June 4. 1908J 



NA TURE 



1 1 



the surrounding membrane. If T be constant or sym- 

 metrical about the axis of the body, the body is 

 symmetrical. But the abnormal eggs that a hen some- 

 times lays, cylindrical, annulated, or quite irregular, are 

 due to local weakening of the membrane, in other words, 

 to asymmetry of T. Not only asymmetry of T, but also 

 asymmetry of p „, will render the body subject to deforma- 

 tion, and this factor, the unknown but regularly varying, 

 largely radial, pressure applied by successive annuli of the 

 oviduct, is the essential cause of the form, and variations 

 of form, of the egg. In fact, in so far as the postulates 

 correspond near enough to actualities, the above equation 

 is the equation of all eggs in the universe. At least this 



T T' 



is so if we generalise it in the form /"+ ,+5;— P 



in recognition of a possible difference between the principal 

 tensions. 



(9) In the case of the spherical egg it is obvious that />„ 

 is everywhere equal. The simplest case is where p„=o, in 

 other words, where the egg is so small as practically to 

 escape deforming pressure from the tube. But we may 

 also conceive the tube to be so thin-walled and extensible 

 as to press with practically equal force upon all parts of 

 the contained sphere. 



(10) If while our egg be in process of conformation the 

 envelope be free at any part from external pressure (that 

 is to say, if p„ = o), then it is obvious that that part (if 

 of circular section) will be a portion of a sphere. This is 

 not unlikely to be the case actually or approximately at 

 one or both poles of the egg, and is evidently the case 

 over a considerable portion of the anterior end of the 

 plover's egg. 



(11) In the case of the conical egg with spherical ends, 

 as is more or less the case in the plover's and the guille- 

 mot's, then at either end of the egg r and r' are identical, 

 and they are greater at the blunt anterior end than at the 

 other. If we may assume that p„ vanishes at the poles 

 of the egg, then it is plain that T varies in the neighbour- 

 hood of these poles, and, further, that the tension T is 

 greatest at and near the small end of the egg. It is here, 

 in short, that the egg is most likely to be irregularly dis- 

 torted or even to burst, and it is here that we most 

 commonly find irregularities of shape in abnormal eggs. 



(12) If one portion of the envelope were to become prac- 

 tically stiff before p ceases to vary, that would be tanta- 

 mount to a sudden variation of T, and would introduce 

 asymmetry by the imposition of a boundary condition in 

 addition to the above equation. 



(13) Within the egg lies the yolk, and the egg is in- 

 variably spherical or very nearly so, whatever be the 

 form of the entire egg. The reason is simple, and lies in 

 the fact that the yolk is itself enclosed in another mem- 

 brane, between which and the outer membrane lies a 

 fluid the presence of which makes p„ for the inner mem- 

 brane practically constant. The smallness of friction is 

 indicated by the well-known fact that the " germinal spot " 

 on the surface of the yolk is always found uppermost, 

 however we may place and wherever we may open the 

 egg ; that is to say, the yolk easily rotates within the egg, 

 bringing its lighter pole uppermost. So, owing to this 

 lack of friction in the outer fluid, or white, whatever shear 

 is produced within the egg will not be easily transmitted 

 to the yolk, and, moreover, owing to the same fluidity, the 

 egg will easily recover its normal sphericitv after the egg- 

 shell is formed and the unequal pressure relieved. 



GEODETIC INVESTIGATIONS IN THE 

 UNITED STATES.^ 

 'T'HE report of the U.S. Coast and Geodetic Survey for 

 1907 has just been received. For the details of the 

 extensive cartographic work of the bureau in the United 

 States proper, Alaska, Porto Rico, and the Philippines, as 

 well as for the account of the progress of the primary 

 triangulation and levelling of precision, the report itself 

 must be consulted. Certain important work of the survev 

 receives bare mention, as, for instance, the results of the 



1 " Report oCthe Superintendent of the Coast and Geodetic Survey show- 

 ing the Pr-^gre^s of the Work from July i, igo6, to June 30, 1907." 

 (Washington : fJovernment Printing Office, 1907.) 



