An alternating-current instrument might be used to read the current flowing in the output circuit , or this current might be rectified by a valve or metal rectifier and a direct-current instrument employed .sx There are , however , several objections to either course .sx In the first place , with the high amplification used there must be valve-noise currents in the output circuit amounting to a few A , so that if rectifiers are used the current can never be reduced to zero for any setting of the optical wedge ; also any vibration of the instrument will increase this current owing to microphonic effects , so that its minimum value will not be constant .sx Secondly , alternating-current instruments are generally less sensitive than direct-current instruments , and if rectifiers are used they are apt to have approximately square-law characteristics for very small currents , so that they are unsuitable for showing .sx when the current is zero within a few hundredths of a microampere .sx In the actual method used there is mounted on the shaft carrying the sector wheel a commutator which reverses the direction of the current in the output circuit at the right times , thus converting the alternating current into a pulsating unidirectional current which is read on a d.c. microammeter .sx The strength of this current is directly proportional to the difference in intensity between the two beams , and is in one direction if one beam be the stronger and in the other direction if the other beam be the stronger .sx This is most important for quick and accurate setting of the wedge .sx There is one serious disadvantage of using a commutator with an amplifier giving such large amplification as that used here , since , owing to the fact that the output circuit must be either broken or short-circuited at each reversal , a disturbance is set up and in some way which we have not yet been able to ascertain causes the galvanometer to be rather unsteady .sx This makes it difficult to tell when the current is exactly zero unless a very heavily damped galvanometer be used which makes observation slow .sx At the Discussion on Photoelectric Cells , I suggested that .sx if instead of an ordinary commutator , one on the principle shown in figure 4 were used , there would never be any break or short-circuit , and the unsteadiness might be greatly reduced .sx In practice the commutator is made by taking a dynamo commutator with about 50 segments and connecting adjacent segments together by a suitable resistance .sx Two segments at the opposite ends of a diameter are connected to two slip-rings through which the current from the amplifier is led in .sx It has not .sx yet been possible to fit such a commutator to the spectrophotometer , but tests made by Dr Perfect and Mr Thomas at the National Physical Laboratory on photoelectric measurements with an amplifier similar to that used here show that the unsteadiness is much reduced .sx The chief effect of fitting such a commutator to the instrument will be to allow readings to be taken more quickly , while observations made when there is little light available will be materially improved in accuracy , so that measurements may be made when the sun is somewhat lower than the altitudes which at present permit of observations .sx The amount of amplification that can usefully be employed is fixed by the unsteadiness referred to above and the galvanometer which it is convenient to use .sx When the amplification is so great that the pointer becomes markedly unsteady , further amplification is useless .sx We have worked with a microammeter which was somewhat heavily damped , reading 6 A for a full-scale deflection , and with this the four-valve amplifier is all that is wanted .sx Direct measurements show that the current amplification obtained is about 108 .sx Since the intensity of daylight in the region of 3110 u. , where the measurements are made , is very small compared to that in the longer wave-lengths , if a single spectroscope were used the light of longer wave-lengths which was scattered by the lens and prism surfaces would be an appreciable part of that falling on the photoelectric cell .sx For this reason a double spectroscope must be used , so that this scattered light is again dispersed and a negligible amount falls on the cell .sx The general arrangement of the instrument is seen in figure 1 , and the relative positions of the slits and the sector-wheel in figure 2 .sx The radiation passes into the instrument through a window W to the first slit S1 and thence to the first dispersing system D1 .sx Three slits S2 , S3 , S4 isolate three narrow bands at 3110 u. , 3265 u. and 4435 u. ( S4 is for measuring the transparency of the atmosphere for wave-lengths unaffected by ozone as described below) .sx The dispersing system D2 is similar to D1 , and re-combines on slit S5 radiations of the proper wave-lengths which have passed through S2 , S3 and S4 , but disperses radiation of other wave-lengths which may have passed these slits , so that it will not fall on S5 .sx Two narrow optical wedges w of neutral gelatine between quartz plates serve to reduce by an accurately known amount the intensity of the radiation which has passed S. Immediately behind S5 is the sodium photoelectric cell C. The sector-wheel d revolves close to S2 , S3 and S4 and admits light from S2 and S3 alternately ( or from S3 and S4 if required) .sx K is the commutator and M the driving motor .sx 3 .sx THEORETICAL BASIS .sx As was stated before , the instrument was designed to work with either the direct light from the sun , the light from the blue sky overhead or the light from a thinly clouded sky overhead .sx Each of these conditions must be considered separately and for simplicity the following notation will be used throughout :sx x x is the equivalent vertical thickness in cm .sx of the ozone present in the atmosphere reduced to