100 Professors Ayrton and Perry on 



vibrations are applicable to circular bars of any cross section, 

 but those from the longitudinal only to bars of small cross 

 section. From a separate consideration of the torsional and 

 longitudinal fixed-free vibrations of a thin circular bar, a 

 discrimination might be made between the effects on the 

 modulus of elasticity and on the rigidity due to definite 

 physical changes. 



By heating up the bar at one end, making that the fixed or 

 free end, and employing (58) and (59) or (65) and (66), con- 

 siderable insight might be gained into the structure. Then 

 allowing the bar to cool and repeating similar observations, 

 the residual effect after any interval might be determined. 

 As to the advantages of determining modification of physical 

 properties by observations on a single bar, remarks similar to 

 those already made will apply. 



By the test of reversion we can also select for our experi- 

 ments a bar originally of great isotropy. 



XIV. The Winding of Voltmeters. By Professors W. E. 

 Ayrton, KR.S., and John Perry, F.R.S.* 



I. npHE use of voltmeters for measuring the potential- 

 J~ difference existing between the mains in electric 

 light circuits, and for enabling us to maintain this potential- 

 difference constant, is so wide in its possible application, that it 

 is unnecessary to dwell on the importance of voltmeters giving 

 accurate indications. Indeed, the sensibility of an incandes- 

 cent lamp is so great (the light, as we have shown in a pre- 

 vious communication to this Societyf, being in many cases 

 proportional to the cube of the potential-difference minus a 

 constant), that it is necessary that voltmeters should record 

 with great accuracy the potential-difference, as well as quickly 

 indicate any changes that from time to time take place in this 

 potential-difference. 



It is therefore desirable to consider what are the most 

 important errors in commercial voltmeters as at present con- 

 structed, and how these errors may be practically diminished 

 or altogether removed. They are : — 



1. An error arising from the sensibility of the voltmeter 

 varying with its resistance, and therefore with its temperature. 

 This change of temperature is due partly to the variation of 

 the temperature of the room and partly to the coils of the 



* Coinmimicated by the Physical Soeiety : read June 13, 1885. 



f " The most Economical Potential-Difference to employ with Incan- 

 descent Lamps/' Proc. Phys. Soc. vol. vii. p. 40 [Phil. Mag. [5] vol. xix. 

 p. 304 (April 1885)]. 



