52 0)1 ihe Compresnlllity of Water. 

 Fiom equation (5) we get 

 Sin^A = 1 — -+ 1 1 h &c. ; wherefore, 



•^"i 'f 3 ^ 45 ^ 189 ^ 14175 ^ ' ' 



€iii»4^ = -89-18; sin i^ = -8335 ; <;> = 56^ 23'. 

 Again, from the equation —— = 0, or 



- Sin cp log. ^^J^ + 1=0, we get 



1 -f sin ^ cos (p 



Q = cos <^ log. - = —. — - ; 



coiisequ'ently, hecause/ = ^, we have 

 / = 2/ tan 4>. 



And hence, from equations (2) and (3), we deduce 



a = y sin <$ 



z = y sin 1$ tan 4> 



X = 2i/ tan <^ sin^^. 

 When the catenary has a small inclination to the horizon, the 

 pull is very great; because a very great proportional force acting 

 nearly in the horizon is required to sustain any proposed weiglit. 

 It is impossible to stretch the chain in a position perfectly hori- 

 zontal, the force necessary for this purpose being infinitely great. 

 As the angle which the curve makes with the horizon increases, 

 the pull dimipishes more on account of tlie increased inclination, 

 than it increases by the greater length of cliain ; and this dimi- 

 nution goes on till, at 56° 28', the minhnum takes phice. Be- 

 yond this limit, the pull increases contiimaliy, as the length of 

 chain becomes greater. 



A. B. 



VIII. Onthe Compressil'dihj of IVater. i?y Jacob Perkins, 

 Esq, Communicnled by the late Right Hon. Sir Joseph 

 Banks, Bart. G.C.B. P.R.S* 



JjLaving believed for many years that water Was an elastic fluid, 

 I was induced to make some experiments to ascertain the fact. 

 This was done by constructing an instrument which I call a pie- 

 zometer, and which is represented in Plate l,fig. 1. The cy- 

 linder, A, was three inches diameter, and eighteen inches long. 

 The end, B, was made water tight by means of a plate which 

 was soldered firmly to it. At the other end, C, a cap was made 



♦ From tlie Transactions of the Royal Sociotv for 1820, Part II. 



to 



