NJl TURK 



S77 



THURSDAY, JUNE 29, 191 1. 



DYNAMICAL MErEOROLOGY AND 

 HYDROGRAPHY. 

 Dynamic Meteorology and Hydrography. Bv Prof. V. 

 Bjerknes and different collaborators. Pp. 146 + 

 36.\ + 3oB + 22c. (Washington, D.C. : Carnegie In- 

 stitution, 1910.) 



IN a lecture delivered at University College in May, 

 1910, Prof. Bjerknes outlined the methods, de- 

 scribed characteristically as rational, by which he 

 hoped to utilise synchronous meteorological observa- 

 tions for a more purely scientific purpose than the 

 preparation of daily forecasts. The present work is 

 the first instalment of a treatise prepared, in collabora- 

 tion with Dr. J. W. Sandstrom, with such 

 investigations in view, and is intended to present in 

 an ordered and rational form the principles and 

 development of meteorology and hydrography viewed 

 from the noint of view of a mathematical physicist. 

 Bjerknes has realised the fact that economy of thought 

 and labour are essential to advance in meteorological 

 and hydrographic investigation, and although his book 

 bears little actual resemblance to Lagrange's 

 " Mecanique Analytique," we cannot help calling to 

 mind that classical masterpiece of scientific economy 

 in reading this volume. 



The existing chaos in meteorological units has led 

 Bjerknes, among others, to the conclusion that a 

 thorough reform in this respect will go far towards 

 making meteorological progres's possible through the 

 practical application of more advanced mathematical 

 treatment than is at present customary. He begins 

 therefore by introducing as suitable units for meteoro- 

 logical purposes the metre, the metric ton, or 10" 

 grams, and the second, and calls this briefly the 

 m.t.s. system. The metre and the ton are chosen on 

 the ground that the centimetre and the gram are too 

 small as units of length and mass for practical appli- 

 cations, in much the same way as the c.g.s. electrical 

 units are in general unsuitable for the practical 

 engineer. The atmosphere, however, resembles a thin 

 plate, and although the vertical dimensions and 

 motions are relatively small, they are nevertheless 

 important. No combination of units will be appro- 

 priate for all cases, and Bjerknes himself departs in 

 some cases from the rational derived units which 

 follow from his scheme. It seems doubtful therefore 

 if it is a wise plan to run the risk of discouraging 

 the reader at the outset by the formal introduction 

 of new units. 



The first two chapters are introductory in character, 

 and deal with the units used in the work and with 

 gravity and the corresponding scalar, gra\ii\ pdtcn- 

 tial. The unit of gravilx potential on lln' m.l.s. 

 system is called the dynamic decinietrc, Ikcuisc ii is 

 equal to the work done in lifting unit ni.iss .igainst 

 gravity through a height wliicli is .ipprdNinialcly equal 

 to a decimetre. For practical apiJJication, liowcver, the 

 dynamic metre is taken, and this unit is fundamental 

 in Bjerknes's work. Its great advantage is that the 

 distance to whirli it coi-responds agrees sulViciently 

 ,\0. 2174, VOL. 86] 



closely with the metre, to make it suitable for ex- 

 pressing approximately geometric heights, and points 

 at the same distance in dynamic metres from the 

 earth's surface (sea-level) are on the same level sur- 

 face of gravity. Bjerknes even makes out a case for 

 publishing the results of geodetic determinations of 

 "height " in dynamic metres, just as in a later chapter 

 he emphasises the need for giving the corresponding 

 values of pressure and temperature in the publication 

 of the results of upper-air observations, instead of 

 height and temperature, the quantities more frequently 

 adopted at present. 



Some care is needed to prevent confusion in con- 

 nection with dynamic decimetres and metres. These 

 are units of work and are invariable, but the heights, 

 with which they correspond, vary with the locality 

 inversely as the value of gravity. 



The m.t.s. unit of pressure is the centibar, but here 

 again it is found convenient to take as the ])ractical 

 unit the bar or the megadyne per square centimetre, 

 and the graduation of the barometer in "millibars " is 

 advocated. It seems necessary to proceed cautiously in 

 this connection. It is proper and scientific to express 

 atmospheric pressure in terms of the megadyne per 

 square centimetre or the bar, and it is legitimate to tak ■ 

 advantage of any practical device which will enable 

 this to be done as easily as possible; but in using the 

 mercury barometer we are primarily measuring a 

 distance, and equal increments of height do not corre- 

 spond with equal increments of pressure at different 

 places, or under different conditions at tlie same 

 place. Meteorologists ought to boNxare of adding 

 another incongruity to the list of those which they 

 ridicule frequently in a good-humoured way when they 

 have become accustomed to the feeling that long usage 

 has made the bonds too strong to be broken. 



Chapter iii. deals with the specific volume and 

 density of air and sea-water. Owing to the fact that 

 the amount of water-vapour present in the atmosphere 

 is a variable quantity, the "constant," R, in tlie 

 equation pv = RT is variable also, and this constitutes 

 a real difficulty in the discussion of atmospheric 

 changes. Bjerknes reduces the difliculty \(r\ con- 

 siderably by adopting the artifice of keeping R con- 

 stant throughout, and using in the equation, not the 

 actual temperature T, but tlie virtual temiiorature r, 

 which is the temperature at whieli dry air would have 

 the same density as tlie air under consideration. By 

 another ingenious device he makes seven small tallies 

 for obtaining the density of sea-water from ihi tem- 

 perature, salinity and pressure cover the same lange 

 as a quarter of a million pages «.! straightforward 

 tabulation. 



The next two chapters are concerned with the prin- 

 ciples of hydrostatics and their aiijilication to the 

 atmosphere in th.e ease of constant tem|)ei-atui-e 

 gradient antl for adialiatie equilihrium. They con- 

 tain .an instructive set of <liaL;rams showing for the 

 same scale of lieight (measnud in dynamic metres) 

 the pressure, densilx, and s|)ei-irie \olume of the atmo- 

 s|)]iere at differeiU le\-els for the four c-ases. homo- 

 geneous atniosj)liere, dry atmosphere in adiabatic 

 equilibrium, atmosphere with constant vertical 



