July 1 8, 1889J 



NATURE 



273 



I have examined some of the stones under the microscope. 

 All have an air-bubble at the centre, and I thought in some I 

 could distinguish a speck of sand or grit as well. The kernel 

 appears to have infinitesimal cracks in the ice, going round the 

 central bubbles in circles. Sometimes these are not spread 

 out all round, but run up to the centre in spokes, widening out 

 as they reach the edge. The dark line between the coatings ap- 

 pears to be composed of small pear-shaped air-bubbles lying with 



1. 



5. 



their narrow end towards the centre, and here and there in the 

 ring are specks of grit or dust. 



In the pear-shaped prominences the minute ice cracks appear 

 to be formed in waving lines. 



In some (Fig. 4), the air-bubbles are formed near the surface 

 round the second or third layer, and are much larger ; in others 

 (Fig. 5), they appear in the kernel instead of the spoke-like 

 formation of cracks. C. D. Holt. 



Sefton Park, Liverpool. 



Use or Abuse of Empirical Formulae, and of 

 Differentiation, by Chemists. 



Prof. Thorpe's review of the work of Mendeleeff suggests 

 to me a question I have several times previously thought of 

 putting, viz. whether chemists are not permitting themselves to 

 be run away with by a smattering of quasi-mathematics and an 

 over-pressing of empirical formula. I do not make the accusa- 

 tion ; I merely put the question as one suggested by an incom- 

 plete and superficial perusal of one or two recent memoirs. 



To make my meaning clear, I will state a few facts, and if 

 they are unnecessarily obvious I shall be glad to find them so. 



Take percentage composition (/), and specific gravity (^) ; 

 J is a function of /, and the question is, whether it is a continu- 

 ous or a discontinuous function. To obtain an answer to this 

 question, the best determinations of s should be plotted on a 

 large scale in terms of /, with the probable limits of inaccuracy 

 laid down, and then the curve should be examined to see 

 whether it possesses, at the points of definite constitution, any 

 kind of discontinuity, whether of slope or curvature. The 

 answer may come out, either that such discontinuity certainly 

 exists, or that it possibly exists, or that, if it exists at all, it must 

 be below a certain specifiable order of magnitude. One of 



these i4the definite kind of statement that can be made, and 

 nothing else. 



In order to assist the eye in forming a judgment, some form 

 of icechanical integrator or differentiator might legitimately be 

 run over the curve, provided due care were taken to avoid the 

 creeping in of errors ; but I doubt whether anything could be 

 certainly delected in the derived curves that ought not to be 

 visible in the original curve itself. 



The process adopted by chemists seems a less satisfactory 

 plan. I speak under correction. They assume some element- 

 ary form of empirical expression for the function, say a quadratic 

 expression with three arbitrary coefficients, and they determine 

 these coefficients to suit three points on the curve, first for one 

 portion and then for another, taking these portions in the stages 

 between one definite constitution and another ; they thus obtain 

 a set of quadratic expressions for s in terms of /, each with a 

 more or less different set of coefficients : in other words, they 

 find bits of parabolas which more or less fit successive portions 

 of the actual curve. They then differentiate each of these, and 



(is 

 plot -^ , and they appear to be struck with the fact that, for 



each portion, these plottings come out precisely rectilinear ; while 

 with the observation that discontinuities exist between successive 

 portions they seem quite pleased. 



They sometimes go on to plot -,, and to deduce fresh support 

 dp' 

 for their facts by means of it.^ 



Now, were it not that eminent persons appear to lend their 

 names to this kind of process, one would be inclined to stigmatize 

 this performance as juggling with experimental results in order 

 to extract from them, under the garb of chemistry, some very 

 rudimentary and commonplace mathematical truths. 



I would not be understood as casting any doubt on the results 

 which may, by ingenious and clear-sighted persons, have been 

 arrived at, even by so questionable a process : I would not be 

 so understood, partly because those results lie out of my pro- 

 vince, partly because the hypothesis of definite constitution for 

 solutions or for alloys seems a very probable one, partly 

 because I have myself plotted the s p curve for dilute ethyl 

 alcohol, and clearly perceive the varieties of slope and 

 curvature detected by Mendeleeff, though the changes are 

 scarcely so sharp and definite at definite points as one might 

 wish them to be in order to support the a prio7-i improbable 

 hypothesis of actual discontinuity. But what I want to assert, 

 perhaps unnecessarily, is, that no juggling with feeble empirical 

 expressions, and no appeal to the mysteries of elementary 

 mathematics, can legitimately make experimental results any 

 more really discontinuous then they themselves are able to 

 declare themselves to be when properly plotted. 



Liverpool, June 29. Oliver J. Lodge. 



CHEMICAL AFFINITY. 



IN the older days, chemists were willing to think that, 

 when they had said of a chemical occurrence, " It is 

 a manifestation of the afitinities of the reacting bodies," 

 they had given a fair explanation of the occurrence. 

 Nowadays, we rather avoid the term affinity. The modern 

 chemist is not comforted by the word as his fathers were. 

 Phrases, he knows, have a way of decoying a man to 

 destruction. But, although he does not use the word 

 afifinity so much, the chemist is more eager than ever to 

 understand the modes of action of affinity. 



Since the latter part of the last century, the prevalent 

 views regarding afifinity have fluctuated between the doc- 

 trines of Bergmann and BerthoUet. Bergmann taught that 

 the causes of chemical action and gravitative attraction are 

 identical ; this cause being manifested, in one case, in an 

 attraction between minute particles, and, in the other 

 case, between comparatively large masses, of bodies. 

 Further, he said that the result of chemical attraction 

 between different kinds of particles is a change of com- 



' Although Prof. Thorpe's review suggested the writing of this letter 

 there is nothing contained in that review which prompts these rernarks. 

 Prof Thorpe does not appear to have fallen into the errors which, in the 

 writings of some chemists, I fancy I detect. 



