[ 5SI ] 
treme circle P be taken away, all the reft being left, 
the interftice f will be taken away, and all the other 
interftices, formed by w circles upon HP, with m 
-circks upon AG, will remain. If again the circle O 
be taken away, befides the interftice f already taken 
away, the two e, f will difappear ; and every circle 
more that is taken away, of thole remaining 
upon HP, from the extremity of the line, two more 
interftices will difappear. If from the row of circles 
HP, the extreme circle H be taken away, the two 
interftices a, will difappear. And if the circles 
Iv, L, M, be taken away fuccelTively, every new 
circle that is taken away, two more interftices will 
difappear, of thofe formed by the two rows AG, HP. 
Again, if the two circles P and H be taken away, 
the three interftices a, will difappear; and 
every circle more that is taken away, from either 
extremity, two more interftices will difappear. Hence 
whatever number of circles be taken away out of 
m circles upon H P, provided they be taken fuccef- 
fively, from either or both ends of the row (and when 
the number of circles upon H P is fuppofed lefs than 
that upon AG, the deficiency muft be at the end, 
not in the middle of the row, otherwife the circles 
remaining would not be in the clofeft arrangement), 
it is evident that the number of interftices which dif- 
appear, of thofe which would be formed by m circles 
upon H P, with 771 circles upon A G, muft be either 
double the number of circles taken away, or lefs 
than the double of that number by i. That is if 
m — a be the number of circles left upon 'HP, the 
number of interftices formed by them, with 771 circles 
upon A G, is left than the number which would be 
2 formed 
