April 6, 191 1] 



NATURE 



IQ 



(Proc. Ed. Math. Soc., 1909—10) which deserves attention 

 as being a very simple image of hyperbolic geometry in 

 Euclidean space. 



We start by taliing a fixed sphere <r, and define a plane 

 B as a spliere which cuts <s orthogonally, a line as a circle 

 which cuts o" orthogonally, a point as a point-pair inverse 

 with respect to a. All the ordinary projective axioms are 

 satisfied ; the angle between two planes is defined to be 

 the angle, in the ordinary sense, at which the representa- 

 tive spheres intersect. If two planes touch, their point of 

 contact must lie on or ; in this case they are said to be 

 parallel. It is easily proved that through any point (not 

 on 0) two planes can be drawn parallel to a given plane a ; 

 triangles exist with each angle zero, and so on. More- 

 over, it is possible to give a definition of length (as the 

 logarithm of a cross-ratio) which enables us to say that 

 if A, B, C are three coUinear points, AB-(-BC=AC. 



If T shrinks up to a point, the geometry becomes 

 Euclidean, though the elements are not the usual ones. 

 We may, however, abstract from the point S, which is 

 ill'- limiting form of n, and define a point A in the 

 ordinary sense. Then line and plane elements are repre- 

 sented by circles and spheres through S. 



It must be remembered that this theory assumes 



irical aiid other properties of ordinary space, and does 

 pretend to put hyperbolic geometry on an independent 



ting. To do this requires a more detailed discussion, 



i the assumption of a hyperbolic space. In a some- 

 wiiat analogous way we may consider the question of 

 dimensions in space. We have a real four-dimensional 



►metry in ordinary space if we take as our primary 



aent a line or a sphere, and so we may construct 

 j, ometries of any dimension we like. But it is another 

 thing to assume a four-dimensional space where {x, y, z, i) 

 can be taken as, say, rectangular Cartesian coordinates 

 of a point strictly analogous to the corresponding point- 

 eliment in three-dimensional Euclidean space. 



G. B. M. 



w 



MICROBIOLOGY IN NEW SOUTH WALES.^ 

 J HEN we consider that the report referred to below 

 deals with more than thirty-three thousand examina- 

 tions, embracing all kinds of subjects, the difficulty of 

 ,c;Aing any adequate description of the contents will be 

 ajjpreciated. As this report is an introductory one, the 

 plan has been adopted of writing an introduction to each 

 section suitable for non-scientific readers, who may thus 

 Ii able to follow intelligently the matter discussed; for 

 h' \ond conducting routine work, the Bureau has set before 

 itMilf the praiseworthy task of becoming a centre of useful 

 knowledge. But it is further recognised tliat in the direc- 

 tion of research the Bureau will find its largest sphere of 

 usefulness. This is no doubt true, and it is for the official 

 mind to recognise that the man engaged in routine ex- 

 aminations cannot even succeed at this unless he too is 

 sometimes allowed to engage in research. 



To turn to the actual work, we find that tuberculosis 

 ranks first in the numbers of specimens (487) supplied, 

 while typhoid fever ranks second with 214. Perhaps an 

 unnecessarily pessimistic view is taken as" to the prospect 

 of being able to control either the " carriers " or the fly 

 in the case of this disease. At present our study of the 

 house-fly is only commencing, and we think it probable 

 that in urban areas it will prove to be very amenable to 

 control. The formula " no dirt, no flies," would express 

 til" position we should take up. 



It is recorded under the diphtheria examinations that 

 cultures very often do not show diphtheria bacilli in 

 twenty-four, but may do so in forty-eight, hours. But 

 surely one may add the progress of knowledge is slow, 

 for this fact was within the writer's experience twenty 

 years ago when examining cultures in a large hospital. 

 With regard to the protozoa, it is extremely interesting to 

 note that malaria, though prevalent in the northern parts 

 of Australia, occurs only as imported casps in New South 

 Wales, though Anophelines abound there. The unravel- 

 ing of that somewhat puzzling condition, paUidismus sine 

 malaria, still demands attention, and here we have another 



' Report of the Government Bureau of Microbiology for the Year 1909. 

 (Legislative Assembly, New South Wales.) 



