142 



SCIENCE. 



[Vol. XXI. No 528 



to slight errnis in the original determination. Dr. O. J. Broch 

 (International Co:n mrtee tt Weights and Measures. Annales de 

 Chimie et Physique, tome X., February, 1887) remarks that the 

 centimetre employed in fixing the dimensions of the original 

 kilogram of water would appear to have been -^^-^^ longer than 

 the present standards. The freedom from air was also a point 

 which was not regarded at that period. 



Weight of Distilled Water, Free from Air, Weighed against Brass 

 Weights, Bar am. SO Inch. 



"Water increases in volume from its maximum density aUabout 

 4° C. (or 39.2° F.) to that at 1GJ° C. in the ratio of I to 1.001120 

 (log. 0.0004863). At the same time its density or speciScgravity 

 diminishes in the same ratio, or as 1 to .998881 (log. 1.9995137) . 

 These figures are taken from government reports. The true 

 maximum density is said to be at 3.945° C, but 4° C. is the ac- 

 cepted standard." 



5. The "Note on the capacity of the litre'' at p. 103 of Mr. 

 Clark's book is: — 



" The relation between the British and Metric measures of 

 capacity depends on the value which we assign to the litre. 



"This value may be obtained as follows. Thelitreis the volume 

 of one kilogram of water at 4" C. in vacuo. If we suppose the 

 litre of water to be raised in temperature to 62° F. , its weight 

 will not change, but its volume will have expanded to 1.00112 

 litres (Chaney, Proc. Roy. Soc, No. 294, Sept., 1890). If 1.00112 

 litres at 62° F. weigh 1 kilogram, or 1.5432.35 grains, then 1 litre 



■will weigh ' — = 15415.08 grains. 



° 1.00113 ^ 



" If -we bring this new litre into the air, and weigh it against 

 brass or bronze vs'eights, it will sustain a further loss of weight, 

 due to the buoyancy of the air. This will amount to 16.491 

 grains, as described below, and the weight of the litre in air at 

 63° F., Bar., 30 in., will then be:— 



15415.08 grains 

 Less loss by weighing in air ' 16.49 



Weight of the litre in London at 63° F., 15398.6 grains 



" The original litre has, therefore, lost 17.25 grains by its expan- 

 sion in volume, and 16.49 grains by the buoyancy of the air act- 

 ing on it and the weights which counterbalance it. Having thus 

 ascertained that the litre of water at 62° F. weighs 15398.6 grains, 

 and the cubic inch 252.386 grains, we easily find that the litre 

 contains 61.0364 cubic inches. 



" The loss of weight in air is thus calculated. Mr. H. J. Chaney, 

 warden of the standards, who has recently re-determined the 

 weight of the cubic inch of water (Chaney, Proc. Roy. Soc, No. 

 294, Sept., 1890), finds that one cubic inch of ordinary air, con- 

 taining an average proportion of moisture and carbonic acid, 

 weighs in London .3077 grains at normal pressure and tempera- 

 ture. 61.0364 cubic inches, therefore, weigh 18.781 grains. The 

 weights, if of bronze, have a specific gravity of 8.4, and if of 

 brass of about 8. Taking a mean density of 8.3 we get 



= 3.29 grains due to the displacement of air by the brass 



weights. Deducting the 2.29 grains from 18.78, the displacement 

 due to the water, we get 16.49 grains, the value used above. 



"It would not be possible to measure tht^ litre or the cubic deci- 

 metre strictly as defined by the French Statutes, for they pre- 

 scribe that the water shall be weighed at 4° C. in measuring ves- 

 sels which are to be correct at 0° C. There is a similar anomaly 

 in the definition of the American gallon." 



6. The values given at p 47 of Mr. Clark's book are: — 



Multiply. Divide. Log. 

 Cube inches into cube decimeters, .016386 61.0270 2.31448 

 " ■ '■ " litres, • .016384 61.04 2.21441 



7. The values given at p. 57 of Mr. Clark's book are: — 



Multiply. Divide. Log. 

 Litres into cube feet, .035332 38.3110 3.54804 



" " inches 61.0364 1.78559 



" cube centimetres, or gram., 1000 3.0000Q 



water at 4° C. 



8. The values given at p. 33 of Mr. Clark's book are : — 



Multiply. Divide. Log. 

 Cube feet into cube metres, .03833 35.3166 3.45303 



" " decimeters, 38.3153 1.45303 



" " litres or kilogs. 28.3110 1.45196 



of water 4° C. 



9. The values given at p. 24 of Mr. Clark's book ai'e: — 



Multiply. Divide. Log. 



Cube decimetres into litres, 1 0.00000 



" " cube feet, .03533 28.3153 3 54798 

 " " " " inches, 61.037 • 1.78552 



10. The values given at p. 61 of Mr. Clark's book are : — 



Multiply. Divide. Log. 

 Cube metres into cube feet, 35.31658 1.. 54798 



" " " " inches, 61037.05 4 78553 



The foregoing quotations, together with Mr. Clark's letter, 

 form a very excellent puzzle-picture, in which, presumably, ihe 

 litre is somewhere to be found. Before, however, I adventure 

 upon the search, let me clear away four small clouds that might 

 otherwise befog the expedition. 



First, Mr. Clark is mistaken in imagining that I had not read 

 his book carefully and that I " confounded the litre with the 

 cube decimetre." No. 1 of the foregoing quotations shows that 

 in my table I specifically drew attention to the distinction be- 

 tween the two measures in question. 



Second, Mr. Clark is mistaken in imagining that, with refer- 

 ence to the values given at p. 47 of his book, I " failed to notice 

 that on this line and the one above it (' into cube decimetres ' ) the 

 two figures aregiven differently, viz., 61.04 and 61.0370." No. I 

 of the foregoing quotations shows that the two figures in ques- 

 tion must have "caught my eye"; for I duly included both of 

 them in my table and took care to show that one referred to the 

 litre and the other to the cube decimetre. 



Third, Mr. Clark is mistaken in imagining that my " article 

 would certainly lead any one to suppose that (he) had given three 

 different values for the litre." Any careful reader of the table 

 (vide quotation No. 1) would see that I cite Mr. Clark as having, 

 given two different values for the litre and a third value for the 

 cube decimetre, which is, in very deed, the case. 



Fourth, quotation No. 2 shows that I took some pains to pre- 

 clude any impression that Mr. Clark's book is not trustworthy. 



Coming now to the main question, let us commence our inves- 

 tigation by summarizing the statements in Mr. Clark's book and 

 letter as to the various measures that all come under the common 

 denomination of " litre." They are as follows: — 



A. — "LITRES" PROPER. 



1. " Litre = 1 cube decimeter, or cube metre, very nearly. 



1000 •' ^ 



The volume of 1 kilogram water at 4° C. . . . It is now under- 

 stood as the volume of 1 kilogram of water, fi-eed from air, at 

 maximum density, and weighed in vacuo" (p. 57). The ac- 

 cepted temperature of maximum density is 4° C. (p. 91). The 

 weight of 1 Kilog. of distilled water, free from air, in vacuo at 

 4° C, is 15483.35 grains (p. 103); and the weight of 1 cubic inch 

 (of 1890) of water under the same condition is 353.839 grains (p. 



1 54S9 ^"^ 

 91). Hence the volume of the standard litre is _ „. =61.036373 



353.839 



cubic inches. 



