488 Mr. W. A. Price on Petrovitch* s Apparatus for 



The index A is continuously adjusted so as to be always at 

 the water surface. The pencil P describes a new curve on the 

 board. The ordinates of P, Q, R measured from a horizontal 

 axis drawn on the board are a?,y, z respectively. The mean- 

 ings of the quantities p, q, r are seen from the figure. 



If the sectional area at the water level of the B template be 

 4>(g), and of the C template yfr(r), and if the sectional area of 

 the tank is M, we have for any small displacements of the 

 templates 



(j>(q)dq + yjr(r) dr + Mdp - 0. 



Since p=l—x, 



q = x-y, 



r=x—z, 



the differential equation becomes 



<£ {oc—y)d(%—y)-\-'ty (w—z)d(a—z) = M.d&. 



If t be the horizontal distance of the board from any fixed 

 point the equations of the curves b and c may be written 



y=fl (*), Mm/, (0 ; 



and we have 



[+{«-/i(0}+*{*-/i(*)}]*i 



T[#{«-/i(*)}/i'.(*)++{«-/»(*)J/. / W]'*»»Ma»? 



a differential equation connecting the cordinates of P of which 

 the curve aa is a particular solution. A series of such particular 

 solutions is obtained by changing the quantity of water in the 

 tank. 



In the particular form in which the apparatus has been 

 constructed by Prof. Petrovitch, the template C is fixed, so 

 that/ 2 (f) is constant, and/ 2 ' (t) =0. The construction is seen 

 in the figures 2 & 3. The paper is attached to a drum turned 

 by an endless screw. The tank is narrow and the flat tem- 

 plates are placed one behind the other. The level of the 

 water is observed by means of a vertical gauge-glass, on the 

 opposite side of the large wooden block on the top of which 

 the drum is mounted. The vertical rods are the guides for the 

 moving templates, and for the rod which carries the pencil. 



M. Petrovitch shows how the instrument may be used in a 

 number of ways : 



(1) As an integrator. 



(2) As an integraph. 



