366 



NA TURE 



[February 20, 1908 



litllc 



wilh ascertained fact to be 



would have 

 of much value. 



I will take this opportunity of mentioning an alternative 

 theory, which has the advantage of being amenable to 

 experimental test. If we suppose that the rate of trans- 

 formation of uranium is much diminished by increase of 

 (omperature, the quantity of radium and of all the other 

 products will be diminished too, and with it the general 

 rale of heat production inside the earth. 



The effect of heat on radium and its products has no \ 

 direct bearing on the problem. Everything is governed by 

 the primary slow transformation — that of uranium. 



There is no experimental evidence on this question so 

 far as I am aware. It could probably be best attacked 

 by comparing the ratio of formation of uranium X at 

 various temperatures. The amount of uranium X which 

 had grown in the course of a few days could be deter- 

 mined bv 0-rav measurements, which might be made after 

 cooling. R. J. Strutt. 



Sunnyside, Cambridge, February 13. 



Ground Ice. 



I SEE in your issue of January 30, p. 295, a letter from 

 the Rev. John J. Hanipson asking some questions on the 

 subject of ground ice. I should like to say that my 

 father, the late Prof. James Thomson, read a paper on 

 this subject at the Natural History and Philosophical 

 Society of Belfast on May 7, 1862, and I think his paper 

 answers most of the questions. Thus he writes, after 

 reviewing and setting aside several older theories : — " My 

 own view is that the crystals of ice are frozen from the 

 water at any part of the depth of the stream ; whether 

 the top, the middle, or the bottom, where cold may be 

 introduced, either by contact or radiation ; and that they 

 may also be supplied in part by snow or otherwise : and 

 that they are whirled about in currents and eddies until 

 ihey come in contact with some fixed objects to which 

 they can adhere, and which may perhaps be rocks or 

 stones or may be pieces of ice accidentally jammed in 

 crevices of the rocks or stones : or may be ground ice 

 already grown from such a beginning. 



" That pieces of ice under water have the property of 

 adhering to one another with a continually increasing 

 firmness, and this even when the surrounding water is 

 above the freezing temperature, has been shown in a set 

 of very interesting experiments by Prof. Faraday. T 

 fhinii too that the readv adhesion to the bottom, or to ice 

 already anchored there, may possibly be increased by the 

 effects of radiation, but I am confident that the anchor 

 ice is not formed by crystallisation at the place where it 

 is found adhering." 



This paper has never been printed hi extenso, but 1 

 hope soon to bring it out in a volume of collected papers 

 written by my father. James Titomsox. 



22 Wentworth Place, Npwcastle-on-Tyne, 

 Februarv u. 



The Stresses in Masonry Dams. 



Mr. M.\rtin at first asserted that my reasoning was wrong 

 on some general principle which I failed to grasp, whereas 

 he has now fallen back on the order of the approximation, 

 .ind appeals to what he terms an axiom of practical mathe- 

 matics, which he illustrates by the statement that between 

 o and 17 a parabola can be found " differing but little 

 from sin x." If by the method of least squares a para- 

 bola be fitted to sin x, it will be found to differ by more 

 than 30 per cent, from the ordinate of sin x when .x' = 5°; 

 w-hether that difference is materia! or not depends entirely 

 on what use is to be served by the correspondence. 



In the memoir which has led to this controversy I 

 showed that the equation for the stress function V, i.e. 

 v-v-V=o, was the same for a thin ' slab and an actual 

 dam. Since writing the paper I noticed that the third 

 equation for the stresses was apparently not the same. I 

 now see that this is only in appearance, for the terms 



^ Only thick plates can bs properly used in dam experiments, for thin 

 pl.-xtes buckle an'! require a side support which destroys accuracy of experi- 

 mental result. Even Messrs. Wilson and Gores plates were at the De as 

 thick as they were broad. 



NO. 1999. VOL. 77] 



which have a coefiicient involving different functions 

 Poisson's ratio for the two cases are 



:,+ -., 





and 1 find that this vanishes by means of the differential 

 equation for V. Hence, as 1 stated in my memoir, thin 

 plates can be used to find experimentally the stresses. Mr. 

 Martin is therefore quite correct in his views on this 

 point, although I cannot still agree with his demonstration 

 of the principle. 



There are, however, far more vital criticisms to be made 

 of the meinoirs recently read before the Institution of Civil 

 Engineers than the mere question of whether the stresses 

 in a slab and an indefinitely long dam differ by 10 per 

 cent, or 20 per cent. A very little experimenting will 

 suffice to show that dams when they collapse go by 

 stretching, and partly at points where there may be no 

 tension at all. The strains measured by Messrs. Gore and 

 Wilson are not those in a real dam at all, and if we now 

 accept the view that the stresses are the same, then we 

 must ask Mr. Martin to allow that their stretches differ 

 by 30 per cent, from those in an actual dam. 



It was this point which I endeavoured to bring out in 

 the criticism of the paper to which Mr. Martin has re- 

 ferred. If their strains correspond to those of a real 

 dam, then their stresses differ widely ; if their stresses 

 are correct, then their strains, upon which ultimately 

 rupture depends, will be very different from those of the 

 actual dam. I must leave Mr. Martin to choose his own 

 horn of the dilemma. 



Again, there is another point which is physically very 

 obvious. If a dam, reservoir empty, were split up by a 

 series of vertical divisions parallel to its length, each plate 

 would be of different height, and compressed under its 

 own weight would be subjected to a different squeeze at 

 the base of the dam. To bring these vertical sheets into 

 contact at the correct points it is needful to suppose 

 shear over the vertical planes at the base of the dam. In 

 other words, there must be a distribution of shear over 

 the base of the dam due solely to its own weight. Since 

 the total shear over the base is zero, this distribution of 

 ■ihear, if the extremity of the toes be vertical, must take 

 some such form as is shown in the diagram. Our experi- 





ments at University College showed that this base shear 

 due to the weight of the dam only was as important as, 

 and probably more important than, the distribution of 

 shear due to the water pressure. 



There is no evidence at all that I can see in Sir John 

 W. Ottlev and Dr. Brightmore's recent paper that they 

 have paid attention to this point. They speak of the 

 " original vertical lines on the inodel," and of measuring 

 the displacement of these lines from " vertical lines on the 

 glass." They speak of the return of the verticiil lines on 

 the model to the vertical lines on the glass on the removal 

 of the water pressure. It would appear, therefore, that 

 thcv have only measured the slide due to water pressure. 

 But to deduce the stresses in the dam they must have the 

 total shear, that due to the weight as well as that due 

 to water pressure. I can find no evidence in their paper 

 of any determination of the shear due to the weight of 

 the dam. They sav that the shear along the base is 

 uniformly distributed.' This, as Mr. Pollard and I showed 

 in our memoir of last July, is rougWy, but only roughly. 



k 



