■May 13, 1880] 



NATURE 



43 



results of measurements of the red, blue, and actinic ligbt of 

 electric arcs, in terms of the red, blue, and actinic light of a 

 standard candle. The fact that the electric light is a vei^ 

 different mixture of rays from the light of gas or of a candle, has 

 long been linown, but has been ignored in statements intended 

 for practical purposes. 



Again, the emission of rays from the heated carbons and arc is 

 by no means the same in all directions. Determinations have 

 been made in Paris of the intensity in different directions, in 

 particular cases. If the measurement is made in a horizontal 



Fig. 3 (Scale about j'o). 



direction, a very small obliquity in the crater of the positive 

 carbon will throw the light much more on one side than on the 

 other, causing great discordance in the results obtained. 



If the electric light be compared directly with a standard 

 candle, a dark chamber of great length is needed — a convenience 

 not always attainable. In the experiments made at the South 

 Foreland by Dr. Tyndall and Mr. Douglass, an intermediate 

 standard was employed ; the electric light was measured in 

 terms of a large oil lamp, and this latter was frequently compared 

 with a standard candle. 



Other engagements have prevented the author from fairly 

 attacking thee difficulties; but since May 1879 he has had in 

 occasional u-e a photometer with which powerful lights can be 

 measured in moderate space. This photometer is shown in 

 Fig. 3, and an enlargement of the field-piece in Fig. 4. A lens 



Fig. 4 (Scale abjut J). 



A, of short focus, forms an image at B of the powerful source of 

 light which it is desired to examine. The intensity of the light 

 from this image will be les; than that of the actual source by 

 a calculable amount ; and when the distance of the lens from the 

 light is suitable, the reduction is such that the reduced light 

 becomes comparable with a candle or a carcel lamp. Diaphragms 

 CC are arranged in the cell which contains the lens, to cut oft' 

 stray light. One of these is placed at the focus of the lens, and 

 has a small aperture. It is easy to see that this diaphragm v ill 

 cut off all light entering from a direction other than that of the 

 source ; so effectually does it do so, that obseivations may be 

 made in broad daylight on any source of light, if a dark screen 

 be placed behind it. The long bM DD, Fig. 3, of about 7 feet 

 length, is lined with velvet — the old-fashioned dull velvet — not 

 that now sold with a finish, which reflects a great deal of the 

 light incident at a certain angle. This box serves as a dark 

 chamber, in wliich the intensity of the image formed by the lens 

 is compared with a standard light, by nienn^ of an ordinary 

 Bunsen's photometer E, sliding on a graduated bar. 



Mr. Dallmeyer kindly had the lens made for the author : he 

 can therefore rely upon the accuracy of its curvature and 

 thickness ; it is plano-con\ex, the convex side being towards the 

 source of light. The curvature is exactly i inch radius, and the 

 thickness is 0*04 inch ; it is made of Chance's hard crown glass, 

 of which the refractive index for the D line in the spectrum is 

 I '5 1 7. The focal length /is therefore I '933 inc'i. 



Let u denote the distance of the source of light from the 

 curved surface of the lens, and v the di-tance of the image of 

 the source B from the posterior focal plane. Neglecting for 



the moment loss by reflection at the surface of the glass, the 

 intensity of the source is reduced by the factor (-^) . But 



"/ 



hence the factor of reduction is 



» -f; 



The effect of absorption in so small a thickness of 



very pure glass may be neglected ; but the reflection at the 

 surfaces will cause a loss of S'3 per cent, which must be allowed 

 for. This percentage is calculated from Fresnel's formulce, 

 which are certainly accurate for glasses of moderate refrangibility, 

 and for moderate angles of incidence. 



Suppose, for example, it is required to measure a light of 8,000 

 candles ; if it be placed at a distance of 40 inches it will be 

 reduced in the ratio 467 to I, and becomes a conveniently 

 measurable quantity. IJy transmitting throUL-h coloured glasses 

 both the light from an electric lamp and that from the standard, 

 a rough comparison may be made of the red or green in the 

 electric light with the red or green in the standard. 



A dispersive photometer, in which a lens is used in a some- 

 what similar manner, is described in Stevenson's " Lighthouse 

 Illumination." Messrs. Ayrton and Perry described a dispersive 

 photometer with a concave lens at the meeting of the Physical 

 Society on December 13, 1S79 (Proc. of the Physical Society, 

 vol. iii. p. 1S4). The convex lens possesses however an obvious 

 advantage in having a real f jcus, at which a diaphragm to cut 

 off stray light may be placed. 



Efficiency of the Electric Arc. — To define the electrical con- 

 dition of an electric arc, two quantities must be stated : the 

 current passing, and the difference of electric potential at the 

 ends of the two carbons. Instead of either one of these, we 



., , . 1 ii •■ difference of potential , 



may, if we please, state the ratio , and 



current 

 call it the resistance of the arc, that is to say, the resistance 



Fig. s- 



which would replace the arc without changing the current. But 

 such a use of the term electric resistance is unscientific ; for 

 Ohm's law, on which the definition of electric resistance rests, is 

 quite untrue of the electric arc ; and, on the other hand, for a 

 given material of the electrodes, a given distance between them, 

 and a given atmospheric pre^sure, the difference of potential on 

 the two sides of the arc is approximately constant. The product 

 of the difference of potential and the current is of course equal 

 to the work developed in the arc ; and this, divided by the work 

 expended in driving the machine, may be considered as the 

 efficiency of the whole combination. It is a very easy matter to 

 measure these quantities. The difference of potential on the 

 two sides of the arc may be measured by the method given by 

 the author in his previous paper, by an electrometer, or in other 

 ways. The current may be measured by an Obach's galvano- 

 meter, by a suitable electro-dynamometer, or best of all, in the 

 author's opinion, by passing the whole current, on its way to the 

 arc, through a very small known resistance, which may be 

 regarded as a shunt for a galvanometer of very high resistance, 

 or to the circuit of which a very high resistance has been added. 

 It appears that with the ordinary carbons and at ordinary 

 atmospheric pressure no arc can exist with a les difference of 

 potential than a'lont 20 volts ; and that in ordmary work, with 

 an arc about \ inch long, the d fference of potential is from 30 

 to 50 volts. As-uming the former result, about 20 volts, for the 

 difierence of potentiaf, the use of the curve of electromotive 

 forces maybe illustrated by determining the lowest speed at 

 which a Tiven machine can run, and yet be capable of producing 

 a short arc. Taking o as the origin of co-ordinates. Fig. 5, set 

 off upon the axis of ordinates the distance o A equal to 20 volts ; 

 draw A B to intersect at B the negative prolongation of the axis 



