MATHEMATICAL SECTION. 161 
I i: f 
equations fully determining ae : et : Ae , &c., in terms of the 
partial derivatives of f. 
Again, suppose (3) the parabolic representative of (2), then 
0 = B,, with 0 = B,, 0 = B,, &c., and consequently by (11) 0 = A,, 
with O= A,,0=A,,...090=A,—,, or the first p—1 of the 
equations (12) are satisfied indifferently whether the = ; = re 
—1 
aS therein contained be derived from (1) or (2); that is, we 
have arrived at Lagrange’s conditions for contact of the (p — 1) 
order, as a consequence of p - punctual contact; and it follows at 
once that the distance between two curves:in the neighborhood 
of ap - tuple common point is of the p™ order when the distance 
along the curves from the p- tuple point is of the 1st order.* 
Note. 
The abstracts of communications to the Mathematical Section 
have each been examined by a special committee, consisting of the 
Chairman, the Secretary, and a third member appointed by the 
Chairman. These third members were as follows: 
Title. Author. Third Member. 
Alignment Curves on any Surface___-- C. H. Kummeitt. A. S. CHRISTIE. 
The Mass of a Planet from Observa- 
tions of two Satellites__________- A HAGE: W. B. Tay or. 
Infinites and Infinitesimals____.---___ M. H. DoouitTLe. G. W. HILL. 
Planetary Perturbations of the Moon__G. W. HILL. EK. B. ELLIoTr. 
The Law of Error practically tested 
bys Larget-Shooting.. 2. =. 2-2. C. H. Kummett. A. S. CHRISTIE. 
Form of Least-Square Computation.__.H. FARQUHAR. R. S. WoopwarbD. 
Rejection of Doubtful Observations.._.M. H. DooLiItTLe. W. C. WINLOCK. 
Special Treatment of certain forms of 
Observation-Equations ----------R. S. Woopwarp. W. C. WINLOCK. 
Contact of Plane Curves _____..._____A. S. CHRISTIE. C. H. KUMMELL. 
* This paper will be continued. 
