent of Light.—To determine the mechanical equivalent of light it is only necessary to know the candle power of the source and the watts energy delivered within the limits of the visible spectrum. The data obtained include these values. The mechanical equivalent of light and its reciprocal, the light equivalent of radiation, will be found in Table XIII. These values for the light equivalent of radiation (2I to 39 candles per watt) are so much larger than those found by some of the previous workers that an experiment was made to determine directly what the value should be. As has been mentioned elsewhere Ångström's results recalculated on a basis of .68p for the limit of visibility gave an efficiency of 21.3 candle power per watt for the Hefner lamp. Charles V. Drysdale' examined the mechanical equivalent of white light from the arc lamp, from the Nernst filament, and also of yellow- green light. His values are I2.4, 8.4, and I6.7 candle power per watt. P. G. Nutting” obtained a value of I3 candles per watt for yellow-green light but did not describe his method. For the direct determination of the mechanical equivalent of light the assumption was made that an 8-cm. water-bath filled with a copper sulphate solution would transmit only visible light. The apparent candle power of the Nernst filament when viewed through this copper sulphate bath was determined, also the energy transmitted. Apparent candle power through 8 cm. copper sulphate bath. . . . . . . . . . . . . . . . . . . . 26.4 C.P. Nernst filament 22.5 cm. from radio-micrometer, shining through bath. (Acts as if 20.5 cm. from instrument.) Deflection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 cm. Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .665 watts, giving a value of .0252 watt per candle or 39.5 candles per watt. The color of the trans- mitted light is bluish green. * Proc. Roy. Soc., 8Oa, p. 19, 1907. 2 Electrical World, 51, 1371, 1908. H 22 HENRY PHELAS GAGE. (Vol. XXXIII. VALUES OBTAINED WITH THE RIGHT ANGLE ARC. The Positive Crater. TABLE I. Values by the prism train apparatus, Current 10 amperes. - - | Directºrough througāra. | Pétat. I peščº Correction, |. water-bath. ugh Pri m. Per . . . .”e - * * -ºº ºº lººm. * ***. 1. 34.25 12.86 § 37.5 4.1.8 X1.105 to 2 37.41 13.90 37.1 \ 41.5 X1.12 3 39.42 11.21 28.5 ; 31.9 4 34.27 12.45 36.3 : 40.7 : 5 41.82 14.06 33.6 37.7 6 44.48 17.36 39.1 43.8 7 41.14 16.90 41.1 { 46.0 8 37.54 14.32 38.2 42.2 9 35.82 13.79 38.4 42.5 10 35.84 13.41 37.4 41.3 11 42.97 17.55 40.9 # 45.5 12 36.08 17.32 48.0 53.8 13 34.86 | 13.30 38.0 42.6 14 52.90 23.10 (13 amps.) || 43.7 48.7 +. ...] ... . . . . . . 42.9 - - • *-ºs.º. º. TABLE II. |Photometric measurements of arc. -- * * * *- —T------—f---- * * -- - Voits. Amperes. watts. S. --> From Energy Input. * * * * * * * * *.* watts per candle.|Candles per Watt. 55 7.5 410 1,550 .265 3.8 10 550 2,300 .240 4.2 15 • 830 3,850 .215 4.65 20 1,100 5,600 .195 . 5.1 TABLE III. Results with water-bath. Radiomicrometer Reading. A - - Amperes. Pěči. Pºst ‘Cörfection. A& W/ te te 7.5 12.43 2.11 17.0 18.5 X1.09 10 16.08 3.2 19.9 21.7 21.86 5.2 24.1 26.2 27.48 6.79 25.4 27.6 22.72 5.70 25.1 27.3 24.45 5.94 24.3 26.5 15 24.47 6.09 24.9 27.1 24.72 6.02 24.3 26.5 21.23 5.36 25.2 27.5 23.52 - 26.96 20 33.04 8.71 26.3 28.7 4 No. 2.] THE RADIANT EFFICIENCY OF ARC LAMPS. I 23 The Negative Crater. TABLE IV. I|W Estimated. WJAZ AIR 40% 8.25% 3.3% º The Right Angle Arc; Alternating Current. TABLE V. Results with the prism train apparatus. Current 15 amperes. -- * / / f I ºf W . . A * ~ * PW Z. P& %nt. peſº, t. Correction. 20.78 8.2 ! 39.5 w 44.2 X 1.12 1744 6.34 36.3 40.7 19.98 ; 6.91 { 34.6 38.8 18.94 4 6.78 35.8 40.1 18.52 6.51 35.1 39.4 - : 40.64 TABLE VI. Candle power measurements. - F E. I º Volts. Amperes. Watts. S. rom Energy Input OWer. W.P.C. C.P.W. 50 15 750 700 1.07 .94 50 20 1,000 1,200 .83 1.2 TABLE VII. Results with water-bath. Amperes. A& - IV/ Pé.&: t. Pe *&nt | R. Watts Radiated. | | Lower carbon shaded. 