418 Prof. F. Himstedt on the 



(as is elsewhere more fully stated) from the formula 



r=n .V^ 2 , (1) 



in which V expresses the potential of the induction-coils here 

 used towards one another. 



If we take as inducing coil a solenoid with only one layer 

 of wire, in comparison with whose length both its own radius 

 and the dimensions of the inducing coil are insignificant, 

 we get 



V = 47r 2 R 2 K.&.(l + 2a); 

 whence follows : — 



r=i7r 2 U 2 K.b.n(l + 2a) i ^^. . . . (2) 

 v ' tan u x v / 



R expresses here the radius of the solenoid, K the number of 

 convolutions in a unit of length, b the total number of convo- 

 lutions of which the induction-coil consists, and 2a a term of 

 correction which expresses the action of the ends of the 

 solenoid. 



According to the experiments described below, the value of 

 2a was always less than 0*03; so that for the determination 

 of r only the exact measurement of the quantities R, b, n, K, 



and - 2 were taken into account. 



tan «i 



The advantages of this manner of experimenting are that the 

 number of the quantities to be ascertained is a comparatively 

 small one, and that all those quantities are omitted which 

 require great care in their accurate determination. I place 

 under this heading the constants and variations of terrestrial 

 and of rod magnetism, the coefficients of induction of the sur- 

 faces of convolution of the wire-bobbin of many superposed 

 layers, the reduction-factor of the galvanometer, the moment 

 of inertia and logarithmic decrement of magnets in oscillation, 

 and, more especially, the exact determination of the resistance 

 of copper wires which are often not all in the same room, 

 and whose temperature can only be approximated to from the 

 temperature of the surrounding air*. 



All length-measurements in the following treatise were 

 compared with a standard which Privy-Counsellor Forster 

 was good enough to correct at the Normal-Standards Com- 

 mission in Berlin by means of the normal metre standard. 



The measurements of time were carried out by means of 



* Compare Roiti, Nuovo Cim. ser. 8, vol. xv., " Diterminazione della 

 resistenza elettrica di un filo in missura assoluta." 



