xx.] METHOD OF VARIATIONS. 445 



Collective Experiments. 



There is an interesting class of experiments which 

 enable us to observe a number of quantitative results in 

 one act. Generally speaking, each experiment yields us 

 but one number, and before we can approach the real 

 processes of reasoning we must laboriously repeat measure- 

 ment after measurement, until we can lay out a curve of 

 the variation of one quantity as depending on another. 

 We can sometimes abbreviate this labour, by making a 

 quantity vary in different parts of the same apparatus 

 through every required amount. In observing the height 

 to which water rises by the capillary attraction of a glass 

 vessel, we may take a series of glass tubes of different 

 bore, and measure the height through which it rises in each. 

 But if we take two glass plates, and place them vertically 

 in water, so as to be in contact at one vertical side, and 

 slightly separated at the other side, the interval between 

 the plates varies through every intermediate width, and 

 the water rises to a corresponding height, producing at its 

 upper surface a hyperbolic curve. 



The absorption of light in passing through a coloured 

 liquid may be beautifully shown by enclosing the liquid in 

 a wedge-shaped glass, so that we have at a single glance 

 an infinite variety of thicknesses in view. As Newton 

 himself remarked, a red liquid viewed in this manner is 

 found to have a pale yellow colour at the thinnest part, 

 and it passes through orange into red, which gradually 

 becomes of a deeper and darker tint. 1 The effect may be 

 noticed in a conical wine-glass. The prismatic analysis of 

 light from such a wedge-shaped vessel discloses the reason, 

 by exhibiting the progressive absorption of different rays 

 of the spectrum as investigated by Dr. J. H. Gladstone. 2 



A moving body may sometimes be made to mark out 

 its own course, like a shooting star which leaves a tail 

 behind it. Thus an inclined jet of water exhibits in the 

 clearest manner the parabolic path of a projectile. In 

 Wheatstone's Kaleidophone the curves produced by the 

 combination of vibrations of different ratios are shown by 



1 Opticks, 3rd edit. p. 159. 



2 Watts, Dictionary of Chemistry, vol. iii. p. 637. 



