374 RECENT PROGRESS IN PHYSICS. 



Hook's universal joint, while the position of the moveable beam is 

 observed at the same time by the microscope. In this manner the 

 most accurate readings are possible. It would have been of advan- 

 tage to those about to construct such an instrument, if the author 

 had given, with his other drawings, a section through the upper part 

 of the apparatus. 



If the greatest possible care has been taken in the construction of 

 all the separate parts, and, above all, when the moveable beam, as 

 well as the handles of the proof planes, or knobs introduced into the 

 apparatus, are insulated as perfectly as possible, very great accuracy 

 in measuring may be expected. The torsion balance, however, is a 

 contrivance which is not altogether adapted to lecture experiments, 

 its principle is sufficiently well known, and the detailed description 

 of the instrument interests only the few who are practically engaged 

 in measuring the density of electricity. For this reason, I do not con- 

 sider it necessary to dwell further upon the subject here. 



With reference, however, to the method of observation and compu- 

 tation of the results, something may be given from Riess's memoir. 



To determine the ratio of two electrical densities at a and h, exist- 

 ing at the same time upon two parts of one conductor, or upon two 

 conductors. Coulomb made a whole series of measurements (generally 

 five) alternately for each place, and as nearly as possible, in equal in- 

 tervals of time. In this manner he obtained, for the first place, three 

 densities, (measured by the angle of torsion at equal elongations of 

 the balance beam,) a, a', a" ; and two values for the density in the 

 other place, h and l' . The measurement of 6 was made between those 

 of a and a' ; and that of a' , between those of h and h' ; thus the mean 

 of a and a! could be considered as nearly simultaneous with b ; the 

 mean of b and b' with a' , &c. The required ratio ot the two densities 

 is expressed by 



i (g - f- a'), or a' or (| a' + a!'). 



6 iWTVh h' 



The mean of these three values is then taken as the true ratio, x of 

 the two densities. This method requires great skill ; for it is not 

 always easy to make the alternate measurements of density at equal 

 intervals, besides exact results cannot be obtained if the two places 

 examined are on two different bodies, one ot which loses its electricity 

 more rai)idly than the other, for then the ratio of the two densities 

 changes at every succeeding moment ; hence the three quotients are 

 no longer three values of the same quantity, differing only in conse- 

 quence of unavoidable errors of observation, but three essentially 

 difi'erent quantities, and the mean from the values of the three quo- 

 tients ,_ consequently, does not give the true ratio of the two electrical 

 densities at any one moment. 



Indeed, this method is not at all applicable where the same density 

 cannot be determined twice as when the existence of the density b de- 

 pends upon an alteration of the density a, a return to which is there- 

 fore impossible. 



liiess employed the following method of observing with success, 

 with two perfectly equal proof balls, having equally well insulated 



