88 



Mr. F. J. Smith on a New 



source of error arising from the position of the spring by 

 which the tension of a belt is estimated. 



There are several forms of ergometer in which a fast-and- 

 loose pulley are connected together by Fig. 1. 



a spring b (fig. 1) or springs, and in 

 which any advance of the loose pulley 

 on the fast one extends the springs. 

 Now as long as the springs are very 

 rigid, such as those used in large ergo- 

 meters, there is but little tendency to 

 bulge out as they fly round and assume 

 the position shown at a (fig. 1). But 

 if the springs are suitable for measuring 

 small quantities, then they are not rigid 

 enough to keep their shape while subject to centrifugal force: 

 such deformation introduces serious error into the total result ; 

 it is therefore necessary that the spring be so placed that it is 

 in no way, or but very slightly indeed, affected by centrifugal 

 force. The author finds that this end can be attained if the axis 

 of the spiral be made to coincide with the axis of the moving 

 pulleys. In fig. 2 it will be seen that the spring A is placed 

 in a hollow shaft B 0, part of which E F is in the form of a link 



rig. 2. 



to take the spring. This shaft carries three pulleys ; of these 

 L is loose, G fast, and D is geared to G by means of three 

 mitre-wheels (part of the wheel G is supposed to be removed 

 to show these). The mitre-wheels K and M are provided with 

 flat pulleys, to which the cross bar P is attached by two pieces 

 of strong catgut. By this arrangement any advance of D upon 

 G extends the spring A, a light rod connected to the cross bar 

 moves in the tubular shaft, and the projecting end actuates 

 either a pointer Q, or an integrating apparatus not shown. 

 With regard to the latter apparatus, the most convenient form 

 perhaps is that in which a diagram of the work done is drawn 

 on a sheet of paper attached to a revolving drum, as used in the 

 ergometer of the late Mr. W. Froude and some others. The area 

 of the diagram can be estimated by the well-known method of 



