476 



NATURE 



[February 17, 19 10 



potassium, enough vapour was obtained to show the absorp- 

 tion spectrum quite definitely. These lines, with the lines 

 measured by Wood for sodium, give good data for testing 

 various formuIiE that have been suggested for representing 

 the series lines. None of the suggested formulae tested give 

 values representing the series within the limits of experi- 

 mental error. In particular, the quantity of Rydberg's 

 formula N„, or of the modified Rydberg formula of Rit., 

 i^ shown not to be constant. One of the most interesting 

 facts arising out of the investigation is that none of the 

 lines of the associated series appear in these absorption 

 spectra. Channeled space spectra appear which arc 

 analogous to the similar spectra for sodium vapour. 

 Further interesting facts noted are in regard to the effect 

 of mixtures of vapours. Some lines or bands appear in 

 spectra of mixtures w'hich are apparently unconnected with 

 the spectra of either constituent. This was specially evident 

 in the case of csesium and sodium ; a set of bands appeared 

 at about \V. L. 3000-3500 which do not appear in the 

 sodium spectrum, nor in the mixture of potassium and 

 caesium spectrum. Other interesting phenomena appear as 

 the density of the vapour is increased in the widening of 

 the lines and the appearance of satellites connected with the 

 lines of the series. The vapour of lithium has not yet been 

 successfully investigated, as it attacks the material of all 

 tubes hitherto tried. — Prof. C. H. Lees : The shapes of 

 the isogeotherms under mountain ranges in radio-active 

 districts. The author shows that for mountain ranges of 

 many different forms of section, the shapes of the isogeo- 

 therms may be accurately determined in cases in which the 

 heat conductivity and radio-activity of the materials of the 

 range may be taken as constants. Curves showing 

 the isogeotherms in three typical cases are given, 

 and it is shown that some of the statements gener- 

 ally made with respect to them are not correct. — 

 F. B. Pidduck : The propagation of a disturbance in 

 a fluid under gravity. The paper relates to the 

 determination of the motion set up in a heavy incom- 

 pressible fluid of uniform depth by a limited initial dis- 

 turbance ; the generally accepted solution in terms of a 

 definite integral represents the disturbance as being propa- 

 gated instantaneously, although the velocities of the simple 

 harmonic wave-trains of which the solution is built up are 

 all finite. In the paper this solution is transformed into a 

 series-solution analogous to that given by Cauchy and 

 Poisson for infinite depth. In the more general problem of 

 one-dimensional motions in dispersive media the integral 

 solution may represent the disturbance as either being 

 limited at any time by an advancing wave-front, or as 

 being propagated instantaneously. A method, based on the 

 examination of the convergence of the definite integral, is 

 given for deciding between these conditions. An investiga- 

 tion is given of the propagation of waves over a slightly 

 compressible heavy fluid. Solutions of the Cauchy-Poisson 

 type give motions which such a fluid can execute ; but these 

 are not due to limited initial disturbances, as they imply a 

 diffused initial condensation. The corresponding result for 

 incompressible fluids is that solutions of the type in question 

 imply a diffused unequilibrated distribution of pressure on 

 release from the initial state. — Dr. A. H. Gibson : The 

 flow of water through pipes and passages having converg- 

 ing or diverging boundaries. \ series of twentv-five pipes, 

 all having the same initial and final area, but having 

 different angles of convergence or divergence, were 

 examined. Some of these pipes were circular in section ; 

 others square ; others rectangular. The following are the 

 main conclusions : — (a) In a circular pipe with uniformly 

 diverging boundaries, the total loss of head attains its 

 minimum value with an angle of divergence 9 of about 

 5° 30'. Owing to the comparatively large effect of friction 

 in a pipe having a small value of S. the value giving the 

 minimum loss of head will be somewhat less in pipes larger 

 than those examined, which had a larger diameter of 

 3 inches and a smaller diameter of i'/; inches. (In largo 

 pipes of the type used in the Venturi meter, experiment 

 shows that this valu? is about 5° 6'.) As fl is increased the 

 loss of head, expressed as a percentage of (v^—v^YJzg, 

 increases very rapidly from its minimum value of about 

 i3'5 per cent, to a maximum of about 121 per cent, when 

 '1 = 63°, afterwards diminishing to about 102 per cent, as 

 A is increased up to iSo° (a sudden enlargement of section). 

