294 Mr. Jourdain on the Transjinite Cardinal 
wide chain of similar density. Pendulum observations at a 
single station do not tell us whether it overlies an island or 
achain. <A gravimetric survey with pendulum stations at 
every 20 miles is required. 
I have so far been excluding all considerations of height. 
Hixperience has shown that pendulum observations give as a 
rule aresult more closely agreeing with the theoretical result, 
when the station of observation is at a low altitude than when 
it is at a high elevation. The higher the station, the greater 
is the deficiency of the observed force of gravity generally 
found to be. This phenomenon has been explained by the 
hypothesis that extra height is generally compensated by a 
corresponding subterranean deficiency of matter. Hence, 
when observations come to be reduced to sea-level, it is 
almost always found, that the largest negative variations 
occur at the highest stations. Now, when we come to com- 
pare Kalianpur and Usira, the table given by Mr. Fisher 
shows that Kalianpur is nearly 1000 feet higher than Usira ; 
it is therefore a somewhat surprising fact, that the negative 
variation at Kalianpur should not be some two seconds greater 
than the negative variation at Usira. This consideration of 
heights would seem to show us, that the amount of matter in 
the Darth’s crust at Kalianpur i is considerably more than at 
Usira, notwithstanding that the force of gravity when 
reduced to sea-level has the same value at both places. If 
the values of heights are included in the discussion, we find 
that a greater amount of matter underlies Kalianpur than 
any other station in the plains of India. As I stated 
above, Kalianpur is the only pendulum station situated on the 
line of the chain. In the tace of this coincidence, it cannot 
fairly be held that the pendulum results tell against the 
existence of a chain. 
Seeing that the accuracy of the old pendulum results has 
been questioned, and that a new series of pendulum observa- 
tions is about to be commenced, I would beg all those 
» interested in the subject to suspend ‘judgment for the present. 
ah 
Dehra Dun, January 28, 1904. 

XXXIL On ie if Phadeane oe ae une of Newbee 
Classes in General. By Puitie EH. B. Jourpain, B.A., 

¥Y Trinity College, Cambridge”. 
N this continuation of my paperf ‘On the Transfinite 
Cardinal Numbers of Well-ordered Aggregates,” to 
which reference was made in § 10 of that paper, I shall begin 
* Communicated by the Author. + Phil. Mag. vol. vii. p. 61 (1904). 
