176 



NATURE 



[June 25, 1903 



LETTERS TO THE EDITOR. 



\7"/ie Editor does not hold himself responsible for opinions 

 expressed by his correspondents. Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 ■manuscripts intended for this or any other part of Nature. 

 No notice is taken of anonymous communications .] 



FcEtal or New-born Giraffes Wanted. 

 Will you give me the opportunity of making a request 

 through your columns to museum curators and African 

 sportsmen? I am especially anxious to obtain for study, 

 preserved in spirit or dry, the head (not the prepared skull) 

 of a new-born giraffe or of a late foetal individual in which 

 the boney ossicusps of the horns are already formed. I 

 should be able to return the specimen after examination to 

 the owner if desired. I should be glad to examine several 

 such heads were it possible to procure them. All expenses 

 of transport would be paid by me. I venture to ask those 

 who can help me to communicate with me without delay. 



E. Ray Lankester. 

 Natural History Museum, Cromwell Road, London, 

 June 23. 



Seismometry and Geite. 

 Before making a few comments on Prof. Milne's secona 

 letter under the above title (Nature, June 12, p. 127), I 

 should like to express my warm appreciation of his devotion 

 to seismological research, and the great impetus it has 

 given to observational work. In pure seismology — apart 

 from applications of elastic solids to earth problems — 

 Prof. Milne's reading is doubtless more extensive than 

 mine, but if he is correct in regarding my first letter as 

 containing nothing new to seismologists, they must, as a 

 class, be singularly prone to a policy of meliora scio 

 deteriora sequor. Novelty in results is, of course, much a 

 matter of opinion. When Prof. Milne says, however, that 

 there is no occasion for my warning as to Young's modulus, 

 I must in reply give a quotation from his first letter, re- 

 lating to the material of his hypothetical core, " it 

 follows that the density ... is 596, or approximately 6. 

 The elastic modulus for a core of this density which con- 

 veys vibrations with a speed of at least 9Skm. per second 

 is 451X10^° C.G.S., or roughly speaking, a little more than 

 twice the Young's modulus for Bessemer steel." The 

 italics are mine. If " the modulus " is not Young's 

 modulus, E, a comparison between it and the E for steel is 

 misleading, because a comparison of numerical results 

 naturally implies that they refer to the same physical 

 quantity. On this view the statement is doubly mislead- 

 ing, because there are two wave moduli, viz. m+n and n. 

 If, as one would infer from Prof. Milne's second letter, 

 *' the " modulus was intended for the wave modulus m + n, 

 the futility of the comparison becomes obvious when we 

 remember that on the ordinary theory (m-fn)/E may have 

 any value between i and 00, according to the value of 

 Poisson's ratio. As a matter of fact, "the" modulus 

 must, I think, have been intended at the time for Young's, 

 though this must have escaped Prof. Milne's memory. If 

 it were meant for m + n, we should have (4514-5-96)* " at 

 least " 95, whereas it is really only 87. If, however, we 

 multiply 451x10" by 6/5 — which would be correct if 

 451X10"' were a Young's modulus in a material where 

 Poisson's ratio had the uniconstant value 025 — and sub- 

 stitute this, we deduce a wave velocity of 9-53km. per 

 second. 



Prof. Milne seems to have misunderstood my treatment 

 of the two wave velocities in the Phil. Mag. (March, 1897, 

 p. 199), and as it bears directly on the question at issue, I 

 should like to make it clear. In previous papers I had 

 ■advanced a variety of considerations- pointing to the con- 

 clusion that, whilst all applications of elastic equations to 

 the earth are more or less speculative, the mathematical 

 and physical difficulties are enormously reduced when we 

 suppose that the deep-seated material — about which we 

 have no direct information — is nearly incompressible, i.e. 

