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Answers to Quertes. 175 
required to ascertain when the metal is sufficiently thin. During 
the subsequent separation and sorting of the leaves all draught 
has to be carefully guarded against.— Ze Decorator & Furnisher. 
Answers to Queries. 
385.—Fungus Growth.—It is impossible for any one to give 
the correct name of a fungus without having examined it. I 
might hazard a guess, that, perhaps, the “red points, about the 
size of a small pin’s head on the bark of many trees,” was /Vectria 
cinnabarina. But if W. J. S. will send me a specimen, I shall do 
my best to name it. H.W. Ler MA. 
387.—Pear-Grafting.—I have been successful, and know many 
others who have been the same, in grafting pear-sclons on moun- 
tain-ash stock, Pyrws aucuparvia. But the stock must have been 
planted for at least two years, or there will not be sufficient vigour 
to establish a union. He We, ALE oie Ac 
395.—Infinite Series.—A divergent series cannot have a finite 
sum, and if any method gives a finite value for such a series that 
method must be mathematically incorrect. In the case of the 
series now quoted as an example by F.S.S., the fallacy is obvious. 
The binomial theorem is only true pvovéded the expansion either 
terminates or is convergent. In fact, all that is proved by the 
binomial theorem is this :--IF the series 
1 + mx +n (n—1) x 2! xr +—ad. inf, 
has a definite value, that value is equal to (1+.)z. Whether the 
series as such a definite value depends entirely on whether it is 
convergent. In the case in point the series has no finite value; 
therefore, the binomial theory fails, and we cannot assert that the 
sum of the series is equal to 1/32. Gis: 
396.—Microscope Lamp.—There are many good and conven- 
ient forms of these lamps in the market. A very handy one is 
made by Baker (244, High Holborn, London), price 17s. 6d. 
These lamps ought to be looked upon more as luxuries than 
necessities, and I think J. H. will find one of the cheap forms of 
paraffin lamps, with about half-inch or one-inch wick, and with a 
burner as little elevated above the table as possible, answer all his 
requirements. These lamps cost about ts. 6d. 
If J. H. has not already got his 1} inch, I should think he 
would be better advised to get a 4-inch instead, as I think he 
will find his }-inch too near in working to his 4-inch and 4 -inch 
of low angle (110°) are now almost as cheap as ¢-inch. For 
