900 
MAJOR P. A. MACMAHOR ON THE THEORY 
No. 1 2 3 4 5 6 7 parts 
7 
1 
6 
15 
20 
15 
6 
1 
61 . 
1 
12 
45 
80 
75 
36 
7 
1 
16 
75 
160 
175 
96 
21 
5D 
1 
22 
120 
280 
325 
186 
42 
43 
1 
18 
93 
216 
255 
150 
35 
421 
1 
28 
183 
496 
655 
420 
105 
4D 
1 
38 
288 
856 
1205 
810 
210 
¥l 
1 
30 
207 
588 
810 
540 
140 
1 
34 
255 
772 
1120 
780 
210 
32D 
1 
46 
399 
1324 
2050 
1500 
420 
3P 
1 
62 
621 
2260 
3740 
2880 
840 
Wl 
1 
52 
489 
1728 
2820 
2160 
630 
22X3 
1 
70 
759 
2940 
5130 
4140 
1260 1 
XD 
1 
94 
1173 
4980 
9300 
7920 
2520 
V 
1 
126 
1806 
8400 
16800 
15120 
5040 
Total 
64 
256 
544 
976 
768 
1888 
3408 
2316 
3172 
5740 
10404 
7880 
14300 
25988 
47293 
[During the considerable time that has elapsed since this paper was read I have 
discovered the general theory of the transformations of Arts. 41 and 75. 
Let Xj, X^, Xg be general linear functions of exhibited in the Notation 
of the Theory of Matrices 
(X]^, X^, Xg) - ( Oj, ag, CKg ) X.2, a!g), 
I I 
j K ^3 
! > 
and considei’ the algebraic fraction 
1 
(l-»,Xi)(l-S2X,){l-vV) 
