A NEW CURRENT WEIGHER, ETC. 533 



the length of the beam is 10 inches (25'4 centime.). A difference in doubled rest- 

 point readings of 7 '9 divisions corresponds therefore to a difference in the mean axial 

 positions of the suspended cylinders of 10 mils (254/ii). In an experiment intended 

 as a check on the expression obtained for the change of force with small axial 

 displacements, the doubled rest-point in a (D + S) experiment was 197*7 in one can 

 and 189 '3 in another, the latter reading being obtained by loading one end of the 

 beam with 10 milligrammea The correct position for maximum force corresponded 

 to a pointer reading of 200'0. In the two experiments the difference in the balancing 

 masses was - 3 milligramme, corresjxHiding to a difference in force of O'OOl, per cent., 

 and from the readings of the doubled rest-points a difference in force of O'OOl, per 

 cent, is deduced. The agreement is satisfactory. It follows that in a determination 

 of current strength the doubled rest-point must not differ from the reading corre- 

 sponding to the position of maximum force by more than 8 divisions if the error 

 introduced by the difference in the positions is to be less than 5 in 1,000,000. When 

 making the observations, the results of which are tabulated in Table XIII., the mean 

 displacement of the suspended coils was always kept within 2 divisions by adjusting 

 the position of one of the riders, and the mean displacement for all the observations 

 is 0'5 division. The greatest error introduced on any occasion was therefore about 

 1 part in 3,000,000. 



We have also to consider the relation between the amplitude of swing and the 

 effective force due to the current. This relation was determined experimentally. In 

 a particular D + S experiment the amplitude of swing was varied from 1 division to 

 28 divisions, but the estimated forces were identical. Other observations confirmed 

 this result, and it was only when the amplitude was very large and the errors of 

 observation great that any difference was observed ; even these differences are of 

 opposite signs and point to the forces being identical. It is certain that within the 

 limits to 28 divisions for the amplitude there is no measurable difference in the 

 effective force. When determining the value of a current the amplitude was in 

 general from 3 to 4 divisions ; there is therefore no correction to be applied for the 

 amplitude of swing. 



The remaining source of error is due to an uncertainty in the value of gravity. 

 No absolute determinations of g have been made at Teddington, and it was 

 necessary to compare the values at Kew and Teddington by pendulum observations. 

 Mr. E. G. CONSTABLE, of the Observatory Department of the National Physical 

 Laboratory, made such observations in March, April, and July, 1905. The pendulums 

 swung were half-seconds pendulums, the property of the Board of Education and 

 used in the " Discovery " Antarctic Expedition. At Teddington two positions were 

 chosen : one was on the concrete block on which the ampere balance stands, and the 

 other was in a lower room maintained at a very constant temperature. At Kew the 

 pendulums were swung in the north room of the small house to the west of the main 

 building. The difference in period of the half-seconds pendulums was determined 



