Jtily 29, 1875] 



NATURE 



251 



roof, facing north ; at Truro they are placed on the roof 

 of the Royal Institution, about forty feet above the ground, 

 in a wooden shed through which the air passes freely ; 

 at Falmouth they are eleven feet above the ground, close 

 to a wall, and in a confined situation ; at Helston we 

 are not informed how they are placed ; and at the Scilly 

 station we are only told that they " are well placed " — a 

 statement which the observations themselves render very 

 doubtful. 



The times of obser\^ation are hourly at Falmouth, 

 9 A.M. and 3 and 9 p.m. at Helston, and as respects the 

 other three stations we have no information. In redu- 

 cing the observations, " corrections for diurnal range " are 

 used in some cases, though the observations themselves 

 show that the range corrections adopted are plainly not 

 even approximately correct for the place. 



A system of meteorological observation which would 

 furnish the data for an inquiry into the important question 

 of a comparison of the local climates of Cornwall requires 

 yet to be instituted. Such a system must secure at each 

 of the stations included within it, uniformity in exposure 

 of instruments, uniformity in hours of observation, and 

 uniformity in methods of reducing the observations. Till 

 this be done, such climatic anomalies, as we have pointed 

 out in the case of Bodmin, will continue to be published, 

 certainly misleading some, and probably leading others 

 to dispute the usefulness of meteorological observations. 



We have much pleasure in referring to the additional 

 meteorological information given in the tables, which is 

 often of considerable value, particularly that supplied for 

 Helston by Mr. Moyle, whose tables have the merit of 

 giving the results for the individual hours of observation, 

 as well as deductions from these. 



LETTERS TO THE EDITOR 



[ The Editor does not hold himself responsible for opinions expressed 

 by his correspondents. Neither can he undertake to return, 

 or to correspond with the -writers of, rejected manuscripts. 

 No notice is taken of anonymous communications. ^ 



Vibrations of a Liquid in a Cylindrical Vessel 



In Nature for July 15, there is a short notice of a paper 

 read before the Physical Society by Prof. Guthrie on the period 

 of vibration of water in cylindrical vessels. It may be of in- 

 terest to point out that the results arrived at by Prof. Guthrie 

 experimentally, and many others of a like nature, may also be 

 obtained from theory. 



In the first place the fact, that the period of a given mode of 

 vibration of liquid in a cylindrical vessel of infinite depth and of 

 section always similar to itself {e.g. always circular) is propor- 

 tional to the square root of the linear dimension of the section, 

 follows from the theory of dimensions without any calculation. 

 For the only quantities on which the period t could depend ar« 

 (i) p the density of the liquid, (2) g the acceleration of gravity, 

 and (3) the linear dimension d. Now as in the case of a common 

 pendulum it is evident that t cannot depend upon p. If the 

 density of the liquid be doubled, the force which act upon it is 

 also doubled, and therefore the motion is the same as before the 

 change. Thus t, a time, is a function of d, a length, and g. 

 Since ^ is — 2 dimensions in time, t <= ^ - J, and therefore in 

 order to be independent of the unit of length, it must vary as ^i 

 inasmuch as^ is of one dimension in length. Hence t oc dh g-\. 

 This reasoning, it will be observed, only applies when the 

 depth may be treated as infinite. 



The actual calculation of t for any given form of vessel involves, 

 of course, high mathematics, the case of a circular section 

 depending on liessel's functions. But there is an interesting con- 

 nection between the problem of the vibration of heavy liquid in a 

 cylindrical vessel of any section and of finite or inhnite depth, 

 and that of the vibration of gas in the same vessel, when the 

 motion is in two dimensions only, that is everywhere perpendi- 

 cular to the generating lines of the cylinder. If \ be the wave- 

 length of the vibration in the latter case,* which is a quantity 

 independent of the nature of the gas, and k = 2 w -^ A, the period 



* Namely, the length of plane waves of the same period. 



T of the similar vibrations in the liquid problem is given by 



/ « —kl 



/jk ( 6-6 ), 

 \/ U -kl 



/ being the depth. The formula shows that in accordance with 

 Prof. Guthrie's observation t diminishes as / increases, and that 

 when / is sufficiently great 



T = 2ir -f- ^g~k. 

 lix be the value of k, viz. 2 tt 4- A, for a circular vessel of radius 

 unity, then the values of x for the various modes of vibration are 

 given in the following table extracted from a paper on Bessel's 

 functions in the Philosophical Magazine for November 1872. 



Thus if d be the diameter of the vessel, the period t of the 

 liquid vibrations is given by 



= ^'\/; 



d_ 



2gX 



so that if d be measured in inches, the number of vibrations per 

 minute, /;, is given by 



30 



n^/d = 



/ 



24 X 32-19 X X. 



For the symmetrical mode of vibration considered by Prof, 

 Guthrie, x — 3-832, giving 



n \Jd = 519-4 

 agreeing closely with the experimental value, viz. 517-5. Even 

 the small difference which exists may perhaps be attributed to 

 the insufficient depth of the vessels employed. 



This mode of vibration is not, however, the gravest of which 

 the liquid is capable. That corresponds to .x' = i -841, giving 



nsj d— 360-1, 

 and belonging to a vibration in which the liquid is most raised at 

 one end ot a certain diameter, and most depressed at the other 

 end. The latter mode of vibration is more easily excited than 

 that experimented on by Prof. Guthrie, but inasmuch as it in- 

 Tolves a lateral a motion of the centre of inertia, it is necessary 

 that the vessel be held tight. 



The next gravest mode gives x = 3.054, and corresponds to a 

 vibration in which the liquid is simultaneously raised at both 

 ends of one diameter, and depressed at both ends of the per- 

 pendicular diameter. In this case the value of n is given by 

 ni^d= 462-7 



Teriing Place, Witham, Ravleigh 



July 15 



Insectivorous Plants 



If further confirmation be needed of Mr. Darwin's discovery 

 of absorption by the leaves of the Drosera rotundifolia, it is 

 afforded amply by the following experiments which ,1 have just 

 concluded : — 



Having deprived a quantity of silver sand of all organic matter, I 

 placed it in three pots, which I shall call A, B, and C. In each 

 of these pots I placed a number of plants of the D. rotundifolia 

 under the following conditions: — (i) Perfectly uninjured, but 

 washed all over repeatedly in distilled water. (2) Similarly 

 washed, but with all the roots pinched off close to the rosette, 

 and with the leaves all buried, only the budding flower stalk 

 appearing above the sand. (3) similarly washed, with the roots 

 and the flower stalk left on, but all the leaves pinched off, the 

 roots being buried in the sand, (4) Similarly washed, roots left 

 on, four leaves buried in the sand, two leaves flower stalk, and 

 roots left above the sand and the roots protected against the 

 possibility of their absorbing anything from the sand. All the 

 plants were carefully watchd!, so that no flies were caught. 



