May 17, 1888] 



NATURE 



55 



These relations are derived from the equation W = M>, the 

 source of all confusion in Dynamic--, and it is gratifying to find 

 from Prof. Mendenhall that a crusade against it is in progress in 

 America. 



It is needless to repeat here the objections against this 

 equation, but it is easy to see how it arose. 



Mathematicians now measure mass in pounds, so that the mass 

 of a body is the number of pounds of matter in the body {the 

 fit in the vernacular) ; and the equation W = Mg means that 

 the weight of M pounds is Mg poundals, according to their 

 definition that "the weight of a body is the force with which it 

 is attracted by the earth " ; but this was not so originally. 



Early writers on Dynamics, before Gauss invented the absolute 

 unit of force, always employed the statical gravitational unit, 

 and then if a weight of W pounds was acted on by a force of 



P pounds, the equation of linear motion was — P. 



g dt' 



W 

 To avoid the necessity of writing and printing — , it was 



g 

 replaced by the letter M, and called the mass ; the unit of mass 

 being thus ^pounds. But now the invariable quantity, the mas<=, 

 is measured in terms of a variable unit, while the variable unit 

 of force is the attraction of the earth on a 1 -pound weight. 



Although such words as "a force equal to the weight of the 

 mass of 10 pound weights" do not occur in Prof. MacGregor's 

 book, they are strictly derived from his own definitions ; and so 

 is the following, " the weight of 32 pound weights on the Earth 

 is at the surface of Jupiter a force of 71 pounds' weight." I 

 bring forward these illustrations to show that the fine distinction 

 between " 10 pound weights " and " 10 pounds' weight " is not 

 workable ; and to show that the addition of the word weight to 

 pounds does not convey the idea of force in ordinary language, 

 and is not clear even in the language of the precisionists. 



Nor can the equation p — gpz in Hydrostatics be defended, as 

 capable of expressing a pressure in pounds on the square foot 

 (or more commonly on the square inch) ; for, if Prof. MacGregor 

 applies this equation to a numerical example, he will find himself 

 dividing by^in one operation, only to multiply by g in the next. 

 The unreal character of these changes of units is apparent when 

 we come to numerical examples ; the defect of our dynamical 

 teaching is that the student is so rarely brought before a practical 

 numerical illustration on a large scale. 



The rest of Prof. MacGregor's remarks I must answer very 

 briefly, for fear of occupying too much space. 



The kilometre was designed to be the centesimal minute of 

 latitude, to replace the geographical or sea mile, which is the 

 sexagesimal minute of latitude ; the quadrant of the earth is there- 

 fore 10,000 kilometres, or io 9 centimetres, and 90 x 60 = 5400 

 geographical or sea miles. 



The cosmopolitan unit of speed at sea is the knot, which is a 

 velocity of one geographical mile an hour ; if 10 knots, spaced 

 about 50 feet apart, pass over the taffrail in half a minute, the 

 vessel is said to be going 10 kno'.s. All civilized nations 

 measure speed at sea in knots, in French nozuds, German knoten, 

 Dutch knoopen, Italian nodi, Spanish nudos, Sec. In precision 

 knots an hour is on a par with atmospheres per square inch. 



It is unfortunate that we have not yet reached uniformity in 

 the use of the words elongation and extension. The French 

 treatises, and our practical writers, Rankine, Unwin, &c, use 

 tension and extension, pressure and compression, to denote 

 simple longitudinal stresses and their corresponding strains ; the 

 ratio of tension to extension, or of pressure to compression, being 

 the modulus of elasticity. This variation in terminology must be 

 settled by some arbitrator, say Prof. Karl Pearson. 



In conclusion, speaking on behalf of engineers and practical 

 men, I beg to say that the treatment of the subjects of weight, 

 mass, and force, in our ordinary text-books of Mechanics is by 

 no means clear or satisfactory, and requires careful revision. 



Woolwich, May 4. A. G. Greenhill. 



Density and Specific Gravity. 



If Mr. Cumming's definition of specific gravity be accepted, 

 the confusion, already serious enough, in the minds of beginners 

 in physics between mass and weight will be much increased. 

 Surely the best and clearest definitions of density and specific 

 gravity are those given in Glazebrook and Shaw's " Practical 

 Physics," p. 105. These make density a quantity having dimen- 

 sions in mass and space, and specific gravity a pure number. 

