November 30, 1899] 



NA TURE 



107 



exclusively devoted to problems. At the present time 

 particular methods are prohibited in answering the ques- 

 tions set in certain papers ; such general restrictions of 

 methods are no longer to be maintained. A special 

 regulation provides that at least half the questions set 

 throughout the examination shall be of an elementary 

 character. 



The Board also proposes to abandon the custom of 

 publishing the list of successful candidates in order of 

 merit, and to follow the method at present adopted in the 

 Classical Tripos. There vvill be three classes (Wranglers, 

 Senior and Junior Optimes), and each class will consist of 

 three divisions, the names in each division being arranged 

 in alphabetical order. 



The proposed changes in Part I. have involved some 

 correspondmg changes in Part II. The class-list is to 

 consist of three divisions only, the names in each division 

 being arranged alphabetically ; and it is to be possible 

 for a candidate to obtain a place in the first division in 

 two ways. He may do so (as at present) by showing 

 special proficiency in one section of the schedule of sub- 

 jects, together with general proficiency in one or more 

 other sections ; or by showing general proficiency over a 

 wider range of subjects. 



The Board hopes that these changes will induce more 

 men to take Part I. in their second year ; it is at present 

 possible to do so under a regulation which came into 

 force in 1893, but very {&\v have actually availed them- 

 selves of the rule (probably not I per cent, of the whole 

 number of candidates since 1892). This is partly due to 

 the fact that 90 per cent, of the candidates cannot cover 

 the whole range of reading in two years, and partly to 

 the natural desire of the more able men to appear in as 

 high a place as possible in the list. By taking the Tripos 

 in their second year, men who intend to study subjects 

 such as physics or engineering will be able to gain a pre- 

 liminary knowledge of mathematics, with indications as 

 to how to extend their knowledge in any special branch 

 which they may need in their future course. The second 

 year Tripos will be of advantage also to the better 

 mathematical men, who now spend half their third year 

 in revision and in acquiring facility of solving artificial 

 problems. Under the proposed regulations these men 

 will have two years after Part I. (instead of one) in which 

 to become acquainted with the ideas and methods of 

 modern mathematics. This will be of special advantage 

 to men who intend to devote themselves to mathematical 

 research. 



It is thought that the abolition of order of merit will 

 assist the aims of the Board by making it possible for 

 the papers to be easier, and by helping to remove arti- 

 ficial problems ; and also by inducing a greater number of 

 men to take the Tripos in the second year of residence. 

 It is further felt by many that the proposed Part I. is not 

 of sufficient extent to even profess to classify the 

 candidates in an exact final order of merit. 



On November 23 the proposals of the Board were dis- 

 cussed by the Senate. As might be anticipated, the 

 scheme was criticised at some length, and particularly 

 the proposal to abolish the order of merit. The Board 

 will now revise its suggestions in the light of the 

 criticisms of the Senate, and the Senate will have to vote 

 on the final recommendations of the Board. 



It seems that the present Tripos must be modified in 

 some way, as the number of candidates has been steadily 

 falling ofif in recent years. Though once the largest 

 Tripos in the University, the Mathematical Tripos is now 

 smaller than both the Natural Science and the Classical 

 Tripos. Taking an average of the candidates for the four 

 years 1869-72, we find that, of the resident under- 

 graduates, one in eighteen passed the Mathematical 

 Tripos ; while for the five years 1895-99, the average falls 

 to one in thirty-five (of course, this relates to Part I. 

 only). 



NO. 1570, VOL. 61] 



THE RESISTANCE OF THE AIR. 

 'T^HE mportance of dfeterminations of the resistance- 

 of the air to moving bodies, in connection with the 

 problem of aerial navigation and numerous other prac- 

 tical applications, has led the Society d'Encouragement 

 pour rindustrie Nationale to offer a prize for investiga- 

 tions of an essentially experimental nature dealing with 

 the reactions on a surface moving through the air under 

 varying conditions as to form and velocity. One series of 

 experiments with this object has been undertaken by M. 

 I'Abbd Le Dantec, and a second set by M. Canovetti.. 

 The following account of these researches is based on the 

 papers communicated by their authors to the Bulletin of 

 the Society, and the report on them by M. Barbet. 



The method adopted by xM. I'Abbe Le Dantec is very 

 simple, and had been used in some previous experiments 

 by him in 1893. It is based on the property that the 

 motion of a falling body is at first accelerated, but the 

 resistance of the air, increasing as the velocity increases, 

 soon balances the weight of the body, and the body thus- 

 soon acquires its terminal velocity, and then moves 

 uniformly. The resistance of the air at this velocity is 

 exactly equal to the weight of the falling body. 



In the present experiments the surface whose resistance 

 is to be observed slides down a vertical wire, which acts 

 as a guide without introducing perceptible friction. Its 

 weight and area can be easily and accurately measured ; 

 and Le Dantec has now devised an electric record- 

 ing apparatus, which enables the time of fall to be 

 estimated with equal precision. A band of paper is 

 unrolled by clockwork action, and on this band an electric 

 arrangement records the vibrations of a seconds pen- 

 dulum. Furthermore, when the falling surface is released,, 

 a current is started whereby a toothed wheel is brought 

 into contact with the paper band, and traces on it a dotted 

 line. The surface at the end of its descent comes in 

 contact with a buffer, the current is broken, and the 

 cessation of the dotted line indicates the exact instant at 

 which the surface reached the buffer. The operator can 

 vary the height in such a way that the descent occupies 

 one, two, three or more seconds, and by subtraction the 

 distances traversed in each successive second are 

 obtained. 



The experiments were conducted in the chapel of the 

 Conservatoire des Arts et Metiers, the nave of which is of 

 considerable height, and their accuracy is verified by the 

 perfect agreement of the results. Thus several experi- 

 ments conducted for the purpose of determining the 

 height through which a surface fell in a certain number 

 of seconds agreed to within a centimetre. The chief 

 conclusions are as follows : — 



(i) Even feeble air currents such as are produced by 

 persons moving about in the neighbourhood of the 

 apparatus suffice to considerably modify the results, and 

 it is important therefore that the experiments should be 

 conducted in a closed building, which must, however, be 

 sufficiently large for the walls not to materially affect the 

 stream-lines of the air flowing past the moving surface. 



(2) A square surface i metre square, moving with a 

 velocity of i metre per second, experiences a resistance 

 of 8 1 grammes. 



(3) Experiments conducted with three different surfaces, 

 each of i square metre in area, but of different forms, viz. 

 circular, square, and of the form of an equilateral triangle, 

 respectively, show that the resistance depends on the forn> 

 of the surface, and the results accord with the hypothesis 

 that the resistance of a surface of given area is propor- 

 tional to the length of its contour. This property appears 

 to be new. 



(4) For velocities varying within certain limits, the law 

 of proportionality of the resistance to the square of the 

 velocity was verified. 



The resistance of the air to a moving surface can also 



