294 



NA TURE 



\yan. 26, 



On some Unapparent Contradictions at the Foundations 

 of Knowledge. 



An argument parallel to that by which Mr. Tolver Preston 

 proposes to prove that Space is nothing will prove with equal 

 cogency that Time is nothing. But if Space is nothing and Titi.e 

 is nothing, then he has the choice of two alternatives, neither of 

 which will he find particularly acceptable. If Space and Time 

 are both nothings, they are identical. If Space and Time are 

 not identical, then they are two nothings which differ. What is 

 the difference between two nothings ? 



I would suggest that Mr. Preston should read Mr. Herbert 

 Spencer's views on "The Relativity of Knowledge," contained 

 in Chapter IV. of "First Principles." On his carefully thinking 

 this out, and understanding it, I am willing to hope that the 

 title I have adopted for this letter may appear to him appropriate 

 to the subject-matter which he has brought under the consideration 

 of your readers. F. Howard Collins. 



Churchfield, Edgbaston. 



Extraordinary Fog in January 1888, at Shirenewton 

 Hall, Chep&tow. 



The recent fog has been so remarkable that it seems desirable 

 to record its principal features. From the 7th to the 14th the 

 air was completely saturated with moisture. The most notable 

 feature was that of cold air passing over a warm ground, for 

 from the nth to the 15th the greatest cold on the grass did not 

 descend to that read at 4 feet. Such a condition of the air as 

 this has not been noticed since I commenced observations in 

 1838. 



The following readings of the thermometers will illustrate 

 this :— 



Throughout the I2th after 9 a.m. the temperature on the 

 grass was above 32°, whilst it was a frost from the height of i 

 foot upwards ; at 10 a.m. the temperature on grass \^as 32° 8, at 

 4 feet 29°"8, and at 10 feet 28° '6. 



The fog lasted from the evening of the 6th till 3 p.m. of the 

 14th. On the 7th the clouds moved rapidly in W. current, and on 

 the 8th they moved rapidly in S.W. current ; on the 9th nearly 

 calm and cloudless overhead ; from the loth to 14th overcast 

 (except from 11 a.m. on the 12th till 12.40 p.m.). The chief 

 direction of the wind was : 8th S.S.W., 9th S.S.E., loth 

 W.S.W., nth and 12th calm, and from 13th to l8th between 

 N. and N.E., and on the 19th E.S.E. 



The fog was wet and yielded much moisture, viz. : — 



7th •079,8th -008, 9th -015, loth -017, nth -031, I2th -013, 

 13th '020, i4ih '020, 15th -023. 



The barometer was very high, and almost stationary, reaching 

 a maximum on the 9th at loh. 30m. a.m., viz. 3075 inches 

 corrected and reduced to the sea-level. 



On the nth the fog cloud moved in a south current till 3 p.m., 

 when it became north, and continued so throughout the 12th. On 

 this day on the side facing the fog current every leaf and twig 

 had a horizontal deposit of ice, increasing in length from half an 

 inch at 4 feet above the ground to fully an inch at 10 feet ; the 

 outside edge of this ice being as thin as the fine edge of a knife ; 

 and the whole upper surface of all laurel and other large leaves 

 that were horizontal had a coating of ice, so thin (although it 

 could be detached without breaking) as almost to resemble gold- 

 leaf, on which were transparent impressions of ..very irregularity, 

 however minute. On the side of trees opposite to this current, 

 instead of rime there were nearly pear-shaped transparent drops 



of frozen water, of various sizes, mostly as large as one-eighth 

 of an inch in diameter ; they were situated not quite at the point 

 of every leaf; no leaf was without a frozen drop, and this had an 

 extraordinary appearance, more especially amongst the crowded 

 leaves of such plants as Pinus insignis, Abies Webbiana, &c. 

