﻿Notices respecting Neiv Boohs. 285 



friction is absent. The motion can be obtained by pro- 

 jection from a spiral which is composed of semicircles as 

 shown in the diagram. 



It will be seen that the amplitudes are in arithmetical 

 progression and the difference for a complete period is 4F/c 2 , 

 which may be called the arithmetic decrement. There is 

 little purpose in using the ordinary definition of decrement, 

 but it may be remarked that on this definition (i. e. ratio 

 of successive amplitudes) the decrement ranges from unity 

 for infinite amplitudes to infinity for zero amplitudes. 



The spiral curve described here does not appear to have 

 been used before in scientific work, and it might be con- 

 veniently called the arithmetic spiral or the spiral of semi- 

 circles. 



XXII. Notices respecting New Boohs. 



Wmther Prediction by Numerical Process. By Lewis P. Richard- 

 son, B.A., F.Inst.P. 4to, pp. xii + ^36. Cambridge Univer- 

 sity Press. 30s. net. 



HPHE usual method employed in weather forecasting is a 

 -*- development o£ that of Abercromby. Distributions of 

 pressure are classified according to standard types, and the vari- 

 ation on any occasion is predicted according to the behaviour of 

 the atmosphere on previous occasions when conditions of the 

 same type occurred. The method is therefore one of sampling 

 inference in which the information utilized is all of one kind. 

 Mr. Richardson believes that other information is relevant to the 

 behaviour of the atmosphere ; and in this book he shows how to 

 make use of the known results expressed in the hydrodynamical 

 equations of motion and the equations of emission, transference, 

 and absorption of heat and water. The method adopted is to 

 work with equations each containing only one partial differential 

 coefficient with regard to the time, so that this can be determined 

 by means of the equation when the other quantities involved are 

 known ; they include, of course, partial derivatives with regard to 

 the position on the map and the height. These are to be found 

 by observation at stations distributed according to a regular 

 pattern, and the rate of change of each meteorological element at 

 each station is to be calculated from them. Complications arise 

 from the facts that the observations must be made at finite 

 intervals both of time and of position, but these are allowed for. 

 The stations required are more numerous than those at present 

 in operation, and observations should be made every three hours 

 to obtain the best results. Observations of upper-air winds and 

 temperatures are required. 



