436 OF CAPILLARY ATTRACTION AND THE COHESION OF FLUIDS. 



in : rp : : rq : ts ; 

 but by the property of similar triangles, it is 



Er : E : : rq : ts; 

 consequently, by the equality of ratios, we obtain 



Er : E : : tn : rp, 

 and by equating the products of the extreme and mean terms, it is 



vrXrp = EtXtn. (320). 



Now, according to the principles of conic sections, we have it, that 

 in the common or Apollonian hyperbola, if the abscissae be estimated 

 from the centre along the asymptote, the corresponding ordinates are 

 to one another inversely as the abscissae ; hence it is manifest, that 

 the curve which the surface of the elevated fluid traces on the plates, 

 is the curve of a hyperbola, whose properties are indicated by equation 

 (320). 



553. Such then is the theory of capillary attraction, in so far as it 

 is necessary to pursue it; but we shall just remark in passing, that 

 other fluids, such as alcohol, spirit of turpentine, oil of tartar, spirit 

 of nitre, oil of olives, and the like, are elevated in the same manner 

 as water, but to a less degree ; thereby showing that the affinity of 

 glass to water, is greater than its affinity to any other liquid. 



Again, on the other hand, some fluids are depressed by the action 

 of the capillary force, such as mercury, melted lead, and indeed all 

 the metals in a state of fusion, are more or less depressed, according 

 to their density or specific gravity ; but an inquiry into the quantity 

 of depression in this place, would lead to nothing new or interesting, 

 and as a subject of practical utility, it is altogether unimportant ; we 

 therefore pass it" over, and hasten to lay before our readers a detail 

 of the experiments performed by the celebrated M. Monge, on the 

 approximation and recession of bodies floating near each other on the 

 surface of a fluid. 



The following are a few of the principal experiments that have been 

 made on this subject. 



554. EXPERIMENT 1. If two light bodies, capable of being wetted 

 with water, are placed one inch asunder on its surface, in a state of 

 perfect quiescence, they will float at rest, and experience no motion 

 but what is derived from the agitation of the air ; but if they are 

 placed apart only a few lines, they will approach each other with an 

 accelerated velocity. 



Also if the vessel be of glass, or such as is capable of being wetted with 

 water, and if the floating body is placed within a few lines of the edge 

 of the vessel, it will approach to the edge with an accelerated velocity. 



