478 



NA TURE 



[February i8, 1909 



SOCIETIES AND ACADEMIES. 

 London. 

 Royal Society, December 10, igo8. — "The E\lension of 

 Cracks in an Isotropic Material." By A. Mallock, 

 F.R.S. 



Any specified strain in a solid can be represented as a 

 combination of shear and volume extension or compression, 

 and both for volume extension and shear there are limits 

 which if exceeded cither cause rupture or leave the material 

 in an altered condition when the stress is removed. 



There is, however, no known limit of rupture for the 

 volume compression of solids.' 



It would be a matter of interest and importance to 

 determine for solids whether, and how far, the existence 

 of one form of strain influenced the limits of the other, 

 whether, for instance, a body subjected to volume extension 

 would require more or less shear to rupture it than when 

 the volume was normal. 



This point has not, so far as the author knows, been 

 made the subject of experiment, but for the purpose of 

 this note it is assumed that if a strain which exceeds cither 

 of the limits is applied to a solid, rupture will be due to 

 that property of the substance for which the limit is least, 

 and that if the distortion limit is the smaller of the two, 

 breakage will occur at right angles to the lines of greatest 

 extension, whereas if the volume limit is the least the 

 direction of the brcaic will be indeterminate. 



If the conditions of strain at the end of the crack arc 

 such that material gives way from over-distortion, the 

 fracture will occur in the plane of the existing crack, which 

 will therefore spread continuously, while if the over- 

 dilatation is the origin the breakage may take place in any 

 direction. If at any place the plane of the new fracture 

 cuts the plane of the crack there will be a rc-arrangement 

 of stresses, and a relatively considerable length of material 

 will have to be strained before further rupture is possible, 

 and thus the cross-fractures will act as a bar to the further 

 extension of the crack. 



It is concluded, therefore, that in materials such as 

 glass or other substances in which cracks spread in nearly 

 constant directions rupture is due to the distortion limit, 

 and that where a crack extends with difficulty in a 

 wandering manner the dilatation limit is the one which has 

 been e.xceeded. 



The rapid alteration of the direction in which fracture 

 takes place may give rise to the fibrous appearance which 

 often shows itself on broken surfaces in such cases. 



When the limits for both /i and k are reached at nearly 

 the same time, a very small change in either, such as 

 might occur in a body nearly, but not quite, homogeneous, 

 would alter altogether the appearance of a fracture. 



In this note only isotropic materials are considered, but 

 it seems probable that the same principles might be used 

 lo explain the cleavage of crystals. 



Challenger Society. Januarv 27. — Sir John Murray in 

 the chair. — Notes on the breeding habits and development 

 of Littorina litiorca : W. M. Tattersall. On changing 

 the water in the aquarium for fresh sea-water, copulation 

 of the periwinkles was readily induced. The eggs arc de- 

 posited in small capsules shaped like a panama hat, and 

 are not attached, which accounts for their not having 

 been recorded hitherto. Of the four British species of 

 Littorina. littorca is exposed only at low spring tides, and 

 is freed as a trochosphere, later becoming a veliger : 

 nbtusata is generally exposed at ordinary low water, and 

 is freed as a veliger : riidis is exposed during the greater 

 part of the day, and is viviparous ; neritoides lives between 

 the high water of springs and neaps, and is also viviparous. 

 Both in habitat and life-history these four seem to re- 

 present stages in adaptation to a land existence. — British 

 Oithonfc : G. P. Farran. It was pointed out that they 

 are four in number, and inhabit, respectively, waters of 

 'ow salinity, ordinary coastal waters, oceanic waters 

 bordering on the coast.i! area, and ourelv oceanic waters. 

 Structural modifications accompanv the increase in salinity 

 1 This may give an explanation of the difference between malleability and 

 duclility._ Under the hammer the strain Is a shear combined with volume 

 compression, while in " drawing " the material undergoes shear romhined 

 ion. In general, a body which is ductile will also be 

 d net hold. 



of the different habitats. — The four species of Polychelcs 

 from the N.E. .Atlantic : S. \V. Kemp. Notes on their 

 habits and on the structure of the vestigial eye. 



Zoological Society, February 2. — Mr. K. tiillcU, vice- 

 pri sident, in the chair. — Christmas Island : Dr. C. \V. 

