94 U. S. COAST AIS^D GEODETIC SURVEY. 



the epoch of u^ becoming 2°, while the average net difference for the 

 aniphtucle of v^ remains unchanged. 



Although there is a fairl}" good agreement indicated by the average 

 differences, it is evident that the inferred constants, especially the 

 epochs, can not, in general, be depended upon for any high degree of 

 refinement. It may be stated, however, that for components with 

 very small amplitudes the epochs as determined from actual observa- 

 tions may be ec[ually unreliable. A comparison of the epochs of 

 several of these small components as determined from series a year 

 in length, with the mean epochs as determined from many years, 

 indicated as much uncertainty as was found among the inferred 

 results. Fortunately, these large probable errors in the epochs are 

 found only in the components with very small amplitudes and are 

 therefore of little real practical importance. 



Form 452 (figs. 30-31) is designed for inference of certain constants 

 in accordance with formulas (345) to (363). The numerical coeffi- 

 cients for the epochs are taken in convenient rounded numbers, since 

 the large uncertainty in the results renders useless an}^ effort to a high 

 degree of refinement. 



Form 452 provides not only for the computation of certain inferred 

 constants in accordance with the given formulas, but also for the 

 compilation of the best-known preliminary values of all the constants 

 that are to be used in the elimination process described in the following 

 section. Of the principal components, the values for M2, Nj, andOi are 

 taken directly as obtained from Form 194, but the values for compo- 

 nents So and Kj may be improved by an approximate elimination of 

 the effects of the components Kg and T2 from the former and P^ from 

 the latter. In a short series the effect of the components upon each 

 other is considerable on account of the small dift'erence in their speeds. 



Let 



yi = A cos (at + a) (364) 



.and 



y,=B cos {ht + , 3) (365) 



represent two components, the first being the principal or predomi- 

 nating component and the latter a secondary component whose eff'ect 

 is to modify the amplitude and epoch of the principal component. 

 The resultant tide will then be represented by 



y = y^ -}- 2/2 = A cos {at + a)+B COS (bt + .5) (366) 



Values of t which will render (364) a maximum must satisfy the 

 derived eciuation 



^asin (a^ + o:)=0 (367) 



and the values of t which will render (366) a maximum must satisfy 

 the equation 



Aa sin {at + a)+Bh sin {U + ,3)=Q (368) 



For a maximum of (364) 



1 = ^^-1^^^^ (369) 



a 



in which n is any integer. 



