NA TURE 



[March 9, 1922 



next sections he gives a theory of the propeller, while 

 chap. 8 deals with the problem of the aeroplane 

 in moving air. Following Prof. E. B. Wilson the 

 treatment is based on the study of forced oscillations, 

 but the reader will do well to follow Dr. Brodetsky's 

 advice and read his alternative treatment by the 

 method of initial motions. This latter method, 

 by the way, opens up an almost unlimited supply 

 of calculable problems which cannot fail to throw 

 light on questions regarding design and control of 

 aircraft which are under the direction of their pilots.^ 



A further important innovation is the insertion 

 of collections of exercises, commonly described as 

 " Examples." Here again Dr. Brodetsky has had 

 the difficult task of striking out in a new line in 

 incorporating the features of a Cambridge text-book 

 in an aeronautical treatise. This feature will,, we 

 hope, be of great use in making the present important 

 developments of applied mathematics available in 

 our honours schools. 



A further contribution to the study of aeroplane 

 mathematics by Dr. Brodetsky appeared in the 

 Mathematical Gazette for May 1921. It dealt mainly 

 with the conditions of equilibrium of the forces acting 

 on an aeroplane in steady motion of different 

 types, such as horizontal flight, climbing, descending, 

 gliding with or without varying the elevator, diving 

 and upside-down flight, load variations, variation of 

 air density with altitude, flight in steady wind, and 

 circHng and helical flights with and without sideslip. 

 In conclusion Dr. Brodetsky remarked : " The present 

 paper will perhaps suffice as an indication to teachers 

 of mathematics and others of how much really useful 

 and interesting information can be obtained with easy 

 mathematics. The introduction of aeroplane mathe- 

 matics into ordinary courses in all our schools and 

 universities would be a great boon to teachers as 

 well as to pupils." 



In addition to strongly supporting Dr. Brodetsky's 

 plea for the study of aeroplane problems by mathe- 

 maticians and their pupils, we would refer to the 

 equally important task which remains, of equipping 

 the workers in the aeroplane industry with a better 

 knowledge of the principles of mechanics involved 

 in aircraft construction and manipulation. In this 

 connection it is to be hoped that the Institute of 

 Aeronautical Engineers, now two years old, will 

 prove a valuable addition to the roll of similar technical 



> Tbe investigations which the writer of this review was able to initiate 

 and undertake with the assistance of a three-years grant from tbe Research 

 Department could not for various reasons be incorporated in Dr. Brodetsky's 

 treatise, but have been published in the Reports and Memoranda of the 

 Advisory Comnuttee for Aeronautics and the Aeronautical Research Com- 

 mittee, Nos 555, 640, 684, 689, and 744, the last two dealing with the general 

 equations of motion of aeroplanes studied from several novel points of view 

 with the use of Brodetsky's notation. The last Report constitutes a brief 

 exposition of the general theory of initial motions in its appUcation to 

 aeroplanes. ''" 



NO. 2732, VOL. 109] 



and professional institutes that have been formed in 

 nearly every other branch of applied science, the ranks 

 of which are largely recruited from the students of our 

 technical colleges and universities. For such students 

 Dr. Brodetsky's book is specially suitable. 



G. H. Bryan. 



The History of Whaling. 



A History of the Whale Fisheries : From the Basque 

 Fisheries of the Tenth Century to the Hunting of the 

 Finner Whale at the Present Date. By Dr. J. T. 

 Jenkins. Pp. 336. (London : H. F. and G. Witherby, 

 1921.) i8i-. 



AT the close of the last century whaling appeared 

 likely to terminate at an early date, in view of 

 the great reduction in the numbers of whales which 

 had been brought about by a " relentless and long- 

 continued persecution. The rate of destruction had 

 been accelerated by the introduction of modern methods, 

 and if new fields had not been discovered whahng might 

 by now be almost a thing of the past. Dr. Jenkins's 

 book contains a large amount of information which 

 will be of great value to those who wish to satisfy 

 themselves whether the lessons of history confirm the 

 forebodings which have been expressed about the future 

 of whales. 



The work opens with an account of whales, their 

 species, habits and migrations, and zoologists may 

 turn with interest to an Icelandic classification (p. 87) of 

 1777, which within its limits is not inferior to the most 

 modern system, or to the excellent account of the 

 Greenland whale (p. 116) given by Edge, who flbok part 

 in Arctic whaling in 1610. The next chapter deals 

 with the products of whales, the method of hunting, 

 and whaling legislation, giving also a brief review of 

 the successive phases of the industry, a subject which 

 is considered in greater detail in later chapters. Whale- 

 oil, a material which was formerly indispensable for the 

 lighting of houses, public buildings, and streets, has 

 remained one of the most important raw materials 

 for the manufacture of soap and glycerine, the great 

 quantities of glycerine which were extracted from it 

 during the war having been of vital importance to 

 this country. Spermaceti, ambergris, and whale- 

 bone are still highly valued materials, while the 

 greater part of the carcasses of whales is utihsed 

 in the preparation of agricultural manure, the flesh 

 being partly converted into cattle-foods or even used 

 for human consumption. 



The first known account of whaling is that of 

 Ochther, who voyaged beyond the North Cape towards 

 the end of the ninth century, and afterwards described 



