October i i, 1906] 



NATURE 



5«5 



him, while away on my holiday, and in a private letter. 

 Dr. Pearl's paper. He has now seen fit, although I twice 

 asked him to wait for a full answer until my return to 

 Cambridge, to challenge ine to show in the pages of 

 Nau're how iny advice was applicable to that paper. I 

 must leave your readers to judge how far I have succeeded 

 in so doing. 



The task has been far from an agreeable one. I should 

 never have thought of singling Dr. Pearl's paper out for 

 public criticism in this manner had I not been challenged 

 10 do so. I can only say that if he feels himself aggrieved 

 .It the result, he can be in no doubt whom ho has to 

 Ihank. .1. J. I-ISTF.R. 



Si. John's College, Cambridge, October i. 



Radium and Geology. 



In the Proceedings of the Royal Society for May and 

 \ugust there appeared important papers by the Hon. 

 K. J. Strutt upon radium in the earth's crust and the 

 earth's internal heat. Taking known values of the heat 

 production of radium, per gram per second, assuming 

 Lord Kelvin's estimate of the conductivity of rocks in situ 

 and Prestwich's estiinate of the temperature gradient at the 

 -urface, Mr. Strutt shows that, if the gradient expresses the 

 .lulHow of heat due to radium in the earth, the radium 

 niusr be confined to a comparatively thin crust, because 

 hi> laboratory experiments prove that the smallest radium 

 content existing in the rocks examined would give a much 

 higher gradient than the one observed if the radium were 

 di>tributed throughout the entire earth. 



In the present connection the crust must be defined by 

 the depth beyond which no heat is caused by radium. In 

 these circunistances, if we adopt a certain temperature 

 gradient at the surface, there is only one value of the 

 radium content which will correspond to any assumed 

 thickness of the crust, and there will also be one corre- 

 sponding temperature at the bottom of the crust and 

 throughout the interior. I have calculated these at intervals 

 of five miles, both for Prestwich's estimate of the gradient, 

 viz. i" F. for 42-2 feet descent, and also for the more 

 commonlv accepted one of 1° !•". for 60 feet. 



Gradient 1° 



in 42-2 Feet. 



577x1 



5-I3XI 



15.57 



F. in 60 Feet. 



go6 

 1277 

 1589 

 19CX3 

 221 1 

 2464 

 2834 



lemperatu 

 at botiom i 

 crust, Cen 



363 

 484 

 606 

 727 

 848 

 969 

 1090 



676 

 894 

 1 112 



1S47 

 1725 

 1984 



From the above tables it appears that the radium con- 

 tents corresponding to such values as are usually assigned 

 to the thickness of the earth's crust bv geologists and 

 seismologists are well within the amounts contained In the 



rocks examined by .Mr. Strutt, and that consequently the 

 surface gradient can be fairly accounted for by the theory. 

 But we have also some indication of internal temperature 

 from volcanic products. Prof. Iiartoli found the tempera- 

 ture of lava issuing from F.tna to be lotio" C. If this 

 caine up from beneath the crust it would correspond to a 

 thickness of from thirty to forty miles, according to the 

 rate of increase which we attribute to the gradient. .So 

 far all seems favourable to the theory. 



.Since any reasonable assumption for the mean radium 

 content of the crust would supply suflicient heat to inain- 

 tain the observed gradient, it follows that no heat can 

 pass up from the interior, because, if it did, the gradient 

 would be higher than it is. The conclusion would be that 

 the earth is not a cooling body, and it is consequently 

 reduced to a state of thermal .stability. 



Thus a fundainenlal belief of geologists is shattered at 

 a blow. Sir .\. Gcikie writes in his chapter on dynamical 

 geology that " it is useful to carry in inind the conception 

 of a globe still intensely hot within, radiating heat into 

 space, and consequently contracting in bulk." . . ."Wide 

 geographical areas htp upraised or depressed." These 

 changes of level are constantly going on, such as have 

 been described by Prof. Hull and Dr. Spencer, and the 

 recency of these movements show's that, if they are due 

 to a cooling globe, that process is still in progress, and the 

 primeval heat not vet exhausted. Although there ma)' be 

 differences of view as to the exact mode of its operation, 

 yet it is not too much to assert that there is a consensus 

 of opinion among geologists that the movements of the 

 crust are chiefly attributable to the ultimate cause so con- 

 cisely expressed by Sir A. Geikie. 



It seems clear that one or other of these views concern- 

 ing the internal heat of the earth must yield. They cannot 

 both be correct ; and if the radium theory is to hold the 

 field, how are the movcinents of the earth's crust to be 

 accounted for? O. Fisher. 



Graveley, Huntingdon, September 28. 



If the internal heat of the earth is mainly due to the 

 radium present therein, must we not assume that the same 

 is the case with the moon? If such were the case, then 

 the internal heat of the latter would be far greater than 

 we have hitherto supposed, and it would be difficult to 

 explain the lack of volcanic activity there. 



The age of our satellite is not sufficient for us to assume 

 that all the radiutn is dead or that none is being produced. 



B. J. P.^LMER. 



Technical Schools, Southend, October 4. 



Vectors, &c., at the British Association. 



In' the report t.\ugust jo) of the discussion on the use 

 and notation of vector analysis at the British .Association 

 it is stated that I " deplored the substitution of vectors 

 for quaternions." The statement is misleading, for was it 

 not Hamilton more than any other single man who taught 

 us how to use vectors in product and quotient combin- 

 ations? What I did and do deplore is the substitution of 

 non-quaternionic vector algebras in all their variety of 

 notation for the Hamiltonian or quatcrnionic vector algebra 

 — a very different thing. 



I should like to add that (notation excepted) I was 

 thoroughly in sympathy with all that Prof. Henrici said 

 in opening the discussion. He showed admirably the con- 

 ciseness of vector methods in attacking both geometrical 

 and physical probleins, and so far as he went in the 

 limited time at his disposal there was absolutely nothing 

 to choose between his mode of presentation and that which 

 Hamilton himself might have adopted in the same situ- 

 ation. In his reply at the end of the discussion he pointed 

 out that the quaternion, 0.9 a quantily, could be got quite 

 easily from his system by taking the difference of his 

 vector and scalar products. That, of course, is self- 

 evident, but it does not seem to me to touch the real 

 issue. It leaves his system still non-associative in vector 

 products, and in higher applications, especially with the 

 differential operator V. this intruduces ditlieullies which 



NO. 1928, VOL. 74] 



