'54 



NATURE 



[September 30, 1920 



"equivalent constant wind" — i.e. the constant 

 wind which produces the same effect at the same 

 time. The latter is obtained by means of a set 

 of "weighting factors" which express the rela- 

 tive importance of the wind at different parts of 

 the trajectory. 



Considering the wind, effect at any given point, 

 the weighting factor for any section of a trajectory 

 is the ratio of the effect at that point of unit wind 

 blowing in that section only to the eiTect at the 

 same point of unit wind blowing throughout the 

 trajectory. If W is the actual wind in ^ny 

 section, and fe is the weighting factor for that 

 section, then the equivalent constant wind is given 

 by the sum of the values of feW for all sections 

 up to the point where the effect of the wind is 

 being considered. 



The same arguments apply to variations of 

 atmospheric density from standard. An account 

 of the application of weighting factors has ap- 

 peared in a recent number of Nature*; we are 

 concerned here with the calculation of them. 



The values of the weighting factors for given 

 sections depend on the point at which the effect of 

 a wind (or change of density) is being calculated, 

 and on the precise effect which is being considered. 

 For example, a wind in the plane of the trajectory 

 produces changes in both horizontal and vertical 

 co-ordinates of the point reached in a given time, 

 and if the wind varies along the trajectory the 

 constant wind which will produce the same hori- 

 zontal displacement will not generally produce the 

 ■ same vertical displacement. 



The four equations of motion of the plane tra- 

 jectory express the relations between the com- 



• Nature, June 17. "The Importance of Mcteorol >kt in GunneiT," br 

 Dr. E. M. Wedderburn. 



ponents of velocity, the co-ordinates, and the time. 

 From them can be obtained, by a process analo- 

 gous to differentiation, four "equations of varia- 

 tion " expressing the relations between the 

 changes in these quantities, for a given time, for 

 any change in conditions which causes first order 

 variations in the plane of the trajectory. (A cross- 

 wind produces only second order effects in this 

 plane, and its treatment is entirely separate.) 



The equations of variation have no formal solu- 

 tion, and step-by-step integration is necessary for 

 numerical work. To find wind weighting factors, 

 the obvious method is to integrate the equations 

 for winds blowing in the sections for which 

 weighting factors are required ; but this is not 

 necessary, for if the integration is performed for 

 three suitable changes of conditions, the results 

 may be combined to give weighting factors, not 

 only for wind, but for density changes as well. 



The numerical work of the process of combin- 

 ing the three solutions is rather heavy and not 

 altogether simple, and a more direct way of calcu- 

 lating weighting factors has been worked out. 

 The equations of variation form a system of linear 

 differential equations of the first order, and by 

 using a certain property of such a system another 

 set of equations (the " adjoint " system) can be 

 obtained, the solutions of which give directly the 

 effect at a given time of a constant wind (or 

 density changes) which begins at a previous vari- 

 able tinjje. Weighting factors are obtained at once 

 by dividing by the effect of a constant wind which 

 begins at the origin, and differencing the results. 



The equations of variation may be applied to 

 any problem in first order variations. The subject 

 of second order variations has not been developed, 

 as its practical importance appears small. 



Obituary. 



' I "HE study of earthquakes in New Zealand and 

 -*- Australia has suffered a serious loss through 

 the death of Mr. George Hogben on .April 20 last. 

 For many years Mr. Hogben acted as secretary 

 of the seismological committee of the Australasian 

 Association for the Advancement of Science, and 

 we are indebted to him for reports of this com- 

 mittee, and for many studies of individual earth- 

 quakes published in the Transactions of the New 

 Zealand Institute and other journals. It was 

 owing to his efforts that the Milne seismograph 

 was erected at Wellington, N.Z., and that, shortly 

 before his death, an order was given for the im- 

 proved Milne-Shaw seismograph. In addition to his 

 contributions to our knowledge of earthquakes, Mr. 

 Hogben was interested in education generally, and 

 was for two years president of the Wellington 

 Philosophical Society. According to a notice 

 issued with the Hector Observatory Bulletin 

 (No. 28, 1920), he also issued a valuable report on 

 proportional representation, and at the time of his 

 death had an improved set of mathematical tables 

 in the press. 



NO. 2657, VOL. 106] 



The Atti dei Lincei (vol. xxix. (i), parts 9-10) 

 contains an obituary notice by R. V'ersari on the 

 late Prof. Francesco Todaro. Born at Tripi 

 (Messina) on February 14, 1839, Todaro entered 

 the University of Messina in i860, but on the entry 

 of Garibaldi he took up arms as a volunteer in the 

 Chasseurs of Etna. On the conclusion of hostili- 

 ties and of service to the wounded, he returned to 

 the University, and was attracted by the German 

 biologists to anatomical and physiological studies. 

 He went for some time to study at Florence under 

 Schiff and others, and in 1865 published his first 

 paper on the muscular system of the human heart 

 and the Eustachian valve. He returned to Messina 

 as professor of human anatomy, and in 1869 gave 

 an address on the renewal of the human body. 

 Todaro was among the earliest to study the ana- 

 tomy of the lower marine animals, and to realise, 

 in accordance with the doctrine of evolution, the 

 importance of comparative anatomy as throwing 

 i light on the anatomy of man. In 1870 he read a 

 paper on the sense-tubes of Plagiostomata, and the 

 following year was invited by Brioschi to the chair 



