Queries. LG 7, 
series is the expansion of (1 + 1)~>by the binomial theorem, and 
is therefore equal to 4. What I desire to know is, whether any 
mathematician has given a way for finding out the values of such 
infinite divergent series, that would be intelligible to a person who 
knows nothing of the binomial theorem. 
Respecting the other kind of series mentioned in my query, 
the fact that both my examples were series of figurate numbers, 
has evidently tended to obscure my meaning. I want to know if 
there is a general name for a// series, the differences between the 
terms of which are in arithmetical progression. Under the word 
“ differences ” I include also the differences between differences— 
z.e., second differences, third differences, andso on. Here are two 
more examples (not figurate numbers this time) :— 7, 8, 8, 8, 9, 12, 
18,. .. etc., the second differences between which are—t1, 0, I, 
Pear etcs Andes, 6, 6, 7, Lames asia. 2. ete., tae thind 
piillerences between which are 2, 3)4be5, .. -.. Efe. 
Colenso, in his “ Algebra,” calls these series a “kind of 
Arithmetical Progression” (or words to that effect); but as an 
Arithmetical series is one in which there is the same difference 
between all the terms, such use of the word is hardly suitable. If 
no other designation has ever been applied, I should suggest 
“ Differential Series” as an appropriate term for all this kind, 
including, of course, the arithmetical. Sia SSP 
396.— Microscope Lamp.—lIs there much benefit to be derived 
from using a lamp specially made for the microscope as compared 
with an ordinary clear-burning petroleum lamp? I intend getting 
a Y%-inch objective, and having never used a higher power than 
y-inch, I would feel much obliged by some one informing me if 
I could work satisfactorily with an ordinary table-lamp, or would 
it be necessary to get one from a microscope-dealer? If the latter, 
please let me know the name of a cheap, handy form, and from 
whom I can obtain it. I would be very glad to know of any 
article in any of the microscopic journals on lamps and the mode 
of using them to the best advantage. | Be 
397,_Camera Lucida.—Would some one kindly recommend 
me a Camera Lucida which is easy to use and of a moderately 
reasonable price? Strasburger, in his “ Practical Botany,” recom- 
mends Abbé’s, price 30/-, but this is only adjusted for eye-pieces 
of the continental size. My microscope is a Beck’s “Star,” with 
Nos. 2 and 3 eye-pieces. I have read that it is better to get a 
camera which can be used with the instrument in a vertical posi- 
tion. I require it for botanical work. leash 
398.—Animal Intelligence.—Have any systematic steps been 
taken lately with a view of ascertaining of what mental progress 
dogs or other animals are capable ? ZOOPHILIST. 
