MATHEMATICS: WEBSTER AND FISHER 
79 
by Silvester in 1912 (lantern slides), while in 1915 Job demonstrated similar permanent con- 
nections in rodents. Thus the study of the development of the lymphatic system affords 
an explanation of anomalies involving connections between the lymphatic vessels and both 
the renal veins and the inferior vena cava. 
The statement has repeatedly been made that hygromata which at the first 
tapping have yielded a clear fluid may be found at all subsequent tappings to 
contain more or less blood. Only one explanation has been offered for the 
presence of the blood, viz., trauma of the wall of the cyst. This explanation 
has always seemed to me an unsatisfactory one because the walls of these cysts 
are as a rule very thin and non-vascular. May it not, in view of the findings 
in our case, be possible that vestigia of lymphatico-venous communications 
are responsible for the admixture of blood which has occasionally been noted 
at only the second and subsequent tappings of lymph-cysts and is more 
frequently found at the first tapping? The negative pressure consequent upon 
the aspiration of fluid from the cyst might divert for the moment a little 
blood from the vein which had given origin to the hygroma's lymphatic bud 
or vessel. Thus the contents of the sac, clear at the first withdrawal, would be 
blood stained at the second. Thereafter, with each tapping blood would be 
aspirated into the sac and hence clear fluid might never again be obtained. 
^ The relation of the cyst to the right adrenal gland was remarkable. In the course of 
stripping the sac's final delicate attachments we exposed a fiat, black surface, evidently the 
spread-out medulla of the adrenal, about the size of a half dollar. Parenchymatous oozing 
from this surface required for its arrest a few mattress sutures of fine silk. 
2 The patient recovered promptly and has enjoyed excellent health since the operation. 
TABLES OF THE ZONAL SPHERICAL HARMONIC OF THE SECOND 
KIND Qi{z) AND Qi'{z) 
By a. G. Webster and Willard Fisher 
Ballistic Institute, Clark University* 
Communicated, January 9, 1919 
In connection with certain investigations that I was asked to make with 
regard to submarines it seemed convenient to have tables of the zonal harmonic 
of the second kind. These are desirable in various problems in mathematical 
physics connected with ellipsoids of revolution, such as problems in mag- 
netism. Failing to find such tables in the literature of the subject, I requested 
Dr. Fisher to calculate tables of the function of the first order and its deriva- 
tive for an interval that will be sufficient for most practical problems. Dr. 
Fisher has now left the country, and the stress of other work that prevented 
their publication being over, I trust that they may be available for peaceful 
purposes. — A. G. W. 
* Contribution from the Ballistic Institute, Clark University, No. 1. 
