April 15, 1886] 



NATURE 



573 



(if circles which have analogous relations to three circles, as the 

 circum- circle, the inscribed, and nine-points circle of a triangle 

 have to the straight lines forming the triangle. 



The rest of Part I. is taken up with a discussion of equations 

 expressed in terms of power-co-ordinates. The " power-co- 

 ordinates " of a point are defined as any multiples of its powers 

 with respect to a system of four circles which have not got a 

 common orthogonal circle. 



The equation of the first degree represents a circle, or straight 

 line ; and the equation of the second degree a bicircular quartic, 

 or circular cubic, and these curves are discussed in some detail. 



Part II. contains merely the extension of the results of Part I. 

 to spherical geometry ; the power of two circles on a sphere is 

 defined to be tan r tan r cos w, where r, r' are their radii, a> their 

 an;^Ie of intersection : the power of a small circle, radius r, and 

 a great circle is defined as tan r cos w, and tlie power of two 

 great circles as cos m. 



The fundamental theorem is as before 



1^6, 7, 8, 9, loj - °' 



connecting the powers of the systems of circles. 



Consequently the results obtained previously are extended 

 with but slight modification. 



In Part III. the method of Part I. is applied to spheres ; it is 

 pr ived at once that the powers of two systems of spheres must 

 satisfy the relation 



/I, 2, 3, 4, s, 6\ _ 

 '^(,7,8.9, 10, II, 12; -°' 



where any of the spheres may be replaced by planes, or the plane 

 at infinity. 



The discussion of the equation of the first degree in power- 

 co-ordinates is much the same as that in Part I. The equation 

 of the second degree represents a cyclide of the fourth or third 

 order, but the reduction of the equation to its simplest form is 

 more complicated than in the case of bicircular quartics. It is 

 shown that there are four distinct canonical forms, each of 

 wh'ch includes several species of surfaces. The different species 

 are then discussed in detail. 



March 25. — ^'* Remarks on the Cloaca and on the Copulatory 

 Org.ans of the Amniota. " By Dr. Hans Gadow. Communi- 

 caied by Prof. M Foster, Sec.R.S. 



The first portion of this communication contains an account 

 of the sphincter and copulatory muscles, the derivation of which 

 from skeletal and from visceral muscles is foUowe 1 up in the 

 Sauropsida and Mammalia, partly aided by the study of the 

 nerve-supply. 



Then follows an extensive description of the modifications of 

 the cloaca of the chief groups of the Amniota. Ilatteria comes 

 nearest the Amphibia. Chelonia represent a type intermediate 

 between that of the Ostriches and Crocodiles, and that of the 

 Monotremes, from which again a continuity of stages up to the 

 highest Placentalia can be traced. 



The anal sacs of the Chelonia are discussed with reference to 

 experiments on their being able to take in water. The peri- 

 toneal canals of Crocodiles and Tortoises are still functional, but 

 in Hatteria they are rudimentary. Muellerian ducts are present 

 in the males and Wolffian ducts in the females of young Croco- 

 diles. Space will not permit to mention mo) e than the following 

 of the general conclusions drawn regarding the phylogenetic 

 development and the homologies of the various organs treated in 

 this paper. 



The whole cloaca of the Amniota consists originally, either 

 permanently or in the embryo only, of three successive chambers, 

 which m.ay be distinguished as follows : — 



I. The Proctodajum (termed thus by Prof. Lankester). It is 

 the outermost anal chamber of epiblastic ori;Tin. With its deri- 

 vatives : (i) bursa Fabricii in birds ; (2) various hedonic glands 

 in most Amniota ; (3) the copulatory organs, the at least partly 

 epiblastic nature of which is indicated by the frequently deve- 

 loped horny armament of the glans, by the various sebaceous 

 glands, and, as shown in this paper, by its development. 



II. The UrodsEum, from olipov and 5a/w. Hy]5oblastic. This 

 is the middle chamber or primitive cloaca, into which open the 

 urinogenital ducts, and through which pass the fxces. With its 

 differentiations: (i) urinary bladder, ventral; (2) anal sacs in 

 Tortoises, dorsal. 



III. The Coprodaaum, from KiJirpo; and Sa((u. This is the 

 innermost cloacal chamber. 



The Urodfeum is the oldest portion of the whole cloaca, then 

 follows the Proctodfeum, and, lastly, the Coproda;um has 

 secondarily assumed cloacal functions. 



