124 



NA TURE 



[December 9, 1897 



each other, but, quite contrary to this theory, actually 

 recede from the sun at regular intervals, is as yet an 

 unexplained problem. In works on astronomy, however, 

 the fact is generally glossed over, and it is made to 

 appear as if the recessions were most satisfactorily 

 accounted for. But on closer examination the supposed 

 explanation turns out to be either mere rhetoric or a 

 series of equations of abstract mathematical problems. 

 Why, if sun and planets constantly attract each other 

 proportionally to their quantities of matter, and inversely 

 proportionally to the square of the distance, do they not 

 fall into each other and all into the sun ? The question 

 is a perfectly legitimate one, seeing that every writer on 

 astronomy has deemed it necessary to offer explanations. 

 But these explanations are far from satisfactory, as we 

 shall now endeavour to show." 



And so they proceed ultimately to arrive at the con- 

 clusion that, 



"while there is no doubt that the curvilinear motion of 

 terrestrial bodies is due to the joint action of two forces, 

 viz. the impelling force and the attraction of the earth, 

 there is no evidence either direct or indirect that 

 planetary motions are due to two such independent 

 forces." 



The ridiculous ideas capable of being formed by men 

 of so-called education concerning the meaning and 

 function of mathematical reasoning is illustrated on page 

 353, where it is said first that Newton's achievement was 

 not what is usually supposed : 



"Newton, however, has done nothing of the kind; 

 nor has he even attempted to do so. What Newton 

 did prove was the proposition that ' A body [acted on] 

 by two forces conjoined will describe the diagonal of a 

 parallelogram in the same time as it would describe the 

 sides, by those two forces apart.' It is the truth of this 

 mathematical proposition that Newton proved, and not 

 that planetary motions are actually due to two such 

 forces." 



And then it is added : 



"Abstract mathematical formulae can never prove a 

 fact in nature." All that mathematics can do may be 

 illustrated by the case of a man sent to market with 

 eighteenpence, who returns with sixpence, then on the 

 hypothesis that he spent the difference on a dozen apples, 

 mathematics enables us to calculate the price of each 

 apple ; or, given the price, it can find the number of 

 apples bought. 



Criticism of this sort is gravely printed. It appears 

 to be literally true that many men, including a few 

 schoolmasters, believe mathematics to be represented by 

 schoolboy studies, and especially by "problems leading 

 to simple equations with one unknown quantity." 



In Section A, at Toronto, recently, Lord Kelvin 

 implied, en passant, that a schoolboy in the very first 

 month of his algebraical studies came across some- 

 thing which when developed led into the heart of the 

 mathematical arcana ; viz. when he came across the 

 imaginary roots of a quadratic equation. No wonder 

 that in Lord Kelvin's perspective quadratic equations 

 are relegated in imagination to something like the first 

 month of a boy's mathematical study ; but, alas, many of 

 us know boys of sixteen who have been for years at what 

 schoolmasters call mathematics, and who have hardly 

 yet arrived at quadratic equations. In the perspective of 

 many a British school, trigonometry forms a sort of goal, 

 and the elements of the differential calculus loom dim 

 NO. 1467, VOL. 57] 



and gigantic in the far future. When feebleness of the 

 kind quoted by the authors is believed to represent any- 

 thing like mathematics, no wonder that practical men 

 and others regard it with aversion thinly veiled by 

 contempt. 



But not only is mathematical reasoning lightly re- 

 garded by our authors, they differ from most of their 

 species in treating experiment also in a slight and un- 

 substantial manner, which though by no means intended 

 for disrespect really amounts to it. A number of ex- 

 periments are quoted, some of them made apparently by 

 the authors themselves, which if they were true would 

 constitute some of the greatest discoveries of the century; 

 but they are obtained in the most casual manner, as if, 

 like the scientific hero of many novels, the authors had 

 only to retire into a back room for about twenty minutes, 

 in order to make the most momentous and fame-bringing 

 discovery. We quote two instances. 



" By heating a body it is made to weigh less : that is, 

 not merely is its specific gravity lowered, but its absolute 

 weight is less, and it regains its former weight on 

 cooling " (p. 380). 



" Our explanation of this is that, though cool to touch, 

 the molecules are still in a state of excitation, and hence 

 their lesser weight" (p. 383). 



"Another experiment was made as follows. A glass 

 tube sealed at one end was contracted in the middle. In 

 the lower portion were placed about 10 c.c. of water, and 

 in the upper portion a stick of dry potassium hydrate of 

 about an equal weight, and the tube was sealed. After 

 cooling, the tube was weighed and then turned upside 

 down, so that the water could flow on to the potassium 

 hydrate. The stick of potassium hydrate partially dis- 

 solved, and the solution crystallised. On weighing it 

 was found to be lighter by about 20 mgr. On shaking 

 the glass the crystals partially redissolved, and the tube 

 became heavier ; but after some time the crystals re- 

 formed, and the tube weighed again less" (p. 384). 



On pp. 397 and 401 we are told that inside the crust 

 of the earth there is a neutral sphere or zone outside 

 which bodies press inwards, but within which they press 

 outwards, so that gravity at a certain depth in the earth 

 is inverted and bodies press upward. So this naturally 

 explains volcanoes, — in fact the earth, if cooled, might 

 explode like a Rupert's drop (p. 402). 



Matter from the interior, if it ever got above the 

 neutral zone, would be found to be light instead of heavy, 

 and hence it is that the dust of Krakatoa took so long 

 to settle (pp. 400 and 407) ! 



After this we can be surprised at nothing, and so we 

 go on to learn : — 



That the axial revolution of the earth is due to the 

 radiation of the sun, like the motion of a radiometer or 

 of a sunflower. 



That the real diameter of the earth's orb is 506,734, 

 and not 8000, miles. 



That by reason of its axial rotation the earth rolls on 

 its own orb, pressing against the zone of neutral attrac- 

 tion, and thus effecting its annual journey round the sun 

 like a coach-wheel. 



That the sunspots are circumsolar planets with 

 satellites, their apparently irregular shape being an 

 easily explained optical illusion. 



That the terrestrial seasons are caused by unequal 

 solar attractions ; and other extraordinary nonsense. 



