British Association for the Advancement of Science. 303 



locity. 2nd, A law giving the resistance of the fluid as a function 

 of the velocity and magnitude of a wave propagated through the 

 fluid, according to the law of Lagrange. These two laws compre- 

 hend the anomalous facts, and lead to the following 



Results. 



1. That the resistance of a fluid to the motion of a floating body 

 will rapidly increase as the velocity of the body rises towards the 

 velocity of the wave, and will become greatest when they approach 

 nearest to equality. 



2. That when the velocity of the body is rendered greater than 

 that due to the wave, the motion of the body is greatly facilitated : 

 it remains poised on the summit of the wave in a position which 

 may be one of stable equilibrium ; and this effect is such that at a 

 velocity of 9 miles an hour the resistance is less than at a velocity 

 of 6 miles behind the wave. 



3. The velocity of the wave is independent of the breadth of the 

 fluid and varies with the square root of the depth. 



4. It is established that there is in every navigable stream a cer- 

 tain velocity at which it will be more easy to ascend the river against 

 the current than to descend with the current. Thus, if the current 

 flow at the rate of one mile an hour in a stream 4 feet deep, it will 

 be easier to ascend with a velocity of 8 miles an hour on the wave 

 than to descend with the same velocity behind the wave. 



5. That vessels may be propelled on the summit of waves at the 

 rate of between 20 and 30 miles an hour. 



On a Species of Balance and its Application to the Measurement of 

 Electrical Repulsion. By W. Snow Harris. 



The principle of this instrument depends on the reactive force 

 imparted to two parallel silk threads without torsion, from which is 

 suspended a horizontal needle or other body. If a needle be sus- 

 pended by two parallel and vertical filaments of silk without torsion, 

 equally distant from the centre, its position of rest will be horizon- 

 tal, and in the vertical plane passing through the silk filaments. 

 When the needle is turned through any given angle, the centre of 

 gravity of the mass is raised, so that the needle will, when aban- 

 doned to the force of gravity, continue to oscillate, and will be in 

 the state of a body falling down a small circular arc. Mr. Harris 

 has examined the law of this force imparted to the threads, and finds 

 it as the weight and square of the distance between the threads di- 

 rectly and as the length indirectly, and that it is exactly proportionate 

 to the angle of deflection of the needle. Upon these principles 

 Mr. Harris has constructed a balance, which he exhibited to the 

 Section, and by which he can estimate any forces of repulsion in 

 electricity however small. The instrument is not liable to many 

 difficulties which embarrass the use of the torsion balance, and may 

 be employed with advantage in many branches of experimental 

 physics. 



