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IX. A new Method of computing the Value of a slowly con- 
verging Series , of which all the Terms are affirmative . By 
the Rev. John Hellins, F. R. S. and Vicar of Potter’s-Pury, 
in Northamptonshire. In a Letter to the Rev. Dr. Maske- 
lyne, F. R. S. and Astronomer Royal. 
Read March 8, 1798. 
REV. SIR, Potter’s -Pury, February 8, 1798. 
That several of the most curious and difficult problems in 
physical astronomy have hitherto been solved only by means 
of slowly converging series, is a truth which you are well ac- 
quainted with, and which may be seen in the works of the late 
learned Euler, and others, on that subject. Of this kind of 
series is the following, viz . ax + bx'+cx 3 +dx*+ &c. ad 
infinitum , when all the terms are affirmative, and a , b, c, &c. 
differ but little from each other, and x is but little less than 
1 ; to obtain the value of which, to seven places of figures, by 
computing the terms as they stand, and adding them together, 
is a very laborious and tiresome operation ; and therefore some 
easier method of obtaining it is very desirable. About five 
years ago, the consideration of this matter was recommended 
to me by Mr. Baron Maseres, (who not only employs his own 
leisure in explaining and improving the higher parts of the 
mathematics, but also encourages others who make the same 
laudable use of their leisure,) to whom I then communicated 
the method of computation explained in the paper inclosed in 
