260 The Rev. H. Moseley on certain Elementary Formule. 
Why blue ice should predominate at intervals in the substance 
of this glacier, —whether the like alternation of structure holds 
good in glaciers generally,—and whether it has any relation to 
a primitive stratification, are problems of great interest and well 
worthy of investigation. 
With regard to the second, I will merely express a belief that 
some such alternation of structure does obtain in glaciers gene- 
rally ; for the appearances presented by good sectional views of 
glaciers, such as that exposed on the north side of the Allalein, 
are so similar to those exhibited by La Brenva, that I cannot 
doubt the identity of their cause. I had been in the habit of 
regarding the appearances referred to as direct evidences of stra- 
tification; but if my supposition be correct, they will merely be 
evidences of an alternation of structure which may or may not 
depend on stratification. 
Yours very faithfully, 
T. H. Huxtey. 
XXX. On certain Elementary Formule, &c. By Henry 
Mosetey, M.A., F.R.S., Canon of Bristol, and Corresponding 
Member of the Institute of France*. 
han development of the value of one of the quantities 2, y, z 
in the equation 
helya= Ghz) "yy, cmt s od dat sneeh Oe) 
in a series ascending by powers of another of them, yields—if it 
be z, in a series ascending by powers of y—the fundamental 
theorem of logarithms ; if it be y, ina series ascending by powers 
of x, the exponential theorem ; and if it be y, in a series ascend- 
ing by powers of z, the binomial theorem. I have endeavoured 
in the following paper to effect these developments by simpler 
methods than those commonly in use, and thus to make easier 
to the student one of the first stages of analytical research. 
First, let it be observed that when, in equation (1), z or z =0, 
then y=0. To determine ~z in terms of y, assume 
2=ZLyt+Zoy?+Zey+Zyit+, . . ». « (2) 
where Z,, Z,... ave unknown functions of z. Now when z 
becomes 22 in equation (1), y becomes 2y+y*. Substituting 
these values for z and y in equation (2), 
2a=Z,(2y+y) + Zo(2y +97)? + Z3(2y +97)? + Zi2y tye +... 
But by (2), 
2v=2Z,y + 2Z,y? + 2Z,y? + 2 yy? +... 
* Communicated by the Author. 
