98 Queries. 
than Blackburn’s pendulum. In this (which will be found 
described in Lord Rayleigh’s “Sound ”) the curves are traced by 
the vibrations of an elastic bar. Take a slip of steel of rectan- 
gular cross section, the sides of the rectangle being very unequal, 
cut it into two parts, and after turning one part about the 
direction of its length through a right angle, let the two pieces be 
again united, so that the plane which contains the smallest 
thickness of one contains the greatest thickness of the other. 
The compound rod, thus formed, is clamped at any point below 
the junction, and, by varying the position of the clamp, the 
frequencies of vibration in the two principal planes may be made 
to bear to one another any desired ratio, a thing impossible if a 
simple rectangular bar alone be used. 
For engraving the curves on glass, I suppose that a writing 
diamond should be attached to the free end. But it seems to me, 
that the resistance produced by scratching the glass would rapidly 
annul the vibrations, and so we should not get a good set of 
figures. I would therefore suggest, that a piece of cardboard or 
paper be blacked with the smoke of burning camphor, and the 
designs traced on this by means of a point attached to the end 
of the instrument. It would be easy, once the designs are made, 
to photograph them on to the glass, orif it be wanted to preserve 
the cards, I believe this may be done by dipping them into balsam 
with benzole. G. H. Bryans 
Queries. 
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365.—Divergent Series.—Can any mathematical reader inform 
me whether a method has ever been discovered for finding the 
sum or value of a divergent series of increasing terms, alternately 
positive and negative—such a series, for instance, as I—2 + 4—8 
+ 16, etc.; Or I — 5 + 15 —35 + 7o — 126 + 210, ete, ? 
Has any zame been given to a series, the differences between 
the terms of which (or the differences between the differences, 
and so on) are in arithmetical progression? For example, 1, 3, 6, 
10; HS, Cte, and 1, 4, 10, 20; 45, etc, Fy SeSe 
