714. TRANSLATOR’S NOTES TO M. MENABREA’S MEMOIR 
§ 
Variables for Results. 
SS 
Veg Vay Vay ME aR IS Vie Ve V3" 
= 
[84] [Ba] [Ba] [Ba] (BA, t [2.4, | 
Sa 
cos cos26 cos3é cos@ (cosé.cos#) : (cos36.cosé) 
(cos 24.cos 6) 
The variable belonging to each coefficient is written below it, as we 
have done in the diagram, by way of memorandum. The only further 
reduction which is at first apparently possible in the preceding result, 
would be the addition of V., to V;, (in which case B, A should be 
effaced from V;,). The whole operations from the beginning would 
then be— 
First Series of Second Series of Third Series, which con- 
Operations. Operations. tains only one (final) operation. 
Wig X 1Vo=!Vop Vix !Vo=!V51 1Vo,+!V5,=2Vo., and 
IV, x 1V,=!V., Vig KV Ves V;, becomes =0. 
Vig x 1Vg==! Veo IV, x!Vo=!Vo5 
LVig iV pe Vay 'V,, x !V;=!Vo4 
We do not enter into the same detail of every step of the processes 
as in the examples of Notes D. and G., thinking it unnecessary and 
tedious to do so. The reader will remember the meaning and use of 
the upper and lower indices, &c., as before explained. 
To proceed: we know that 
cosn§.cos#=ceosr+16+4n—1.9 . . ~ (3) 
Consequently, a slight examination of the second line of (2.) will show 
that by making the proper substitutions, (2.) will become 
BA|+BA, .cos#+BA, .cos26]+BA, .cos3 6 
+5B,A_ .cosé 
4+43B, A, +3.B, A, .cos2 
+3B,A,. cos 6 +3 B,A;. cos 3 4 
+3B, A;.cos2é +3 B, Aj.cos46 | 
C, C, C, C,; C, 
These coefficients should respectively appear on 
Voo Vor Voo Vos Vo: 
We shall perceive, if we inspect the particular arrangement of the 
results in (2.) on the Result-columns as represented in the diagram, 
that, in order to effect this transformation, each successive coefficient — 
upon V,, V3, &c. (beginning with V,.), must through means of — 
proper cards be divided by éwo*; and that one of the halves thus — 
* This division would be managed by ordering the number two to appear on — 
any separate new column which shouid be conveniently situated for the pur- _ 
pose, and then directing this column (which is in the strictest sense a Working-_ 
Variable) to divide itself successively with V2, V33, &c. " 
= 
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