 has a Poisson's ratio approaching 05. Such a hypothesis, 

 for one thing, rendered it unnecessary to assign to the 

 rigidity and Young's modulus values largely in excess of 

 anything yet encountered at the earth's surface. There 

 remained, however, the fact of the high velocities observed 

 in the more rapid earthquake waves, which had been gener- 



NO. 1756, VOL. 68] 



ally supposed to imply enormously large Young's modul 

 such, for instance, as the value 45x10" given by Proi 

 Milne. The problem stood as follows : — 



In an infinite isotropic elastic medium there are neces- 

 sarily two wave velocities. If we know them both we can 

 deduce all the elastic properties of the medium, provided 

 we know the density ; if we do not know the density, wi- 

 can still deduce Poisson's ratio. If the medium is not 

 infinite, but is bounded by a plane surface, then, as shown 

 by Lord Rayleigh, there is a special type of surface wave the 

 velocity of which, especially when the material is nearly in- 

 compressible, approaches closely to that of the slower or 

 rigidity body wave natural to the material. If the bound- 

 ing surface be not plane, but spherical or spheroidal, thfi - 

 is doubtless a wave answering to the Rayleigh wav 

 which within moderate distances of its origin may 1 

 expected very closely to resemble the Rayleigh wave in typi-, 

 when the depth to which it penetrates and the wave-length 

 are both very small compared to the central radius. If the 

 medium have a Poisson's ratio of 025, the velocities of th<> 

 two body waves must be in the ratio of ■s/3(or 1-73) : i. 



In the earth there seems distinct evidence of only two 

 types of waves. For the more rapid, supposing them to 

 travel straight through. Prof. Milne himself would 

 apparently take lokm. as the most probable value at depths 

 below the immediate heterogeneous crust. It was important 

 for my object not to understate this veloc;jty, and I took 

 the somewhat higher figure of i2-5km. The second type— 

 which Prof. Milne terms the " large " waves — travel much 

 slower. If they go straight through, their velocity is less, 

 of course, than if they travel along the surface. On the 

 former hypothesis. Prof. Milne might make them a trifle 

 slower than the value I took, viz. 2-5km. per second. If, 

 instead of 12-5 and 2-5, we took 10 and 2, we should obtain, 

 of course, the same value of Poisson's ratio as before, 

 0-48 approximately, with a value for E somewhat less even 

 than the very moderate value (about 10x10" C.G.S.) 

 obtained in my paper. If we took 10 and 2-5, or even 10 

 and 3, for the two velocities, we should get 047 and 045 

 for the values of Poisson's ratio. 



The uncertainty as to whether the " large " waves were 

 body waves or surface waves — or, as I thought more likely, 

 a combination of the two — was not overlooked, as Prof. 

 Milne's letter might suggest, but was dwelt on at some 

 length in the paper. If they are entirely surface waves, the 

 heterogeneous nature of the earth's crust, and the irregu- 

 larities of mountain and ocean, are such as to introduce 

 extreme uncertainty into any mathematical calculations. 

 In this event it is doubtful whether any conclusion can be 

 drawn either for or against the hypothesis of great in- 

 compressibility in the core ; its explanation of the high 

 velocity in the faster waves would, however, be unaffected. 

 The discussion of magnetograph results by Prof. Milne 

 in the B.A. Reports for 1898 and 1899 (1888 is surely a 

 misprint) was familiar to me as a contributor of data, but 

 it did not seem to render my letter unnecessary. I suspect, 

 however, that I partly misunderstood Prof. Milne's letter 

 on this part of the subject, as I did not fully realise that 

 he did not recognise the distinction between anomalous and 

 merely high values of the horizontal force H. The fact 

 that H is nearly twice as large at Batavia or Bombay as 

 at Kew is natural, owing to their proximity to the mag- 

 netic equator. Whether the values at these stations are 

 higher or lower than one would expect from their geo- 

 graphical position cannot be said with certainty until the 

 completion of magnetic surveys. What my letter suggested 

 was the advantage for critical purposes of records at a 

 station where there is known to be a true large magnetic 

 anomaly— e.^. in N.E. Ireland or the Scottish Highlands. 

 Variations in the value of g are, relatively considered, 

 trifling compared to those in H, and the larger gravitational 

 anomalies present systematic features to wj^ich there seems 

 no parallel in magnetics (c.f. Bourgeois' discussion of g 

 in the " Rapports pr^sent^s au Congr^s International de 

 Physique," Tome iii., Paris, 1900). Apart from the ques- 

 tion of the unit, I am a little puzzled by Prof. Milne's 

 gravitational data for Kew, and I should warn him that 

 there, as at some other stations, the agreement between 

 different observers at different times has not been such as 

 to warrant much reliance in any one observer's value for 

 g — y {i.e. gravity observed less calculated). C. Chree. 