 (V) The effect of making the pipe trumpet-shaped so as to 

 NO. 2103, VOL. 82] 



give a rate of change of velocity uniform per unit length 

 of the pipe may in some cases be to increase, in other cases 

 to reduce, the loss of head. In the only case tried in the 

 circular pipes the loss in the trumpet-shaped pipe was 23"5 

 per cent., as against I7'3 per cent, in a straight taper pipe 

 of the same length, and having equal to 10°. In the case 

 of a rectangular pipe, however, boundaries curved to give 

 respectively uniform retardation in time and length {dvldt = 

 const.) and (dti/d.v = const.), showed that the loss, as com- 

 pared with that in the corresponding straight-taper pipe 

 (0 = 20°), was reduced respectively by 5'3 per cent, and I2'i 

 per cent. Further experiments are desirable to determine 

 precisely the form of curve giving least loss of head, (c) 

 The loss of head in a pipe of square section is greater — at 

 the least 20 per cent, greater — than in a circular diverging 

 pipe of the same length and same initial and final area, 

 while the minimum loss is obtained when the angle between 

 opposite facas of the pipe is approximately 4°. (d) A change 

 in the shape, as opposed to the area, of the cross-section of 

 a pipe leads to considerable loss of head. Thus, by 

 changing the section of a pipe from that of a square of 

 2'66 inches side to a rectangle i'33 inches by 5'32 inches in a 

 length of 9'94 inches, a loss of head equal to o'484 v"l2g 

 was experienced, (c) Where a rectangular pipe has one pair 

 of sides parallel and the second pair uniformly diverging, 

 the loss of head is much greater than in a circular pipe 

 having the same length and the same initial and final areas. 

 The minimum loss is obtained with 9 about 11°. (/) The 

 critical velocity of flow in a circular pipe with uniformly 

 converging boundaries is. much greater than in a parallel 

 pipe of the same mean diameter. The critical velocity 

 increases rapidly with the angle of convergence, its lower 

 value, at 57'5° F. in the experimental pipes (from 3 inches 

 to I '5 inches diameter), being as follows at the point where 

 the diameter is 2^ inches : — 



C.V. (ft. p:r second) 



27 



3 '4 



4 3 



57 



The lower critical velocity in a parallel pipe of the same 

 mean diameter is o'i3 foot per second at this temperature. — 

 R. Rossi : The effect of pressure upon arc spectra : — 

 Titanium. The work is on the range from A4000 to A4601', 

 examined with the 21^ ft. concave grating spectrograph of 

 the Manchester University Physical Laboratory, which 

 gives on the photographic plate a dispersion of i'3 Angstrom 

 units per millimetre. The arc was formed between a 

 carbon pole and a graphite tube filled with titanium 

 carbide. The pressures at which the photographs were 

 taken were 15, 30, 50, and 100 atmospheres. The broaden- 

 ing, reversal, displacement, and changes of relative intensity 

 of fifty-two lines were studied. All lines were found to 

 bioaden out with an increase of pressure, the amount and 

 t\pe of broadening being different for different lines. 

 -Several lines were found to reverse under pressure, some 

 symmetrically and some asymmetrically. All lines were 

 found to be displaced towards the red end of the spectrum, 

 the displacement being a linear function of the pressure 

 within the limits of accuracy of experiment. The value of 

 the displacement varies for different lines, and the unre- 

 versed lines cannot be grouped into sets giving the same 

 displacement. The reversed lines, however, with the excep- 

 tion of one, can be formed into two groups, their mean 

 displacements being very nearly in the ratio 3 : 5. The 

 mean displacement per atmosphere of all the titanium lines 

 studied is found to be 0003652 Angstrom unit. The limited 

 number of lines studied, both in this work and by other 

 workers on the Zeeman effect, do not enable one to obtain 

 any relation between the pressure displacement and 

 magnetic separation. The relative intensity in nearly all 

 lines is altered by pressure, and a list is given of the lines 

 which are thus enhanced or weakened. — Sir James Dewar 

 and Dr. H. O. Jones : The change of carbon disulphide 

 into a gaseous product condensable and explosive 

 near the temperature of liquid air. 



Physical Society, Tanuarv 2t. — Dr. C. Chree, F.R.S., 

 president, in the chair. — R. E. Baynes : .Saturation 

 specific heats, &c., with van der Waals's and Claiisiufe's 

 characteristics. Bv use of a special variable, exact ex- 

 pressions may be found with van der Waals's characteristic 

 for the specific heats s, s' of saturated liquid and vapour 

 and for all other magnitudes connected with the state of 



