90 



NATURE 



[September ig, 1912 



either forming a regular series or constituting an 

 irregular sea. In these approximations allowance can 

 be made for the effect of water-resistance to the 

 rolling motion — a most important factor in the problem 

 which could not be dealt witli until experimental re- 

 search had been made, and results had been subjected 

 to mathematical analysis. In addition, Froude laid 

 down certain practical rules for the guidance of naval 

 architects, and the application of these rules has been 

 shown by long e.xperience to favour the steadiness — 

 that is to say, the comparative freedom from rolling — 

 of ships designed in accordance with these rules. In 

 short, a problem which had proved too difficult when 

 attacked by Daniel Bernoulli in purely mathematical 

 fashion was practically solved a century later by 

 Froude, who employed a combination of mathematical 

 treatment and experimental research. 



Another example of the contrast between earlier 

 and present methods is to be found in the treatment 

 of the resistance offered by water to the onward 

 motion of ships. From an early date mathematicians 

 have been attracted to this subject, and many attempts 

 were made to frame mathematical theories. When 

 steam-propulsion for ships was introduced, the matter 

 became of great practical importance, because it was 

 necessary to make estimates for the engine-power 

 required to drive a ship at the desired speed. In 

 making sucli estimates it was necessary to approxi- 

 mate to the value of the water-resistance at that 

 speed, although the required engine-power was also 

 influenced by the efficiency of the propelling apparatus 

 and propellers. In addition, it was obvious that the 

 water-resistance to the motion of a ship when she was 

 driven by her propellers at a given speed would be in 

 excess of the resistance experienced if she were towed 

 at the same speed, and there was no exact knowledge 

 in regard to that increment of resistance. The earlier 

 mathematical theories of resistance proved to be of little 

 or no service, and they were based on erroneous and 

 incomplete assumptions. Rankine devised a "stream- 

 line " theory which was superior to its predecessors, 

 but it also for a time had no effect on the practice 

 of naval architects. William Froude, adopting this 

 stream-line theory, dealt separately with frictional 

 resistance, and devised a "law of comparison" at 

 corresponding speeds, by which from the "residual 

 resistance " of models — exclusive of friction — it became 

 possible to estimate the corresponding residual resist- 

 ance for ships of similar forms. At first he stood alone 

 in advocating these views, but subsequent experience 

 during forty years has demonstrated their soundness. 



E.xperimental tanks for testing models of ships, such 

 as Froude introduced, are now established in all mari- 

 time countries, and the results obtained therein are 

 of enormous value to the designing of steamships. In 

 regard to the selection of the forms of ships, naval 

 architects are now able to proceed with practical cer- 

 tainty ; but in connection with the design of screw 

 propellers, even after model experiments have been 

 made with alternative forms of screws, there is still 

 great uncertainty, and dependence upon the results 

 obtained on "progressive" speed trials of ships is 

 still of the greatest service. As yet the " law of com- 

 parison " between model screws and full-sized screws 

 has not been determined accurately. The condition of 

 the water in which screws act, as influenced by the 

 advance of a ship and her frictional wake, the pheno- 

 mena attending the passage of the water through a 

 screw, and the impression thereon of sternward motion 

 from which results the thrust of the propeller, the 

 effect upon that thrust of variations in the forms and 

 areas of the blades of screw propellers, and the causes 

 of "cavitation," all form subjects demanding further 

 investigation. In these cases the only hope of finding 



NO. 2238, VOL. 90] 



solutions lies in the association of experimental re- 

 search with mathematical analysis. There have been 

 very many mathematical theories of the action of 

 screw propellers, but none of these has provided the 

 means for dealing practically with the problems of 

 propeller design, and there is no hope that any purely 

 mathematical investigation ever will do so, because 

 the conditions which should be included in the funda- 

 mental equations are complex and to a great extent 

 undetermined. 



In connection with other branches of engineering, 

 model-experiments have also proved effective. 

 Examples are to be found in connection witlT the esti- 

 mates for wind-pressure on complicated engineering 

 structures, such as girder or cantilever bridges. Ex- 

 perimental methods are also being applied with great 

 advantage to the study of aeronautics and the problems 

 of flight. 



The association of the mathematical analysis of past 

 experience with designs for new engineering works of 

 all kinds is both necessary and fruitful of benefits. A 

 striking example of this procedure is to be found in 

 connection with the structural arrangements of ships 

 of unprecedented size, which have to be propelled at 

 high speeds through the roughest seas, to carry heavy 

 loads, to be exposed to great and rapid changes in the 

 distribution of weight and buoyancy, and to be sub- 

 jected simultaneously to rolling, pitching, and heavy 

 motion, as well as to blows of the sea. In such a 

 case purely mathematical investigation would be use- 

 less; the scientific interpretation of past experience 

 and the comparison of results of calculations based 

 on reasonable hypotheses for ships which have seen 

 service with similar results of calculations for ships 

 of new design are the only means which can furnish 

 guidance. 



In the past the association of mathematicians and 

 engineers has done much towards securing remark- 

 able advances in engineering practice ; and in 

 future it may be anticipated that still greater results 

 will be attained now that the true place of mathe- 

 maticians in that practice is better understood and 

 utilised. 



UNIVERSITY AND EDUCATIONAL 

 INTELLIGENCE. 

 \ GRE.AT cause of anxiety to those who are respon- 

 sible for evening continuation schools and classes lies 

 in the spasmodic attendances and lack of continuity 

 of the casual student. The prospectus of the Muni- 

 cipal Technical Institute, Belfast, shows that the 

 authorities in that city deal with this source of trouble 

 courageously. Students must submit to an entrance 

 examination, and must follow a course of study, and 

 " anv student who does not wish to conform to the 

 regulation as to attending a definite course of study 

 or passing the entrance examination can obtain 

 exemption on making application at the office and 

 paying treble the fee for the class it is desired to 

 join." Side bv side with these restrictions there is 

 every opportunity and incentive to the serious student 

 to equip himself thoroughly for his business. 



The London County Council announces that the 

 evening classes held in Polytechnics, technical insti- 

 tutes, schools of art, commercial centres, and evening 

 schools will shortly be reopened. The programme 

 which the Council has prepared includes classes to 

 meet all kinds of needs. The enrolment of students 

 began on Monday, September i6, and a leaflet giving 

 full particulars as to where the classes are held, and 

 as to fees (which it may be stated are very low), can 



