Memoirs presented to the Cambridge philosophical society on the occasion of the jubilee of Sir George Gabriel Stokes, bart., Hon. LL. D., Hon. SC. D., Lucasian professor.

THE STUDY OF THE PROPERTIES OF CONSECUTIVE INTEGERS. 19
and it is convenient to add the implied condition
~l > (4 (e).
We obtain, for ETalN2cN3a3N4a4,
Q i-.i.4.-1
1 - abeNi. 1 - N 1 Y1b - N4
b ad b2ce
and, eliminating d and e, this is
Q 1
b1 a b-c
which, eliminating c, is
1-\ N1N22N3N4
Q1 b
1-abN. 1 — N2.1 - NN.1-b N1N2N4. 1 - NN2N3N4
and, eliminating a, this becomes
- i1 - N-12N22N3N4
the term 1 - N- NN22N34 disappearing.
This is equal to
I- V'2N'22AI3N4.1 - _2 b
1- NN2 T3N4 AT-YbN. 1 - N1N2 1
(:3 1 2 N1N2N
^ 1l b2NN2N3] - A12N2N3N41- - N 4N N N12N2'N3N4
1 -,. - N11\. 1 - N1NN2. 1 - N1N2N3N4
N1N2N
f b2 1
1 - b2NIN2,3.1 - bN 1 - N -
+>1 -bN.l-.12N1NN4 l-N1N2*1-NN2NN4
3-2