a layer of pure gas at 0 C. and 760 mm .sx of mercury ; .sx a , a a , a the absorption coefficients of ozone per cm .sx of pure gas at 0 C. and 760 mm .sx for the wave-lengths 3110 U. and 3265 Au. ( a = 1.275 , a = 0.122 ) ; .sx I0 , I0 , I0 I0 , I0 , I0 the intensities of the wave-lengths 3110 U. , 3265 U. and 4435 U. as received from the sun on the outside of the atmosphere ; .sx I , I , I I , I , I the intensities of the same wave-lengths as received at the earth's surface ; .sx K K the constant of the optical wedge used for the wave-length 3265 U. ; .sx Z Z the apparent zenith distance of the sun at the place of observation ; .sx C C the zenith distance of the sun at the place where the sun's ray which reaches the observer cuts the ozone layer ; and .sx , , , , the extinction coefficients of the atmosphere due to scattering by pure .sx air and small particles , for the wave-lengths 3110 AU. , 3265 Au. and 4435 AU. respectively .sx ( For average conditions at Oxford = 0.44 , = 0.36 , = 0.11. ) .sx ( a ) Measurements with direct sunlight .sx We have shown that the amount of ozone in the atmosphere is related by the formula .sx to the intensity of direct sunlight received at the earth's surface .sx The value of log , and similarly of log , can be found from a series of observations .sx extending throughout the day , and having different values of sec or sec Z , when the atmospheric conditions are remaining uniform .sx Since log is a linear function of sec , the observed values of log should lie on a straight line when plotted against sec ( see CD , figure 5 ) , and by extrapolation of this line the value of log may be found .sx The value of log is found in a similar way .sx The value of ( - ) will depend on the clearness of the atmosphere , but the variations will generally be small since the wave-lengths have been chosen as near together as other circumstances will permit .sx In our older , photographic measurements this value was assumed to remain constant and it was known that a very small error must result .sx In the new photoelectric instrument log is measured also and since the corresponding wave-lengths are outside the ozone absorption band this allows us to determine ( - ) when we have found the value of log , which we assume to remain constant .sx We can calculate the value of ( - ) from .sx ( - ) if we know how varies with the wave-length .sx Two formulae for this have been proposed .sx Formula ( 1 ) supposes that the scattering may be treated as made up of two parts , one due to particles which are large compared to the wave-length and which therefore scatter all wave-lengths alike , and one due to air molecules and small particles which scatter according to the inverse-fourth power of the wave-length .sx ( 2 ) The second formula divides the scattering into two parts of which one is due to air molecules only and varies as the inverse-fourth power of the wave-length and the other to particles in the air which scatter according to A-1 .sx 27. For our present purpose it does not make any great difference which of these two formulae we use except in the case of very hazy days .sx With regard to changes in the emission from the sun , neither log nor log will remain absolutely constant , but it may be shown that variation in these values will lead to wrong values of ( - ) and ( - ) , but will cause very little error in the amount of ozone deduced .sx ( b ) Measurements using the light from the zenith blue sky .sx All the measurements of the height of the ozone layer indicate that the average height is about 45 to 50 km .sx At these heights the pressure will be about 10- of the surface pressure , and it is evident that , as MM .sx Cabannes and Dufay have pointed out , nearly all the light received from the zenith sky will have been scattered out of the direct solar beam by the atmosphere below the ozone layer except when the sun is very low .sx The absorption by the ozone will therefore be exactly the same as that in the direct solar beam , i.e. proportional to ax sec In this case there is obviously no fixed value corresponding to log in the measurements on direct sunlight .sx It is found , however , that if log for the light from the clear zenith sky be plotted against sec C the points lie on a straight line ( see figure 5 , lines GH and GH ) though the line is naturally different from that for direct sunlight .sx It is easy to calculate from this observed line , GH , and the amount of ozone ( found from observations on direct sunlight ) another line JK , figure 5 , which will also be straight , representing the values of log which would have been obtained from the measurements on the blue zenith sky if there had been no ozone present .sx This line will be the same for all clear days and may be used to determine the amount of ozone according to the .sx formula , where log is the value of log given by the line referred to above for the .sx particular value of sec at the time of observation .sx On days when the sky is hazy the values of log for the zenith sky may be corrected by means of the values of log in the same way as for a cloudy sky ( see below) .sx The light received from the clear zenith sky must be composed of light scattered from the direct solar beam by the atmosphere ( 1 ) below the ozone layer , ( 2 ) within the ozone layer , and ( 3 ) above the ozone layer .sx As indicated above , ( 1 ) may be expected to be predominant when the sun is high , but , as Dr Gtz has recently pointed out , when the sun is low the light of short wave-lengths may be so reduced in passing through the ozone layer and by scattering that ( 2 ) and ( 3 ) become important .sx This seems to be the explanation of the fact that when observations on the clear .sx zenith sky are continued till the sun is nearly setting , it is found that while log decreases at first , it afterwards becomes constant and finally increases again .sx