The various modifications of these three chambers, their func- 

 tion, and the gradual separation of faaces, urine, and genital 

 products have been discussed in the third chapter. 



We can derive the types of the intromittent organs and of the 

 cloaca of the Amniota from conditions which are still represented 

 by the Gymnophiona and by Ilatteria, viz. from the walls of the 

 Proctotla.nim in connection with a certain uro-proctodceal fold. 

 Then Lizards and Snakes followed one line leading to the deve- 

 lopment of paired organs, whilst the other Amniota modified 

 the same substratum into another, unpaired, ventral form. The 

 Carinatoe show a degeneration in this respect. 



The extraordinary resemblance of the organs dealt with in 

 this paper to those of the Chelonia and young Crocodiles can 

 hardly be explained by homoplastic coincidence, but strongly 

 favours the phylogenetic relationship of the Mammalia with the 

 Reptiles. This, however, is but one more link in the long 

 chain, which, being anchored in the Triassic Theriomorpha, 

 makes the Amniota more akin to each other than to the 

 Amphibia. 



April I. — "Description of Fossil Remains of Two Species of 

 a Megalanian Genus {Mdohiiiia, Ow.) from Lord Howe's 

 Island." By Sir Richard Owen, K.C.B., F.R.S. 



In a scientific survey by the Department of Mines, New 

 South Wales, of Lord Howe's Island, fossil remains were ob- 

 tained which were transmitted to the British Museum of Natural 

 History, and were confided to the author for determination and 

 description. 



These fossils, referable to the extinct family of horned Sau- 

 rians described in former volumes of the Philosophical Transac- 

 tions (vol cxlix., 1858, p. 43; ib. 1880, p. 1037 ; ib. 1S81, p. 

 1037) under the generic name Megalania, form the subject of 

 the present paper. They represent species smaller in size than 

 MegahDiia prisca, Ow., and with other differential characters on 

 which an allied genus Mciolania is founded. Characters of an 

 almost entire skull with part of the lower jaw-bone, of some 

 vertebrae and parts of the scapula and pelvic arches, are assigned 

 to the species Mciolania platyceps. Portions of a cranium and 

 mandible are referred to a Mciolania minor. Both species, as 

 in Megalania, are edentulous with modifications of the mouth 

 indicative of a horny beak, as in the Chelonian order. The 

 cranial and vertebral characters are, however, sauroid. Horn- 

 cores in three pairs are present, but shorter relatively, especially 

 the first and third pairs, than in Megalania prisca. The indi- 

 cation of a seventh more advanced and medial horn is feeble, 

 and the author remarks that in the small existing lizard (Moloch) 

 this horn has not an osseous support. The tail of Mciolania is 

 long and stiff ; the vertebra; being incased by an osseous sheath, 

 developing, as in Megalania, tuberous processes in two pairs, 

 corresponding with the vertebrae within : such defensive parts 

 are less developed, relatively, than in Megalania prisca. 



The locality of these singular remains is an insular tract not 

 exceeding 6 miles by i mile in extent, situated midway between 

 Sydney and Norfolk IsLind, in lat. 31° 31' S., long. 159" 9' E. 

 The island is formed of three raised basaltic masses connected 

 by low-lying grounds of blown coral-sand formation, consisting 

 of rounded grains and fragments of corals and shells. In the 

 parts of this formation converted into rock were found the 

 petrified remains which are the subject of the present paper. It 

 is accompanied by drawings of the most instructive fossils : 

 these form the subjects of five plates illustrative of the text. 



Mathematical Society, April 8. — Mr. J. W. L. Glaisher, 

 F. R. S., President, in the chair. — The followin,; communica- 

 tions were made : — On the number of linearly independent 

 invariants (or seminvariants), reciprocants, or in general of 

 integrals of any assigned type of a homogeneous and isobaric 

 linear partial differential equation, by Prof Sylvester, F.R.S. — 

 On some results connected with the theory of reciprocants, by C. 

 Leudesdorf.— The President (Mr. Walker, F.R.S., in the 

 chair) gave an account of the work he has been for some time 

 engaged upon in connection with elliptic functions, the special 

 points he drew attention to being the use of the twelve 

 elliptic functions, and of twelve zeta and twelve theta 

 functions. The two latter systems of functions depend upon 

 the quantities E, G, I, where C — E - k'K .and I = E - K. 

 — Mr. A. B. Kempe, F.R.S., communicated a note on an 

 extension of ordinaiy algebra differing from the latter in the 

 substitution of three arbitrary quantities 2, /, and «, for the 



