491 
moment of R”t” round AH 
= R"t" cos R"U" sin NU" R”. 
And for the refracted ray, 
moment of R’t’ round AH 
= AR'x R't'cos R'U'sin NUR’. 
But we have 
AR! AW sin NW 
cos WR’ cos WR’ sin NR’ 
and, therefore, the moment is 
= R't’ ae cos R’U' sin NU'R’. 
And the vibrations Rt, R’t", R’t’, as before, are as 
sin R’LR':sn RLR': sn RLR’, 
whence the equation given by the principle of equivalent mo- 
ments is precisely that of Theorem 11.” 
Mr. M. Donovan exhibited and described a moveable ho- 
rizontal sun-dial, invented by himself, which shows apparent 
solar time within a small fraction of a minute. 
