March 9, 191 1] 



NATURE 



61 



c. Coefficient of oblique air pressure (Lanchester). The 

 value of this depends on the aspect ratio of the surface. 

 From Duchemin's rule for square surfaces it is 2 ; Eiffel 

 gives a value of 3 ; Lanchester gives hypothetical values 

 between 2 and 3. 



|. Ratio of skin friction on a double surface to the 

 normal resistance of the plane of the same single-surface 

 area. 



/3. Angle of incidence (Radians). 



V. Relative velocity of air to surface. 



/. Length of surface in the direction of flow. 



A. 



L — Frictional Resistance deduced from the Head, or 

 Total Resistance of Dirigible Balloons. 



The resistance of a well-shaped dirigible is, like that 

 of a ship, almost entirely due to skin friction. The 

 aerodynamic resistance of cars, rigging, &c., is almost 

 negligible in ratio to the skin friction, certainly not 

 exceeding 30 per cent, thereof. 



If, then, the area of the skin is A,, and that of the 

 maximum cross-section is A^, and k is the ratio of the 

 skin friction to the aerodynamic resistance of a normal 

 ■-'irface with the same shaf>e as the mid-section, this defini- 



in of k mav be written : — 



CpAg 



(I) 



the coefficient fc has been measured for several dirigibles, 

 md forms the basis of this computation. 



Ao 



Niime Length D'ameter 



Renard and Krebs 50'42 m. 8'4 m. 



Ai A2 /?■ / 



1330 sq.m. 554 0-4 0000033 



(tspitallier, Genie Civil, 1902) 

 |8ooo 100 o'45 o'oooo25 



(Moedebfck's Pocket Book) 

 2000 80 o'3i o '000030 



(Ditto.) 



67rD2 JttD'^ o"i6 o'ooooi4 



(Moleswor.h's Pocket Book 1) 



Total 



0"000I02 



Mean va'ue ... ... ... ... ... o'oooo2s 



Deduct 30 per cent, for other rtsistance ... o ooocoS 



o'ccooi 



The value 0-000025, seeing that it certainly includes 



some aerodynamic resistance due to im{>erfect form of 



t envelope and the resistance of car and rigging, should be 



I regarded as the absolute maximum. 



IL — Frictional Resistance deduced from the Efficiency 

 of a Plane Aerofoil. 



According to TurnbuU {Physical Review, March, 1907), 

 the lift-to-drift ratio is a maximum for planes of an aspect 

 ratio of two, when the angle of incidence is 3^ degrees, 

 and it has then a value of 5-1 (3^ degrees = o-o6 radian). 



Employing Lanchester's notation, this ratio (also called 

 by Turnbull the " efficiency ") 



_ Ccp AV^B 



~ 4C7aV2 + CrpAVV 



c, according to Lanchester (compare Dines, Eiffel, and 



Rateau), is alx>ut 2-5, so that ^ — 0-020 for the double 



surface and /= ^Cp=: 0-000032 for the double surface, or 

 for the single surface 0-000015. 



HI. — Frictional Resistance in Air deduced by Comparison 

 with that of Water. 



The investigations of F"roude have led to a fairly 

 accurate knowledge of the frictional resistance of water, 

 and it has been thought by many that a simple ratio exists 

 between this and that of air in similar circumstances. 



Froude's coefficients are between 0-003 ^^'^ 0-005, '^^ 

 total resistance varying with a power of the velocity from 

 1-83 to 2-0 when there is considerable turbulence. It is 

 probable that the lower density of air renders it more 



1 This result is apparently after Pole's figures, but the resistance stems to 

 have been under-estimated. 



NO. 2158, VOL. 86] 



easily subject to turbulent conditions, so that there can 

 be little doubt as to the approximate truth of the velocity 

 squared hypothesis. 



(a) Assuming that the friction is purely dependent on 

 the density, since the density of water is about 800 times 

 that of air, / may be = o-oo4/8oo = o-ooooo52. 



(b) Assuming that the friction varies as the density, and 

 also as the square root of the kinematic viscosities, an 

 assumption consonant with hydrodynamic theory, 



/ = sq. root of 12x0-004/800 = 0-000017. 



IV^. — Zahtn's Investigations. 



Prof. Zahm, by experimenting in a wind tunnel on 

 boards, obtained a formula as follows : — 

 /=o-oocx)o8 /-""7 Vi8--'i 



for smooth surfaces and no vibration, increasing up to 

 /=o-ooooi (total resistance varies with V^) for turbulent 

 conditions and buckram-covered surfaces. 



V. — Lanchester's Investigations. 



Index of velocity variation = 2. 



Mr. F. W. Lanchester, experimenting with gliding 

 models, and also with an aerodynamic balance (similar to 

 that designed by Ritter von Loessl), obtained various 

 results. 



Na'ure of surface 

 Mia 



Varnished cedar 

 Polished ,, 



>» >« 



Glass paper ... 



Method 

 Gli'^ing angle of models 



I'f vrtiiable area 



Gliding angle of model .. 



Ballasted aeroplane 

 Aerodynamic balance 



Coefficient 



ooocor? 

 0000016 

 0000019 

 0-000005 

 o "000008 

 o 000013 



6 )o'oooo78 



Mean value for moderately smooth surfaces o "00001 3 



Yl.— Collected Results. 

 I. From the resistance of dirigibles 



II. TurnbuU's observations 



III. Hydrodynamic theory and Froude's 

 observations of water 



IV. Zahm's observations 



V. Lanchester's observations 



00000 1 7 

 0-000015 



0-000017 



O-OOOOIO 



0-000013 



General mean 



5 ) 0-000072 



... 0-000014 

 Herbert Chatley. 



BIOLOGY OF THE EEL-FISHES, ESPECIALLY 

 OF THE CONGER. 



DURING the Atlantic and Mediterranean cruises of the 

 Danish research steamer Thor, in the winter of 

 1908-9 and summer of 1910, a very large material has been 

 collected of the larvae of the eel-fishes (Leptocephah), 

 These belong to at least twelve different forms, and several 

 of them can be referred to their parent species. 



The material is specially rich in a few of the forms, and 

 this permits of important conclusions being drawn with 

 regard to the biology of these species. At the same time, 

 it has yielded valuable information regarding the occur- 

 rence of the very youngest stages (pre-Leptocephali)— 

 information which has long been desired and sought after ; 

 and, lastly, it has aided us in the determination of the age 

 of the older Leptocephali, a question which the hitherto 

 available information has been quite unable to settle. 



The species of eel which is of the greatest practical 

 interest in Great Britain is the Conger, and of this we 

 have now a very large and complete material. Several 

 hundred specimens have been taken— in all stages, from 

 a length of onlv 9 mm. up to ca. 160 mm. 



The larvze are not difficult to determine, in part 

 the number of myomeres, which in ten specimens I 

 found to vary between 153 and 159, thus quite the same 

 as in the adult Conger ; below 35 mm. the most posterior 



from 

 have 