 Andrews, .\ttention was directed to the differences in the 

 fauna associated with influx of population. — Preliminary 

 account of the life-history of the leaf-insect, Phyllium 

 cnirifolium, Serville : H. S. Leigh. The leaf-insects occur 

 in the tropical regions of the Old World, and seem partial 

 to insular life. The eggs, which resemble the seeds of 

 certain plants to a remarkable degree, require to be kept 

 in a constantly warm and moist atmosphere to enable 

 them to hatch ; they hatch very irregularly, and the period 

 of incubation often extends over three or four months. 

 When young the larvae are active as compared with oldf- 

 individuals. The metamorphosis is incomplete, and the 

 adult form is attained by a gradual increase in size ; fully 

 developed tegmina and wings only appear in the adult con- 

 dition. The adult females are large and leaf-like in 

 appearance, but the males are much smaller, and not 

 foliaceous. — The mammals of Matabeleland : E. C. Chubb. 

 — Pathological observations at the society's gardens during 

 1908 : Dr. H. <i. Plimmer. 



Linnean Soci-tv. Febiu ay 4. — Dr. A. S.. 1 b w. ,..).. aril, 

 F.R..S., vice-president, in the chair. — Fkcus spiralis, Linne, 

 or Fucus platycarpus, Thuret ; a question of nomenclature: 

 Dr. Borgesen. The purport of the paper was to show 

 that recent statements by Prof. Sauvageau as to the 

 validity of the name Fucus spiralis, Linn., are not sup- 

 ported by the history of the plant, nor by specimens in 

 the Linnean herbariuin. — Observations on the cBConomy of 

 the Ichneumon manifcstator, Marsham (nee Linn.) : an 

 historical note ; C. Morley. The writer referred to the 

 account given in 1794 by a former secretary of the society, 

 Thomas Marsham, of an insect observed in Hyde Park. 

 Mr. Cockayne found recently in the same place a specimen 

 of Ephialles extensor, Tasch., a Continental species not 

 hitherto noticed in Britain ; the paper concludes by pointing 

 out the similarity of the two occurrences, and the difliculty 

 of clearing up the synonymy. — The Polyzoa of Madeira : 

 Rev. Canon Norman. For more than forty years the late 

 Mr. J. Yate Jolmson was residing at Madeira, and 

 diligently studied both its flora and fauna. He especially 

 devoted himself to the marine fauna, and the Polyzoa did 

 not escape him. From time to time he submitted th'^ 

 species which he found for determination by naturalist- 

 who specially worked at this class — first lo Prof. Busk 

 after his death to Rev. Thomas Hincks, and subsequentlv 

 to Mr. Waiors. The total number of species found hv 

 him was 52 ; the present paper contains 130. Previous 

 writers on the Polyzoa of Madeira have been unable tc 

 give particulars as to the circumstances (habitat, depth, 

 &-C.) at which the various species lived. These particulars 

 the author supplies as regards most of the species previously 

 known as Madeiran. With respect to the additions now 

 made, there are some species new to science ; others 

 previously known in the Mediterranean ; others which have 

 been recently described from the Prince of Monaco's dredg- 

 ings, and two species the occurrence of which is certainly 

 interesting. 



Royal Anthropological Institute, February 9 —Prof. W. 



Ridgewny. pnsid, nt, in the ihair. — Dene-holes : Rev. 

 J. W. Hayes. It was held that these excavations were 

 merely chalk wills or chambers from which chalk was 

 taken for builders' mortar or for manure for the fields. 

 The author did not contest that all the dene-holes were 

 modern ; some may well have been dug in Saxon or even 

 in Roman times, but others were certainly not more than 

 100 years old, and some were dug within the last quarter 

 of a century. Evidence was adduced to show that even at 

 the present day the farmers in some parts of the country, 

 Hertfordshire, for example, still get chalk for the '-tnd 

 from similar pits. The use of chalk for building was 

 j enlarged upon, and the author was able to show that the 

 Chislehurst caves were nothing more than an old chalk 

 mine, the so-called altars, or steps, being merely platforms 

 left purposely to enable the workmen to reach the roof of 

 the cavern. The author was also able lo show that where 



NO. 2051, VOL. 79] 



