6 Transactions of the Society. 



amplitude, and consequently show negative values for the cal- 

 culated amplitude in certain parts of the light curve. For the 

 mere determination of relative magnitudes this is unimportant, 

 since semi-amplitudes must have the same proportions inter se that 

 the corresponding amplitudes have. But when we go further and 

 ask what is the resulting amplitude if two adjacent and isophasal 

 antipoints encroach the one upon the other, it then becomes im- 

 portant to realise that the negative values in Airy's curve do not 



-3 A 



2 siu u 



-2 A 



2 sin u 



-K 







Fig. 2. 



2 sin u 



2\ 



2 sin u 



3A 



2 sin a 



count against the positive. The coincident amplitudes have then 

 to be compounded according to the relative retardation of the one 

 as compared with the other ; whether expressed as positive or nega- 

 tive quantities on Airy's curve makes no difference for this purpose. 

 The following diagram will make this clear. Here, in fig. 3, we have 

 the full amplitude curve of the " false disc," and it will be observed, 

 that at every point it has a positive and a negative half, each equal 

 in point of mere magnitude to the other. Hence the full ordinate 

 is in this curve proportional at every point to Airy's ordinate, but on 

 the other hand no one has either a positive or a negative value, and 

 any two may be compounded indifferently either by addition or by 

 subtraction. This corresponds to nature, for, in fact, two ordinates 

 are to be compounded by addition when they have a phase difference 

 of n X, n being any integer, and [are to be compounded by sub- 



