HARMONIC ANALYSIS!) AND PREDICTION OF TIDES 65 
sin (p—m) 7 cos | w—m) 7 r| 
a. ' BS 4 
sindpusinamu=i 
ae fg CL T 
n 
sin (p-++m) 7m cos [ +m) aay aE r| 
—} == " (270) 
ane 
n s 
es sin (p—m) 7 cos | om) —— r| 
COS @ PU COS @ MW AANA ________-~ 
nel sin 2—™ 5 
nN 
sin (p+m) 7 cos [ @+m) n—Pim | 
Sie epee a marae (271) 
sin T 
pean) sin (p—m) 7 sin | em) i r| 
De SCO ce ee ea 
a7 sin 2 T 
sin (p-+m) = sin | o+m) n—Pe™ | 
i 
sin 1 
n 
194. If p and m are unequal integers and neither exceeds > the 
above (268) to (272) become equal to zero. Thus, 
a=(n—1) 
sina m u=0 
a=o 
a=(n—1) 
>) cosam u=0 
a=(n—1) x : 
>) sinapusinam u=0 (273) 
ase) 
cosapucosam u=0 
ee 
>) sna pu cosa m u=0 
a=0 
195. If p and m are equal integers and do not exceed > formulas 
(270), (271), and (272) will contain the indeterminate quantity 
Bas => and also when p and m each equal > the indetermin- 
Tv 
sin 
sin (p+m)m_ 0 
ate quantity = 
sin oe p 
