456 
WILLIAM FERREL. 
“ tides as it has been used thus far in determining the moon’s 
“ mass. The perfection of the tidal theory so as to represent 
“ accurately the results of observations at all tidal stations 
“ and give a correct mass of the moon depends now mainly 
“ upon the study of the shalloTV-water terms.” This deter¬ 
mination of the mass of the moon forms an interesting 
episode in Ferrel’s elaboration of the tidal theor}L His first 
computation of this mass was published in 1871, based on 
the tides of Boston, and is reproduced in chapter Vll of his 
“ Tidal Researches ” (Cambridge, 1874), with extensive am¬ 
plifications relative to the relations between deep-water and 
shallow-water tides. 
This last-mentioned most important work on the tides, 
while summing up Ferrel’s work up to the date of publica¬ 
tion, does not represent all of the minutiae subsequently 
elaborated by him. Besides containing the tidal formulae 
in a form convenient for the use of tidal computers and the 
numerical relations that hold good strictly between the co¬ 
efficients that enter into these formulae, it contains numer¬ 
ous results of special discussions made by Ferrel and out¬ 
lines the work that he still thought necessary and much of 
which he subsequently accomplished. In the concluding 
chapter of miscellaneous phenomena he gives the results of 
his discussion of the tides of Tahiti and, again, of the tides 
in Lake Michigan; these latter, as he was able to show, 
have an actual existence entirely in accord with his own 
tidal theory. From a geodetic point of view his discussion 
of the variation of the mean sea-level at various points 
along the shore of an ocean will always be of value, since 
he shows that in view of the effect of winds and currents 
we have a right to expect permanent differences of the 
mean ocean-level so great as to be easily perceived by accu¬ 
rate levelling operations; in other words, the mean sea- 
levels determined from tidal observations in a moving ocean 
do not coincide with the sea-levels of a stagnant ocean as 
represented by the liquid in the tube of a delicate level. 
Here, also, Ferrel rewrites his earlier results on the tidal re- 
