Measurement of Mechanical and Electrical Forces. 



93 



quantities of which the error3 themselves are small. The 

 geometrical representation (fig. 15) makes this clearer. The 

 two sets of errors may be considered as ordinates of two 

 curves drawn to the same abscissa. The point p, where the 

 curves intersect, corresponds to that inclination at which the 

 two errors are made equal, and the origin to the central 

 position. Since both errors are of a kind which are inappre- 

 ciable at first, the two curves will have the axis of x as a 

 tangent : and since the two errors are of a kind which grow 

 in the same kind of way, i. e. at first slowly, and at an increa- 

 sing rate as they grow, the curves must be nearly similar ; 

 and since they have the common point p, they must be nearly 

 identical. The distance between the curves at any part gives the 

 actual error there: and this being small in comparison with the 

 ordinates at that part, is inappreciable in comparison with the 

 whole distance of that part from the line z z. In the parti- 

 cular case the ordinate p m is about 4 per cent, of p Q; so the 

 actual error may be safely neglected. But, finally, should 

 there be any error that can be detected at all, such error may 

 be almost entirely eliminated by putting a few extra turns of 

 wire near the ends or the middle of each half of the movable 

 solenoid, according as the curve of the magnetic error between 

 and p is below or above the curve of the versed-sine error. 



Assuming the truth of what is stated in the last paragraph, 

 we find the tangent of the inclination proportional to the rate 

 at which energy is being expended. But the speed of rotation 

 of the cylinder is proportional to the tangent of the inclina- 

 tion; therefore the number of turns of the cylinder, given by 

 the counting-mechanism in the box over the cylinder, is a 

 measure of the total energy expended. As in the other energy- 

 meter, so in this, if the electric current is helped at any time 

 instead of being used, then the integrating-cylinder will turn 

 the other way, and take off from the record an amount which 

 is a measure of the work expended on the current. 



There is a point about the solenoid energy-meter which is 

 worthy of notice. The movable solenoid has an equal number 

 of turns in opposite directions; so it is independent of the 

 magnetic field in which the instrument is placed, and so this 

 meter may be used in workshops or near dynamo-machines 

 without its action being interfered with. For the same reason, 

 when used in houses as gas-meters are for gas, it will be im- 

 possible for the householder to tamper with its indications by 

 placing magnets round the instrument. 



"When very powerful currents are employed, it is well to 

 shunt a certain proportion of the main current past the meter, 

 or, when the electromotive force is very great, to introduce 



Phil. Maq. S. 5. Vol. 13. No. 79. Feb. 1882. I 



