219 
/ and /, the difference of these parameters, if they refer to the 
same moment, being constant, viz. =d. For points of the Zand Z, 
curves, which have thus simultaneously arisen, the two abscissae 
cl and c/' will, therefore, always differ by the same amount, viz. cd. 
The initial points of the curves are such points that have arisen 
simultaneously '); we have, therefore, only to measure their abscissae 
taken to the found zero points on the axes, and to take the diffe- 
rence between them to find ed. 
When in the graphically found functions I and II we choose the 
variables equal, i.e. when we measure equal portions cl and el! 
on the axes from the points MN and N' (hence independently of 
the earlier meaning of / and /'), we find from equations (21) and (22): 
my 
2 [i (m)dos 4 ce lmdm= fl (el) 2 2. «1 (28) 
my 
2 fx (m) sin 4x lm dm = — flI(cl) . . . . (24) 
At first our intention was to solve C'(l) and S(/) from equations 
(4) and (13), and substitute them in (7). This would come to the 
same thing as the introduction of C(l) and S(/) into equations (23) 
and (24), in order to determine them from this, and substitute them 
in equation (7). The same result, the formula for p(«), can be 
reached more quickly by the consideration that according to Fourigr’s 
integral theorem 
ro + oo oo 
1 Ff 
p(z) = x(m) == fom am aefn (5) cos Sa dE + „en am afs (5) sin Sa da, 
0 — 00 0 at oo 
When we now choose m for §, and put ¢—4a/, and when we 
besides consider that y(m)=O for m,<m<m,, the equation 
reduces to: 
my 
oo My oo 
x (mn) = es 4 lm a fzo cos 420 lm dm 4- 4 fin 4a Um anf (m) sin 40 lm dm. 
0 
ma 0 ma 
Making use of equations (23) and (24), we may replace these by: 
Go 
y(n) TAL (cl) cos Aar lm dl — 2f | LL (cl) sin Aar Im dl. 
0 
As we only try to find the shape of the curve y, we may put 
1) The light may also be suddenly intercepted for a moment. 
15 
Proceedings Royal Acad. Amsterdam. Vol. XXII. 
