478 



disturbance, we know obeys a solar diurnal law ; and if independent 

 of lunar action, a sufficiently large series of observations might suffice 

 to eliminate it, as combining with and forming part of the regular 

 solar diurnal variation. If, however, the series is not very large and 

 the irregular disturbance considerable compared with the variation 

 sought, it may be desirable to omit or modify the marked irregu- 

 larities. 



As regards the first assumption referred to above, the results 

 obtained hitherto seem to show the error to be small, and the only 

 way to determine its amount will be to consider it zero in the first 

 instance, and thereafter a more accurate calculus may be employed. 

 For the second assumption, it is certain that the solar diurnal law 

 varies considerably in some cases within a lunation. At the mag- 

 netic equator, for example, the law of magnetic declination is inverted 

 within a few weeks near the equinoxes. The attempt to correct the 

 error due to considerable change in the solar diurnal variation by 

 taking the means, as has been done, from shorter periods than a 

 lunation, is liable to the serious objection that the resulting hourly 

 means are affected unequally by the lunar action, so that the sums 

 (A) take the form, 



where the second term in each expression is a variable. In the 

 discussion to which I am about to allude, the following plan has been 

 followed. The hourly means for the following series of weeks were 

 taken, namely 



m l from 1st, 2nd, 3rd, and 4th weeks of the year. 

 m 2 2nd, 3rd, 4th, and 5th 



m 3 3rd, 4th, 5th, and 6th ,, 



The means of m l and m 2 were then taken as normals for the 3rd 

 or middle week, of m 2 and m 3 as normals for the 4th week, and so 

 on : these means were then employed for the differences from the 

 corresponding hourly observations of the weeks to which they 

 belonged. 



With reference to the irregular effect, it is evidently desirable that 

 we should know in the first instance whether it may not be a function 

 of the lunar, as well as of the solar, hour- angle ; for this end it is 



