II. 



ELECTKICAL RHEOMETKY. 



55 



The sources of error are very numerous, and what is worse, they have a great 

 influence on the results ; an error of half a degree in the first and less deviation, 

 which is the fundamental one, may alter the proportions at least one-tenth, and I 

 have found that the difference of the radii in the different rings which compose the 

 circle of eight, may have an influence on the hundredths of the above proportion. 



From the short experiment which we have before us in the precediug table, we 

 may perceive how rapidly the force of the current must increase in order to cause 

 a corresponding increase in the deviation of the needle. I have made a first trial 

 of a table of proportional degrees, which can be used for a circle and needle of the 

 dimensions above given. I have taken for unity the force that produces a deviation 

 of 10°, and I calculated some of the most remarkable positions of the needle, which 

 I have marked with asterisks in the following table. The other numbers are de- 

 duced from the graphic construction founded on the numbers resulting from the 

 calculus. 



Table of Proiiortional Degrees. 



Degrees. Forces. 



10° 1.* 



13 1.4* 



20 2.0 



25 2.7* 



30 3.6* 



35 4.7 



40 5.9* 



45 7.9* 



50 10.45 



55 12.6 



60 16.96* 



65 18.6 



70 23.38* 



80 50.05* 



81 56.00*0 



The last numbers show the very rapid increase, which we have already men- 

 tioned. It is clear that this table can be used for every compass of tangents in 

 which the proportions of the length of the needle to the diameter of the circle are 

 such as has been supposed here, viz., as 1 to 2.18. 



It remains, finally, to be seen whether the theory hitherto assumed by the philo- 

 sophers about the compass of tangents is exact or not. It is taken for granted in 

 this instrument that the intensity of the forces is in proportion to the tangents of 

 the deviations produced. This is the same as supposing that in the formula {in, § 7) 

 the function / (c, d) which multiplies the quantity /.; is constant. Now, on com- 

 paring the values of/ (c, d) obtained in the case of the needle placed in the centre, 



(') I haye made, by means of this compass, the comparison of various kinds of voltaic batteries. 

 the appendix, I shall give the results of their relative forces to be calculated by this table. 



In 