 There are many advantages in defining specific gravi'y as a ratio 



and not the least among them is that the numbers in tables of 

 specific gravities are independent of any system of units, while 

 in a table of quantities having dimensions the numbers given 

 depend on the system of units used. Thus the density of platinum 

 would have to be given in an English table as 134375 pounds, 

 or in a metrical table as 21 '5 grammes. Again we should lose 

 the very useful analogies between the definitions of density and 

 thermal capacity and specific gravity and specific heat, to which 

 I drew attention in a letter to Nature, vol. xxxiii. p. 391. 



Prof. Carey Foster seems to think it would be useful to 

 have a table telling us the force with which unit volume of any 

 body is attracted towards the earth, and that this should be 

 called a table of absolute specific gravities. But I fail to see 

 any advantage in this, for it is adding a totally new definition to 

 be remembered, and one which would certainly create con- 

 fusion in a beginner's mind ; and the objection applies to this, that 

 the numbers given would depend on the system of units used, to 

 say nothing of the value of gravity at the place for which the 

 table was calculated. Supposing even that the latter were 

 ignored, it is not more troublesome to convert, with the aid ol 

 the known weight of unit volume of water, the specific gravity 

 of any material into the weight of a given volume of it, than to 

 convert a number given in one system of units into the numbe - ' 

 representing it in the system we may happen to be using. 



If we are to take Mr. Cumming's definition as he expresses it, 

 I would submit that a pound avoirdupois is a quantity of matter 

 and not a force ; and to say that the specific gravity of water is 

 62 - 5 pounds avoirdupois is simply taking the density of water 

 and calling it specific gravity. Pace Mr. Greenhill and the 

 engineers, it is hard enough to eradicate the notion that the 

 quantity of stuff in a body and the force with which it is pulled 

 towards the earth are one and the same without having the task 

 made more difficult by our definitions. 



50 City Road, E.C. Harry M. Elder. 



The Cornish Blown Sands. 



In the description of the raised sea beach at Newquay, which 

 Sir Henry De la Beche has given in his " Survey of Devon and 

 Cornwall," he makes no reference to a curious feature observable 

 in a part of the beach, and to which I should like to direct 

 attention, with a view to obtaining some explanation of the cause 

 of its formation. As far as I know, the appearance is only to 

 be found at one spot, on what is known as Little Fistrel, to the 

 westward of the town. It consists of a number of cylinders of 

 indurated sand, separated from each other by thin walls, often 

 only an inch or two thick, and forming the base of the cliff or 

 bank, which is perhaps 10 or 15 feet high at the place. These 

 cylinders rest upon a bed of rock (argillaceous slate ?), which runs 

 down from the bottom of the bink to the sea in a series of 

 shelving ledges. The cylinders, which are locally known a> 

 Pixie Holes, weather out from the bank, but unfortunately few or 

 none of them are now to be seen in a perfect state, their walls 

 having been broken down by people scrambling up the bank, and 

 also by quarrying operations, which I learn have recently been 

 carried on close by. I am told that formerly the cylinders were 

 very perfect, and often of large size ; I myself have seen them, 

 fifteen or sixteen years ago, standing up like little towers along the 

 base of the cliff, and I have often sheltered myself perfectly from 

 a shower of rain by standing in one and covering myself with my 

 umbrella. I have recently had a photograph taken of the best 

 group to be found, and a copy of this, together with a piece of 

 the wall of one of the cylinders, is with Mr. Goodchild, of the 

 Geological Survey, Jermyn Street, who will show it to anyone 

 interested in the matter ; the size of one of the cylinders 

 photographed is 5 1 inches deep and 28i inches in diameter. 

 1 R. H. Curtis. 



[The sand in question is well known to geologists as an 

 example of blown sand agglutinated into a compact stone by car- 

 bonate of lime derived from the solution of calcareous organisms, 

 which here on the surface consist largely of land-snails. The 

 tubular cavities are no doubt due to the removal of the calcareous 

 cement by percolating water, and are thus of the same nature as 

 the pot-holes in chalk, and the cavernous holes and tunnels in 

 hard limestone. — Ed.] 



Self-induction in Iron Conductors. 

 Mr. Sumpner quotes (Nature, May 10, p. 30), in support of 

 the idea that iron conductors may have less self-induction than 

 copper ones of the same dimensions, a suggestion of mine that 