 On the opposite side of these fir-trees the appearance was 

 equally singular, as each leaf looked like a knife-blade of one- 

 sixth of an inch in width, with a ^square apex. The ground- 

 temperature being above 32°, the vivid green of the gra.ss was a 

 great contrast to the ice on the trees. E. J. Lowe, 



" The Art of Computation for the Purposes of Science." 



In a paper with the above title, in Nature, vol. xxxvii. p. 237, 

 Mr. Sydney Lupton refers to some of our work as affording a 

 good example of "the natural tendency of the human mind 

 . . . . to exalt the accuracy of one's own experiments." 



The experimental work referred to was a determination by the 

 dynamical method of the vapour pressures of liquid benzene. A 

 curve was drawn to represent these relations ; three points were 

 chosen, and the constants for the formula log p = a -V bat were 

 calculated. Mr. Lupton finds fault with the number of decimal 

 places given for these constants, and makes three statements 

 which are intended to put the experimental work in as unfavour- 

 able a light as possible so as to heighten the contrast with the 

 extreme accuracy of the calculations. Mr. Lupton says : 

 " Nine places of decimals are given with apparent confidence, 

 when (i) only three of the whole number of experiments were 

 made even in duplicate." We do not quite understand this state- 

 ment, for on reference to the original paper {Phil. Mag., Jan. 

 1887) it will be seen that the last six experiments in Series I. 

 overlap the first six in Series II , while the last seven of Series 

 II. are within the same limits of temperature as the first four of 

 Series III. The second slati^ment is that "the last pressure, 

 755, was obtained not by experiment at all, but by extrapolation 

 from a freehand curve, the highest experiment being 79° '6 and 

 743'i mm." We would point out that the experiment referred 

 to is not the highest, for on the preceding page in our paper 

 the bo ling-point 79°'9 at 753*4 mm. is given. Again, the curve 

 was not drawn by freehand, but by means of engineers' curves, 

 which give very much more accurate results. It is quite true 

 that the last pressure was obtained by extrapolation, but an 

 extrapolation ofo°'i, or even of 0° '4 does not seem very excessive 

 with a range of 80°. Mr. Lupton states, thirdly, that " a 

 difference of ^° at low temperatures produced no change in 

 pressure which was appreciable by the apparatus used." But, as 

 a matter of fact, at 0° a difterence of o°'i corresponds to a 

 difference of pressure of 0'i5 mm., which is quite appreciable on 

 our gauge. Perhaps, however, Mr. Lupton refers to the ex- 

 periments at 36'I5 mm., in which at the same pressure two 

 different thermometers registered temperatures which differed 

 by r. 



Mr. Lupton lastly gives much simpler constants, calculated 

 from our data, and compares the pressure at 60°, calculated from 

 them and from our constants, with the pressure given by 

 Regnault. It happens that the number obtained with the 

 simpler eonstants exhibits greater concordance with Regnauh's 

 value. Now while we would agree with Mr. Lupton in classing 

 Regnault (as far at least as some of his work is concerned) with 

 the select few who are entitled to an extra number of decimal 

 places, yet we would point out that Regnault did not always 

 succeed in obtaining perfectly pure substances to work with, and 

 some of his results are rendered almost valueless on that account. 

 In this case, for instance, the melting-point of Regnault's sample 

 of benzene was 4°'44, whereas after the most careful purification 

 we find that it melts at 5°'58, and the value obtained by Fischer 

 ( Wiedemann'' s Annalen, xxviii. 400) is almost exactly the same 

 as ours. Again, Regnault failed to obs^^erve the existence of a 

 difterence in the vapour pressure of solid and liquid benzene,- 

 (and other substances) at the same temperature, while this 

 difference has been measured by Fischer by the statical and by 

 ourselves by the dynamical method. 



We are quite willing to admit that our decimal points are 

 carried further than is necessary for the calculation of the vapour 

 pressures, but we have frequently had occasion to calculate the 



values of -i/ for various substances, and we have found that 



dt ■ 



in order to obtain regular values a large number of decimal 

 places are required ; if a smaller number are employed the 