NO. 20I4j vol. 781 



investigation of the earth's figure, based on geodetic 

 operations in the United States. This is owing to the 

 fact that these results were communicated to the Inter- 

 national Geodetic Association in a preliminary report 

 which has been published. 



Soon after the California earthquake of April iS, 1906, 

 it became evident that the permanent horizontal displace- 

 ments of large areas covered by triangulation in California 

 had so changed the lengths and directions of the lines 

 joining the triangulation stations as greatly to diiuinish 

 the value of the triangulation for its primary purpose as 

 a framework for future surveys. During the year, there- 

 fore, new triangulation extending from Point Arena to 

 stations south of Monterey Bay was done, which serves 

 to restore the value of the old triangulation by determin- 

 ing the new positions of sixty-one of the old triangula- 

 tion stations. The triangulation included the Farallon 

 Lighthouse, twenty-two miles to the westward of the great 

 fault accompanying the earthquake, and the stations 

 Mocho and Mount Diablo, thirty-three miles to the east- 

 ward of the fault. The new triangulation serves to trace 

 the permanent distortions and displacements of the earth's 

 crust for many miles back from the fault in eacli direc- 

 tion, and to show that they follow certain regular laws. 

 This is the most extensive and accurate determination by 

 triangulation of the effects of an earthquake which has 

 yet been made anywhere in the world. Appendix 3 of 

 the report gives a full report of this investigation. 



A report on the measurement of six primary bases with 

 steel and invar tapes in 1906 is printed as .Appendix 4. 

 The invar (nickel steel) tapes have a coefficient of ex- 

 pansion about i/2Sth that of steel tapes, hence it is much 

 less difficult to keep the temperature errors within the 

 required limit with invar tapes than with steel tapes. 

 Invar tapes had not been used in the United States until 

 1906 in primary base measurements. The thorough tests 

 of these tapes, made by Hsing them on six bases in con- 

 junction with the steel tapes formerly used, showed that 

 measurements may be made more conveniently, accurately, 

 and at smaller cost per mile than with the steel tapes, and 

 that the invar tapes are sufficiently durable and stable for 

 safe field use. This demonstration is believed to be a 

 distinct step in advance in base measurement. 



The steady progress in the magnetic survey of the United 

 Stales, and accumulation of magnetic observational data, 

 as mentioned in Appendix 5 of the report, should be of 

 special interest to the surveyor and the navigator, as well 

 as to those pursuing the study of the science of terrestrial 

 magnetism. Throughout the year the measurements of 

 the earth's magnetism were made at places distributed 

 over a majority of the States and territories of the United 

 .States, and at numerous places at sea along the Atlantic 

 and Pacific coasts of North and South America, and in 

 Porto Rico and the Philippines. Important information 

 was secured in the equatorial regions. Numerous 

 " repeat " observations were made throughout the country 

 in order to follow as closely as possible the secular change 

 in the magnetic elements. Five magnetic observatories 

 were maintained in continuous operation, and important 

 seismological data were also obtained. The facilities of 

 the observatories were afforded to all investigators who 

 desired to make standardisation coinparisons of their 

 instruments, and in response to numerous requests in- 

 formation or observational data was furnished for prac- 

 tical application or for use in special investigations of 

 terrestrial magnetism and allied phenomena. 



.Appendix No. 6, constituting the concluding portion of 

 a manual of tides, treats of the flow of water, of river 

 tides, tidal currents, permanent currents, annual inequality, 

 lake tides, seiches, and miscellaneous tidal matters. 

 Charts of co-current lines are given for the principal 

 marginal waters along the .Atlantic coast of the L'nited 

 States. The numbers upon these lines sho'w the titnes of 

 the inaximum flood current. The dependence of the per- 

 manent ocean currents and the annual height inequality 

 upon the prevailing winds is briefly pointed out. Seiches 

 are shown to exist in harbours and other tongues of 

 water, as well as in lakes, but their character is funda- 

 mentally different in some respects. The analyses of 

 observations upon the tides of Lake Superior show that 

 they follow closely the equilibrium theory, allhoiigh the 