457 15 9.37 { 1.53 16.4 17.77 618 20 12.66 - 2.44 19.25 20.9 Lower carbon unshaded. 590 15 12.08 . 1.74 | 14.36 15.61 Arc between the craters. 6.5 watts 1.67 .335 20 21 .85 per cent. of Crater I 24 HENRY PHELPS GAGE. [Vol. XXXIII. TABLE VIII. The yellow flame arc. Entire arc. All W. A& Lyſ WLR Correction. 50.4 46.8 12.51 29.2 X 1.087 54.1 50.86 12.25 26.1 Suspension constant 68.9 52.32 12.98 27.0 3,540 divs. per 60.8 56.35 12.56 24.0 watt at one cm. 55.8 53.62 13.16 26.6 r 52.6 5.2.1 13.59 28.4 64.5 55.3 55.7 52.9 57.1 52.0 26.9 R = 430 watts From Energy Input. Amperes. . . . . . . . . . . . . . . . . . . . . . . . . . 13.5 Watts per candle. . . . . . . . . . . . . . . . . . . . .23 Volts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44.5 Candles per watt. . . . . . . . . . . . . . . . . . . . 4.3 Watts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600 Candle power. . . . . . . . . . . . . . . . . . . . . . 2,580 TABLE IX. The yellow flame arc. Arc stream. Pééat. Pºnt. ref&nt. L|R Calculated. 78.5 48.5 35.8 39.8 76.0 47.0 32.5 47.5 73.5 49.7 45.9 45.6 7.2.1 49.3 49.1 35.4 78.8 50.5 81.0 e Found 76.8 49.0 41.45 37.60 Adjusted - - values 79 49.5 39 TABLE X. Distribution of energy in the different bright bands of the spectrum of the arc stream. ... 100 per cent. is the energy of the visible part of the spectrum. Energy which gets through water-bath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 per cent. Luminous energy; red -- blue -- green . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Green + blue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25.5 Blue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.0 Green. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20.5 Red . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.5 Infra-red (which gets through water-bath) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Red -H infra-red. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100.5 No. 2.] THE RADIANT EFFICIENCY OF ARC LAMPS. I 25 TABLE XI. The white flame arc. Entire arc. refºnt. A& W/ Pěčát. Pěčnt. Correction. 44.4 56.93 16.28 28.6 31.1 X1.087 45.7 59.45 17.41 29.4 32.0 45.3 57.35 16.42 28.7 31.2 47.3 56.72 16.94 29.9 32.5 46.0 57.76 17.14 29.7 32.3 45.58 57.64 =476 watts 31.82 From Energy Input. Amperes. . . . . . . . . . . . . . . . . . . . . . . . . . 13.5 Watts per candle. . . . . . . . . . . . . . . . . . . . .44 Volts. . . . . . . . . . . . . . . . . ** * * * * * s • * * * * 47 Candles per watt. . . . . . . . . . . . . . . . . . . 2.27 Watts. . . . . . . . . . . . . . . . . . . . . . . . . . . . 635 Candle power. . . . . . . . . . . . . . . . . . . . . 1,440 TABLE XII. The white flame arc. Arc stream only. L|W WLR L|R L|R Calculated. Per Cent. Per Cent. Per Cent. Per Cent. 54.3 50.5 27.85 27.4 Adjusted values 54.5 50.5 27.5 Probable Accuracy of Results.-No very exact results with arc lamps are possible on account of the wide fluctuations continually occurring in their behavior, hence it is necessary to be content with a rather rough approximation. - With the apparatus used in the present investigation there are ap- parently no inherent instrumental errors of greater magnitude than the settings for photometric equality. ANGSTRöM's RESULTs. his paper on “Energy in the Visible Spectrum of the Hefner Stand- rd,” Ångström determined the following: The distribution of energy in the infra-red. The percentage of the total energy of wave-length less than .769; Lºs/R. The value of LA for various wave-lengths. (The energy of the light of all wave-lengths less than A.) From this, the distribution of energy in the visible part of the spectrum. These last two were expressed in the form of curves. *PHYS. REV., I 7, 302, Igo3, Nova Acta, Royal Society of Science, Upsala, 3d series, Vol. XX. I 26 [VOL. xxxHI. HENRY PHELPS GAGE. TABLE XIII. Summary of results. * - ********* * Watts. As Radiated. At to & * of Eff. tº L| W WLR || LIR º * º g Source. +r à C. P. Per | Per Per Q > | Q :