Slichter—Harmonic Curves of Three Frequencies. 451 
If n and r are prime to each other, this^reduces to 
(n-l)(a-l) {r l)(/3 1) (a-1)03-1) 
2 ” r ~ 2 2 ^ 
If n is prime to both r and s , this reduces to 
(w -l )(g -l) 
2 w 
If n, r and s are prime to each other, there will be no double 
points at all. 
The derivation of these formulas is given in Mr. Comstock’s 
paper, which immediately follows the present one. 
Madison , Wis., Nov . #7, 1897. 
