TOL. XXXII.] PHILOSOPHICAL TRANSACTIONS 595 



the hands, and grow on them again ; and at the particular provision made for 

 producing these particles in the palms of our hands and bottom of our feet; 

 whereas we do not by far meet with such a quantity of particles constantly pro- 

 duced in other parts of the body; for if we observe those who work much with 

 the back of their hands, we shall not meet with any of that hard skin we have 

 been speaking of, but only a kind of tumour, or rising, as the dry-sheerers, 

 or those who dress cloth, have on their left hands. In short, the manner of 

 the production of these small particles will be a mystery to us, though our 

 hands and feet must be fortified with such a matter, to enable them to support 

 all that force and pressure, which they are obliged to bear. 



Of the Reducing Rational Algebraic Fractions to Simpler Fractions; and of 

 Summing any Terms of Series at equal Distances from each other. By Mr* 

 Abraham Demoivre. N° 373, p. 162. 



This paper by Mr. Demoivre was afterwards enlarged and improved, and 

 made the 1st and 2d books of his Miscellanea Analytica, to which it is proper 

 to refer for the more perfect state of the paper. 



A Defence of the Dissertation of Running JVater, published in the Philos. Trans. 

 N" 355, against the Animadversions of Sig. Pet. Ant. Michelotti. By Dr. 

 Jurin, Sec. R.S. N° 373, p. I79. Translated from the Latin. 



S. Michelotti's animadversions in his book De Separatione Fluidorum in Cor- 

 pore Humano, on a dissertation of Dr. Jurin's on the Motion of Running 

 Waters, published in Philos. Trans. N° 355, are partly owing to his not 

 thoroughly understanding the drift of that dissertation, and partly that some 

 things are not put in so clear a light as they are capable of: to obviate which, 

 the Dr. first explains, what is to be understood by the motion of water running 

 out at a hole in the bottom of a vessel; for, there is a wide difference between 

 the motion, or the quantity of motion of water, running out at a hole in a 

 vessel, which motion is in a compound ratio of the quantity of water running out 

 at the hole in any given time, and of the velocity with which it runs out, and 

 between the motion of the whole quantity of water or cataract of water, 

 descending within the vessel towards the hole, and immediately about to flow 

 out; this motion being in a ratio of the sum of all the products of each particle 

 of water, constituting the cataract, multiplied into their respective velocities. 

 The Doctor observing that one of these motions was often taken for the other, 

 chose to illustrate the latter in his said dissertation, and bring it to a calculation, 

 and apply it to the fluids in animal bodies. 



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