598 
PHILOSOPHICAL SOCIETY OE WASHINGTON. 
the assurance of our sincere condolence with them in the affliction they 
have suffered. 
Mr. G. W. Hill read a paper on The Disputed Mass of Titan. 
This paper was published in full in No. 176 of the Astronom¬ 
ical Journal, Boston, July, 1888, under the title The Motion of 
Hyperion and the Mass of Titan. 
Mr. Ormond Stone also made a communication on the same 
general subject, the title of his paper being The Orbit of Hyperion. 
The following is an abstract of this paper-: 
[Abstract.] 
A pure ellipse having a mean longitude equal to three times the mean 
angular distance of the radius vector of Hyperion from that of Titon was 
taken as an intermediate orbit. The difference between the equations of 
motion for the intermediate orbit and those for the disturbed orbit gave 
new equations, which were solved by indeterminate coefficients. An ap¬ 
proximate solution gave for the mass of Titan ¥ dir times that of Saturn. 
The following paper on Problem-Solving was read by Mr. A. 
Hall : 
Every one who has a taste for mathematical studies must have had 
some experience in solving problems. That this is a good exercise for a 
beginner no one can doubt. Such practice serves to clear his ideas, to show 
the power of theory, and to give confidence. Two centuries ago, when 
the differential calculus was coming into use, it was common among mathe¬ 
maticians of the Jirst rank to propose questions to each other, and these 
questions or challenges had an important influence on the progress of 
mathematics. Thus the modern theory of probabilities had its origin in a 
question proposed to Pascal by one of his friends, the Chevalier de Mere, 
who having failed to solve a question in gaming declared with a high tone 
that arithmetic was crazy and lied. “ He has,” says Pascal, “ a very good 
mind, but he is not a geometer, which is a great defect.” The questions 
proposed were nearly always such ^s involved the consideration of a 
principle, and thus the study of them was fruitful. Another example is 
that of the pendulum. The simple pendulum having been discovered by 
Galileo, Huygens undertook to solve the problem of the compound pendu¬ 
lum. He obtained a correct result, but his assumptions and arguments 
were doubted and criticised. At length Janies Bernoulli gave the correct 
formal solution, which afterwards led to a’ great extension of the theory 
of dynamics. Such questions are worthy the labor of the ablest men. 
There are still questions of this nature that are under discussion, and the 
followers and representatives of the former investigators of the higher 
problems are our present writers on applied mathematics. 
