ON PLANIMETERS. 523 



It seems to me that we have here a new principle for making inte- 

 grators which might be called linkage integrators ; viz., if we take a linkage 

 and move one point T along a given curve, then any other point T' will 

 describe another closed curve whose area is dependent on that of the given 

 curve. 



As a simple example, take a Peaucillier cell with fixed pole (fig. 18). 

 Give QT a wheel W and QT' a wheel W. We have now two planimeters, 

 OQT and OQT'. If OT=r, OT'=r', then we have always rr'=P, where 

 A,-2=OQ2-QT2. 



If T describes a closed curve, T' describes another, and 



{T)=atv, {T)=aiv', where QT=a 



Al 



SO (T)-=^\r-dd if 6 is the angle which OT makes with a fixed line, and 



)=j,i/«=ip 



(T')=4p«, 



Hence, as T describes a closed curve, T' describes another whose area is 

 fdt) 



r.2 ' 



J 



proportional to - 



If dS denotes an element of the area (T), the last integral becomes by 

 Stokes' Theorem about the conversion of a line- into a surface-integral 



Hence 



2]r' JJr" 



(T')=A;* I — , which is measured by tv' 



The origin must be outside the area (T) to avoid r=0. 



Oil Methods that have been adopted for Measuring Pressures in the 

 Bores of Guns. Bij Captain Sir A. Noble, K.G.B., F.B.8., 

 M.Inst. C.E. 



[Ordered by the General Committee to be printed in extenso.'] 



The importance of ascertaining, with some approach to accuracy, the 

 pressures which are developed at various points along the bores of guns 

 by gunpowder or other propelling agent is so great that a variety of 

 means have been proposed for their determination, and I j^urpose, in this 

 paper, to give a very brief account of some of these means, pointing out 

 at the same time certain difficulties which have been experienced in their 

 employment, and the errors to which these methods have been in many 

 cases subject. 



The earliest attempt, by direct experiment, to ascertain pressures deve- 

 loped by fired gunpowder was that made by Count Rumford in his 

 endeavour to determine the pressures due to difierent densities of charge. 

 He assumed, the principles of thermodynamics being then unknown, that 

 charges fired in a small closed gun-barrel would give pressures identical 

 with those given by charges doing work both on the projectile and on the 



