July 1, 1899.] 



KNOWLEDGE. 



153 



Ratio to total 



It will be observed that there is no striking 

 deviation from the theoretical ratio, except 

 in the case of stars of the 9-0 to 9'5 magnitude, 

 where the actual ratio is three and a halt 

 times the theoretical amount for a half mag- 

 nitude. 



For comparison with the above I have con- 

 structed, from the data contained in Uranometria 

 Oxoniensh, the following table, which contains 

 the stars in the northern hemisphere down to 

 the sixth magnitude ; — 



Eatio to total 

 of preceding stars. 



2-35 

 2-33 

 2-14 

 2-12 



The above table shows that, so far as the 

 sixth magnitude, the stars are really much 

 more regularly distributed than appears from 

 the Durchmustemwj, and suggests that the 

 irregularities from the sixth to the ninth 

 magnitude are due to errors in the estimation of 

 magnitude. 



Another question that arises is whether the stars of 

 various magnitudes are scattered indiscriminately in the 

 sky, or whether bright and faint stars are aggregated 

 in definite localities. In order to test this point, I have 

 made an enumeration of all the stars in the Durchmusterumj 

 lying between 1' N. and 1° S. declination, with the 

 following result : — 



Magnitude. 



1-0 to 1-9 



2-0 to 2-9 

 3-0 to 8-9 

 4-0 to 4-9 

 5-0 to 5-9 

 0-0 to 6-9 

 7-0 to 7-9 

 8-0 to 8-9 

 9-0to9'5 



It will be seen that, while the actual proportion of the 

 stars of each magnitude varies considerably from that in 

 the whole hemisphere, there is a similar marked increase 

 in the number of stars below the 8th magnitude. 



The accompanying diagram (Fig. 1) represents an ideal 

 section through the stellar universe, showing how stars of 

 equal intrinsic brightness would have to be distributed in 

 order to appear as they are shown in the above table. 

 When we look through a telescope, the stars included in 

 the iield of view actually lie in a cone, having the eye at 

 the apex, and the volume of the cone is as the cube of the 

 distance to which the telescope penetrates. Now, in this 

 diagram, the stars within the cone are plotted on a plane 

 sector, the area of which is as the square of the distance 

 from the centre. The distance of a star has been assumed 



to be inversely as the square root of the apparent bright- 

 ness. Hence, in order that the distribution, as shown on 

 the plane surface, may truly represent to the eye the 

 assumed distribution in space, the number of stars of 



11I.\-V 



Section through the Stellar Universe. 



each magnitude has been multiplied by a co-efficient. 

 Further, the stars here dealt with, viz., those within one 

 degree of the equator, were divided into groups, each 

 occupying thirty minutes of right ascension, and each 

 group plotted in its proper sector. The following table, 

 showing the calculation for one group, will explain the 

 process : — 



A similar calculation was gone through for each thirty 

 minutes of E.A., except that stars under the sixth 

 magnitude were taken together, on account of their small 

 number. The numbers in the last line are those shown on 

 the diagram. 



A glance at the figure shows the general character of 

 stellar distribution in the plane of the equator. The dis- 

 tribution is approximately uniform towards the centre, 

 with a marked increase of density towards the circum- 

 ference, which becomes emphasised where the equinoctial 

 plane crosses the Milky Way. 



The increased number of stars below the eighth mag- 

 nitude is very remarkable if it is fact ; but this depends 

 entirely on Argelander's magnitudes being photometrically 

 correct. There is, in fact, reason to beUeve that thS' 

 magnitudes of the fainter stars are over-rated. An 

 examination of the first six hours of zone — 0° showed that 



