MECHANICAL PRINCIPLES OF FLUIDS. 63 



what will be the pressure on any portion of a base 

 in an oblique position; and hence, by certain mathe- 

 matical artifices which make an approach to the 

 Infinitesimal Calculus, he finds the whole pressure 

 on the base in such cases. This mode of treating 

 the subject would take in a large portion of our 

 elementary Hydrostatics as it now stands. Galileo 

 saw the properties of fluids no less clearly, and 

 explained them very distinctly, in 1612, in his 

 Discourse on Floating Bodies. It had been main- 

 tained by the Aristotelians, thai form was the cause 

 of bodies floating; and collaterally, that ice was 

 condensed water; apparently from a confusion of 

 thought between rigidity and density. Galileo as- 

 serted, on the contrary, that ice is rarefied water, as 

 appears by its floating ; and in support of this, he 

 proved, by various experiments, that the floating of 

 bodies does not depend on their form. The happy 

 genius of Galileo is the more remarkable in this 

 case, as the controversy was a good deal perplexed 

 by the mixture of phenomena of another kind, due 

 to what is usually called capillary or molecular at- 

 traction. Thus it is a fact, that a ball of ebony sinks 

 in water, while a flat slip of the same material lies 

 on the surface; and it required considerable sagacity 

 to separate such cases from the general rule. Gali- 

 leo's opinions were attacked by various writers, as 

 Nozzolini, Vincenzio di Grazia, Ludovico delle Co- 

 lombe; and defended by his pupil Castelli, who 

 published a reply in 1615. These opinions were 



