78 



NATURE 



[May 26, 1898 



:(.+.t). 



, = 9(, + .t), 



k—- -^ -— is the smaller of the two, and we proceed to find its 



value. We have as a first approximation to the behaviour of 

 gases, 



pv = Q,{\ +aT), 

 where T is the temperature centigrade on a gas-thermometer. 

 We therefore have, as approximate equations, 



^ _ Co 



We may further assume that — = ^, since the degrees are 



■' dt dl ^ 



practically equal on the two scales. 

 We therefore obtain, approximately, 



-( 



dv ^Ca 

 dt p ' 

 Using these approximate values, we have 

 , S£ _^dv ^ kti It 

 "Sp ' 'dt~ C^Sp . 

 _k_ It 

 Co Slog/ 

 and the equation for t becomes 



dt Co Slog/ 

 If now, further, we use the approximate values of v and — 



in the term v -=- — , we shall obtain 

 dt 



t=l+T + ^-^. 

 a Co 5 log p 



This is the formula usually given. 



This method of working appears to me to be incorrect, for the 

 following reason : — 



In the equation 



t=(v + kll)-^^ 

 V Sp/ dt 



there are two terms on the right-hand side, one of which, 



^—- -i- -5^, is small compared with the other. We may there- 

 of!' dt 

 fore neglect it as a first approximation, and we then obtain 



- = function of p, in accordance with the laws of a perfect gas. 



If we wish to proceed to a closer approximation, we may use 



the perfect-gas laws as sufficiently good in the term k — -r- -^, 



Sp dt 

 because that is a small term, and the departure of the actual gas 

 from the perfect gaseous laws will consequently in this term 

 introduce only errors which depend on the squares of small 

 quantities. But we are not at liberty to use the perfect gas laws 



in the remaining term v-^^, because it is not a small quantity, 



and we have therefore no guarantee that the use of such an 

 approximation will not introduce errors of the first order of small 



quantities — that is to say, comparable with the term k — . -f- _ 

 _ Ip dt 



itself. With such errors introduced, the second approximation 

 would not necessarily be better than the first. 



The mistake in principle, which I have indicated, appears to 

 be widespread, since it has crept into several of our well-known 

 text-books. Thus the discussions gi%'en in Tait's " Heat" (pp. 

 338-339). in Baynes' "Thermodynamics" (pp. 126-127), and 

 in Maxwell's "Heat" (pp. 211-214), all appear to me in- 

 fected by this source of error. It is true that in these discussions 

 the mistake is introduced more subtly, and is covered with a 

 mass of symbols ; whereas in the faulty investigation given 

 above, I have purposely made the paralogism as glaring as 

 possible. But hi substance the mistake occurs in each of the 

 discussions above named. John Rose-Innes. 



May 13. 



NO. 



I49I, VOL. 58] 



Printer's Ink and Photographic Plates. 



In a paper on the action exerted by certain metals and other 

 substances on a photographic plate, by Dr. W. J . Russell ( Proc. 

 A'.S., vol. Ixi. p. 424), the author mentions that the IVestminster 

 ^Gazette is printed with an ink which readily acts on a photo- 

 graphic plate. The printed paper in some experiments is placed 

 in contact with the photographic plate, in the dark, and after 

 being left in contact for some time, in the dark, the plate is 

 developed, and the printed letters come out clearly. Dr. 

 Russell nientions the names of several periodicals the print of 

 which acts on a sensitive plate. To these the following example 

 of the same phenomenon may be added : a photographic plate 

 wrapped up in an advertisement sheet of Modern Society on 

 development showed the printed characters very clearly, the 

 words reading from left to right, not being reversed, so that the 

 action must have taken place through the thickness of the 

 paper. This sample of the action of printer's ink on a photo- 

 graphic plate (the property of Mr. W. B. Croft) has been in the 

 excellent physical laboratory museum at Winchester since 1892. 

 The print is good and clear, and probably one of the earliest 

 observed instances of the action of printer's ink on a photo- 

 graphic plate in the dark, in which the physical conditions were 

 known and recorded. F. J. Jervis-Smith. 



Oxford, May 16. 



Heavy Rainfalls. 



I THINK it worthy of record that at a place called Nedunkeni, 

 in the Northern Province of Ceylon, the rainfall on December 

 15-16, 1897 (24 hours), was 3176 inches. The average annual 

 rainfall of this place was 647c, but in 1897 the amount totalled 

 121-85 inches. 



The heaviest recorded rainfalls (as given in the " Encyclop. 

 Britt.") are at Joyeuse, France, 31 '17 inches in 22 hours ; at 

 Genoa, 30-00 inches in 26 hours; at Gibraltar, 33*00 inches in 

 26 hours ; on the hills above Bombay, 24 inches in one night ; 

 and on the Khasia Hills, India, 30-00 inches on each of five 

 successive days. 



The rainfall in Ceylon, referred to above, is therefore 

 notable. The greatest annual rainfall occurs, as is well known, 

 on the Khasia Hills, with 600 inches. The wettest station in 

 Ceylon is Padupola, in the Central Province, with 230-85 inches 

 (mean of 26 years), the rainfall for last year being 243*07 

 inches. C. Drieberg. 



School of Agriculture, Colombo, Ceylon. 



Hermaphroditism in the Apodidae. 



I AM not sure but that the tone of Prof Lankester's demand, 

 in Nature of May 12, that I should " at once " withdraw my 

 " assertions," or confirm them by " some evidence," would not 

 have justified my ignoring it altogether. For those of your 

 readers, however, who may be interested in this subject, may I 

 say that I have produced "some evidence" {Ann. and Mag. 

 Nat. History, xvii., 1896, plates xi. and xii.), and no counter 

 evidence whatever has yet been forthcoming to shake my faith 

 in the justness of my conclusions. Henry Bernard. 



Streatham, May 17. 



MAGNETISM AND SUN-SPOTS. 

 "\X rHEN Sir Edward Sabine was preparing his paper ^ 

 *^* "On Periodical Laws discoverable in the mean 

 effects of the larger Magnetic Disturbances — No. ii.," in 

 which he discussed the magnetic observations made at 

 the temporarily established Colonial observatories at 

 Toronto and Hobarton, he found that there existed at 

 these places, in the years 1843 to 1848, a progressive 

 increase in amount both of magnetic disturbance and in 

 extent of diurnal range of the declination magnet, the 

 values of diurnal range for the year 1843 having become 

 in 1848 increased by some 40 per cent., the Toronto 

 values for these years being 8''9o and i2'-ii respectively, 

 and the Hobarton values 7'-66 and io'-63. This was an 

 altogether unlooked-for result, one that engaged his 

 special attention, such increase of value from year to year 



1 Read before the Royal Society, May 6, 1852. 



