loS 



NA rURE 



[November 30. 1899 



be measured by attaching the surface to 'a small truck 

 which is allowed, to descend an inclined plane under 

 gravity. If there were no resistance to motion the 

 square of the velocity at ciny point would be equal to 

 ^wice the product of the vertical height fallen into the 

 acceleration of gravity, but since friction and atmospheric 

 resistance retard the motion, and the latter resistance 

 increases with the velocity, the truck soon acquires its 

 terminal velocity, and in the uniform motion which 

 follows, the total resistance is equal to the weight of the 

 moving body resolved down the plane. By experimenting 

 with the truck alone, the resistance experienced by it can 

 be obtained separately, and by subtraction the portion of 

 the resistance due to the surface under observation is 

 found. 



This method forms the basis of M. Canovetti's ex- 

 periments. Instead, however, of an inclined plane, a 

 copper wire was employed, three millimetres in diameter 

 and 370 metres in length, of which one end was fixed on 

 the side of a hill, and the other on the level ground at its 

 base. This arrangement is similar to that used in many 

 countries where bundles of wood are sent down from the 

 hills by means of a wire. Owing to the wire hanging 

 in a catenary, the lower part of the wire was much less 

 steeply inclined than the upper, the wire even sloping 

 upwards near its lower extremity. For this reason 

 Canovetti did not take into account the last ninety 

 metres of the path. 



The mode of suspending the various surfaces by a 

 trolley is shown by the accompanying figures. The 

 wheels of the trolley were provided with ball bearings. 

 In order to determine what part of the resistance was due 

 lo the trolley itself, the latter unloaded was allowed to de- 

 scend a wire at an inclination considerably smaller than 

 that employed when it carried one of the surfaces, the 

 smaller resistance of the unloaded trolley rendering a re- 

 duction of the gradient necessary in order that the 

 resistance might be calculated under similar conditions 

 as to velocity. The experiments indicated that the re- 

 sistance of the trolley alone was proportional to the 

 velocity. 



In determining the velocity, Canovetti contented 

 himself with reading on a chronometer the instant of 

 starting the trolley and the instant at which it passed a 

 mast placed 90 metres in front of the stopping point. By 

 dividing the 280 metres traversed by the time occupied 

 between the two readings, the average velocity of descent 

 was obtained, and this average velocity formed the basis 

 of Canovetti's conclusions. 



The most interestmg of these results are those referring 

 to the relative resistances of circular and rectangular 

 planes, and the effects of attaching a cone or hemisphere 

 to a circular disc forming a bow or stern. Canovetti 

 finds that the resistance of the air on an area of one 

 square metre moving with a velocity of i metre per second 

 is 90 grammes for a rectangle and 80 grammes for a 

 circle. 



A right cone, whose altitude is 1-5 times the diameter 

 of its base, attached to the rear face of the circle reduces 

 the resistance to 60 grammes. 



A hemisphere placed in front of the circle as a prow 

 (Fig. i) reduces the resistance to 22"5 grammes. 



Finally, in a double cone, formed by placing a cone of 

 altitude double the diameter of the base in front of the 

 circle, and a cone of altitude equal to the diameter of the 

 base behind (Fig. 2), the resistance is reduced to 15 

 grammes, or less than a fifth of the original resistance. 



Canovetti made a series of further experiments on 

 solids resemblmg in form the Chalais balloon by sus- 

 pending a cone and hemisphere, joined by their bases in 

 a net (Fig. 3). In one of these observations the resistance 

 was equal to 80 grammes. This high resistance was due 

 largely to the net, but also in part to the instability of 

 motion, which caused the whole model to undulate. In 



NO. 1570, ^'OL. 61] 



proof of this latter influence experiments were separately 

 made on models rigidly attached to and freely suspended 

 from the trolley. By taking a model formed of a cone 

 and hemisphere, and attaching it to the trolley by rigid 

 supports fixed one near the common base and another near 



the vertex of the cone, a coefficient of resistance equal to 

 one-seventh of that of the corresponding circular disc 

 was obtained. 



To sum up, then, Le Dantec's experiments appear to 

 have been conducted with every precaution to secure 



Fig. 2. 



accuracy. The coefficient of resistance which he calcu- 

 lates from determinations made in a room from which 

 draughts are carefully excluded must be regarded to some 

 extent as the limiting value of a physical constant ob- 



tained under conditions which are difficult to realise in 

 practice. We may compare such determinations, e.g. with 

 the determination of the weight of a cubic centimetre of 

 absolutely pure water, since in all probability a large 



