152 



KNOWLEDGE. 



[July 1, 1899. 



s full recognition of the possibilities and limitations of 

 metabiosis may have. At present we can scarcely claim 

 to do more than stand on the threshold of the new study. 

 Up to now the aim of the bacteriologist has been chiefly 

 to isolate single kinds of bacteria, and by cultivating them 

 in a pure state to study each species by itself, ascertaining 

 its exact nature and its power of work ; but in the future 

 he will find this is only the preliminary to the more com- 

 plicated study of combination, and he will have his most 

 fascinating work in combining, adding, and subtracting, in 

 endless variation, diilerent species of bacteria in the same 

 medium, and thus get an infinite number of independent 

 results. Here is a simple example of a combination that 

 has been artificially brought about. 



A certain bacterium has been found to have the power 

 of fermenting starch into glucose, and a certain yeast, it 

 has been ascertained, can change glucose into alcohol. 

 Now by putting together pure cultures of this particular 

 bacterium and of this particular yeast into starch, alcohol 

 can be obtained as a result of their joint eiJorts. This 

 simple illustration of the power of combination merely 

 points the way to others of greater import which may be 

 arranged in the future, and, in fact, in judicious blending 

 and combining probably lies the greatest development of 

 bacteriology in the near future. 



The ripening of the curd in cheesemaking is now shown 

 to be the work of bacteria whose home is in the milk, and 

 this is proved by the fact that if the milk is sterilised prior 

 to cheesemaking no proper cheese can be produced, as the 

 curd never ripens. But no single bacterium is responsible 

 for the whole result, rather several species are involved, 

 «ach contributing part, and part only, of the whole work, 

 and living almost certainly in metabiotic relationships. 

 .'For example, in certain investigations made by Dr. 

 Weigmann in this matter, he found in several instances 

 that tyo different forms of bacteria were present, and that 

 a characteristic smell and taste accompanied their develop- 

 ment ; but when these two forms of bacteria were isolated 

 and cultivated separately, neither was able alone to give 

 the specific taste and smell, and not until the companion- 

 ship was restored was the original result attained. 



So, too, in buttermaking. It is bacteria again who are 

 responsible for turning the cream sour and who bring 

 about the changes in its constitution which give aroma 

 and flavour to the butter. Dr. Weigmann, in his observa- 

 tions at Kiel, discovered that no culture of single species 

 alone could give a good taste with stability when intro- 

 duced into cream. Perfection of flavour with " keeping" 

 properties were invariably the result of a blending together 

 of several forms of these germs, and that if artificial 

 souring was to be successful, a knowledge of judicious 

 .blending was absolutely necessary. This implies nothing 

 more nor less than metabiotic relationships between the 

 diflferent kinds of the bacteria concerned. These instances 

 are sufiicient to indicate, at any rate, the vital importance 

 of metabiosis in our study of the lives and works of the 

 •innumerable species of bacteria, and the great stress that 

 ;must be laid on a right comprehension of this relationship 

 :in all future considerations in this direction. 



DISTRIBUTION OF STARS IN SPACE. 



By Gavin J. Burns, b.sc. 



IS the stellar universe infinite ? As the power of the 

 telescope is augmented, do we penetrate further and 

 further into infinite space, ever encountering fresh 

 systems of stars '? Or do the stars ultimately come 

 to an end leaving unfathomable and unknowable 

 space beyond ? These are questions which the study of 



sidereal astronomy forces on our attention, and which we 

 cannot help seeking to answer however unanswerable they 

 may be. 



But although we may be unable to give a definite 

 answer, yet we may obtain evidence as to the most 

 probable hypothesis. A study of the distribution of stars 

 of different magnitudes leads to results as to distribution 

 in space of stars of different intrinsic brightness. Let us 

 begin by supposing that stars of every grade of intrinsic 

 brightness are scattered indifi'erently throughout all space. 

 As there is no possible reason for supposing that stars of 

 any one intrinsic brightness occupy one portion of the 

 stellar universe rather than another, this is antecedently 

 the most probable hypothesis of stellar distribution. Now 

 consider the appearance which such a universe would 

 present to an observer placed at any point in it. Let 

 us, in the first place, confine our attention to stars of 

 some given intrinsic brightness. Let .c be the distance 

 at which such a star appears to be of the first magnitude. 

 Then, if 2-512 be the light ratio of two successive magni- 

 tudes, a star of equal intrinsic brightness will appear of 

 the second magnitude at the distance ('2 5liT.» = 1-585 .r; 

 of the third magnitude at the distance (1-585)-' .r; and of 

 the nth magnitude at the distance (1-585)" 'j;. Next, 

 imagine a series of spheres of the radii x, 1-585 x, 

 (l-585)=,v, (1-585) .(■, (1-585)" 'a-. Then the first sphere 

 will contain all the stars of the first magnitude and 

 over, the second sphere all the stars of the second 

 magnitude and over, and the wth sphere all the stars 

 of the wth magnitude and over. Since the content 

 of a sphere is as the cube of the radius, it follows 

 that the number of stars in each successive sphere 

 will be as the numbers 1, (l•585)^ (1-585)", (l-585)», 

 etc., or nearly as the series, 1, 4, 16, 61, 256, etc. 

 In the second place, let us take the stars of some 

 other given intrinsic brightness, and let y be distance 

 at which such a star appears of the first magnitude. 

 Then imagine a series of spheres of radii y, l-585y, 

 (l-585)-y,...(l-585)'"j/. As before, each successive sphere 

 wiU contain all the stars which appear to be of each 

 successive magnitude or over, and which are of the order 

 of brightness under consideration. The number of stars 

 in each sphere will also be as the series 1, 4, IG, 

 64, 256, etc. Precisely the same reasoning will hold 

 good of stars of any other order of intrinsic brightness. 

 The final result is that the number of stars of each 

 magnitude and over will form a series proportional 

 to the series 1, 4, 16, 64, 256, etc., provided only that 

 stars of each grade of intrinsic brightness are scattered 

 indifi'erently throughout space. This result is quite inde- 

 pendent of the relative numbers of stars of each grade 

 of brightness. 



It appears, further, that if the number of stars of 

 the first magnitude and over is represented by 1, the 

 number of stars of the second magnitude and under 

 the first is represented by 4 — 1 = 3, of the third 

 magnitude and under the second by 16 — 4 = 12, and 

 so on, the series being 1, 3, 12, 48, 192. Further, 

 the number of stars between the « and » — 1 magnitude 

 will always be three times the total number of stars over 

 the M — 1 magnitude. Let us compare these results with 

 observation. 



The following table, showing the number of stars of 

 each magnitude in the northern hemisphere, is given on 

 the authority of Mr. Plummer.* The table is derived from 

 the data in Argelander's Durchmiisterung : — 



* Monthly Notices, XXXVII., p. 436. Tlie numbers in the last 

 column hare been added by myself. 