NO. 2162, VOL. 86] 



example of it. A large number of new species of bird 

 Plasmodia are recorded, though whether these " species " 

 could be distinguished if it were not known from what 

 birds the blood came is, we think, very doubtful. Several 

 new hsemogregarines are also recorded from snakes and 

 tortoises. Besides these scientifically interesting parasites, 

 th<e(re are several diseases of unknown causation in cattle of 

 economic importance, e.g. endemic hsematuria in cattle, 

 jaundice in lambs, and black disease in sheep, but piro- 

 plasmosis is not recorded. As regards entozoa, those of 

 New South Wales make quite a respectable list, but per- 

 haps by dint of including rarities. Hydatids appear to be 

 the commonest entozoal parasite in Australia, occurring in 

 man, sheep, cattle, and pigs, but rarely in horses. 



A very interesting parasite affecting cattle is a filaria- 

 like worm coiled up in subcutaneous tumours, known as 

 " worm-nests." These have excited considerable interest 

 among health officers in London and Liverpool lately, 

 owing to their occurrence in frozen carcases from 

 .'Australia. They are about the size of a spht walnut, and 

 occur, for the most part, over the brisket. It does not 

 appear to be possible that they can be injurious to man. 

 It should be mentioned, however, that it has been stated 

 by one observer that they are associated with tuberculosis, 

 but this is against the weight of evidence. The sanitarian's 

 scruples may, indeed, be allayed by the evidence we have 

 that, although such carcases are used as food in New 

 South Wales, no injurious results have ever been known 

 to arise therefrom. 



An examination of telephone mouth-pieces (50) failed to 

 detect tubercle or diphtheria bacilli. The examination of 

 milk preservatives leads to the conclusion that to delay 

 manifest change for even twenty-four hours involves the 

 use of medicinal quantities, the long-continued ingestion of 

 which may be injurious. In the milk question, the means 

 of salvation is, we think, clear — prevention is better than 

 cure. Finally, the rabbit problem must be referred to, and 

 the interesting proposal to destroy rabbits by destruction of 

 females and liberation of males is now being tested. 



The director and his colleagues deserve warm com- 

 mendation for the results of their first year of evidently 

 very laborious work which this report chronicles, and which 

 must soon justify itself, not only scientifically, but also 

 economically. 



SCIENCE AND EDUCATION IN THE CIVIL 



SERVICE ESTIMATES. 

 'T'HE Estimates for Civil Services for the year ending. 

 March 31, 1912, together with a memorandum by 

 the Financial Secretary to the Treasury, have been issued 

 as a Parliamentary Paper. The following particulars with 

 reference to the money under this vote to be devoted to 

 science and higher education are taken from this paptvr. 



Under the sum required for Public Works and Build- 

 ings, the Estimate for the Royal Parks and Pleasure 

 Gardens shows an increase of 5725/. on the year, in which 

 provision is made for completing the new laboratory in 

 the Edinburgh Royal Botanic Garden at a further cost of 

 3790Z. Under Surveys of the United Kingdom (which 

 have shown an annual decrease of cost since 1902-3, when 

 the expenditure amounted to 237,130/.), there is a further 

 decrease of 5452'. for the year, the estimated net charge 

 amounting to 187,344/. 



Under the heading Salaries and Expenses of Civil 

 Departments, the Estimate for the Board of Agriculture 

 and Fisheries shows a net increase of 9204I. ; 43,589/. is 

 included in respect of the expenses of a scheme for the 

 Improvement of Light Horse Breeding. The expenditure 

 for this purpose, less a sum of 5000/., will be recouped 

 by a grant from the Development Fund, and the grant 

 of 5100/. hitherto paid to the Royal Commission on 

 Horse Breeding ceases after the year 1910-11. 5000/. of 

 the increase is, therefore, in effect a transfer from this 

 latter Vote. 2250/. is included as grants to local authori- 

 ties in aid of the provision of local insp«>ctors for the 

 purpose of the Destructive Insects and Pests Acts, 1877 

 and 1907, and 1050/. additional is required for the Collec- 

 tion of .Agriculture and Fishery Statistics. 



The Estimate for the Government Chemist appears for 

 the first time as a separate Vote. In previous years the 

 salary of the principal chemist was borne on the Treasury 



