324 PHILOSOPHICAL TRANSACTIONS. [aNNO 17 17. 



slowness of its motion made me at that time conclude that it had none, and 

 that it was rather a nebula than a comet. 



However, suspecting that it might have some motion, I attended the next 

 night, June 11, at the same hours, when with some difficulty, by reason of 

 the thickness of the air, I found the two little stars, but the nebula could 

 not at that time be seen, which I then imputed to the want of a clearer sky. 

 But on Saturday, June 15, the moon being absent, and the air perfectly clear, 

 I had again a distinct view of the two stars, with an entire evidence that there 

 remained no sign of it in the place where we had first seen this phenomenon, 

 which we therefore now found to be a comet; and that being far without the 

 orb of the earth, and in itself a very small body, it appeared only like a small 

 Speck of a cloud, such as would scarcely have been discerned in an ordinary 

 telescope, much less by the naked eye. 



An Account of Books, viz. 1. Joannis Poleni in Gymnasio Patavino Phil. 

 Ord. Prof, et Scient. Societatum Regalium, quce Londini et Berolini sunt, 

 Sodalis, De Motu Aqua mixto, Lihri duo, &c. 4to. Patavii 1717. N° 354, 

 p. 723. 



The subject here treated of not having hitherto fallen under the consideration 

 of mathematical writers the author is obliged to make use of several terms, 

 which are either wholly new, or at least are applied in a sense somewhat differ- 

 ent from their common acceptation; for which reason he begins his work with 

 a set of definitions. 



Next follows a short history of the original, and progress of the doctrine of 

 running waters, the invention of which our author justly ascribes to the learned 

 Castelli, and defends him agahist Fabretti, who has maintained that Castelli's 

 fundamental proposition of the quantity discharged being cseteris paribus in 

 proportion to the velocity, was known, and publicly taken notice of before 

 him by Frontini. The author allows Castelli to have been mistaken in deter- 

 mining the velocity of water running out at the bottom of a vessel, he having 

 asserted that velocity to be as the depth of the water, instead of the root of 

 that depth. 



Three years after Castelli's book came out, this mistake was corrected by 

 the famous Torricelli, who was the first that maintained, that the velocity of 

 the water running out was in a subduplicate ratio of the depth ; but gave no 

 demonstration of it. This proposition, says our author, was confirmed by the 

 experiments of Maggiotti, Mariotte, and Guglielmini, and has since been de- 

 monstrated by M. Varignon, by Herman in his Phoronomia, and John Ber- 

 nouilli, as reported by Herman in the Acta Lipsiensia. 



