OF ARTS AND SCIENCES. 



185 



Finally, we have a severe test in the agreement of the values of n 

 computed for parts of the revolution which were not observed. In 

 order to adapt the equations, for example, to successive ten degrees of 

 revolution, the coefficients of the first equation must be multiplied by 

 •jJj?:j — .694, and those of the second equation must be multiplied by 

 ^-a = .556. We shall then have : — 



(1) n = — 18.5 sin a; -J- 4.1 cos a; — 0.1 sin 2 x -J- 0.6 cos 2x; 



(2) n = — 16.2 sin x -j- 5.4 cos x — 1.1 sin 2 x -J- 0.7 cos 2 x. 



Substituting x = 0°, 10°, 20°, &c. in these equations, and com- 

 paring the results, we have the following discordances expressed in 

 millionths of an inch : — 



Number of millionths, 12 3 4 



Number of cases, 5 7 17 3 4 



