## 3-15-40. George Howard Darwin to H. Poincaré

Oct. 22.01

Newnham Grange–Cambridge

Dear Monsieur Poincaré,

Your M.S. has arrived.^{1}^{1}Poincaré a annoncé l’envoi de son
mémoire par lettre (§ 3-15-39).
I shall venture to annotate it a little in red ink with
instructions to the printers in English as I think it may save much
trouble in the proofs. Of course I have experience of their ways which
you cannot have.

I think it might be useful if I append a note in my own name to
explain the identities of your $R$’s and my $\U0001d513$ and
$\mathbf{P}$. It has taken me nearly half an hour to make it out & I
may as well save others the trouble. In doing this however I have
discovered two things. I am unable to find any ${R}_{0}$ in the
*Acta,* but I gather from your M.S. that it must denote
${\U0001d513}_{0}(v)$ a constant or unity.

Secondly in y^{r} explanation you do not really follow y^{r} notation of
the *Acta*.^{2}^{2}In the published memoir, Poincaré notes that
he and Darwin do not employ the same notation, and that he employs a
notation different from that employed in his *Acta* paper
(1902, 335–336).
You write there ${R}_{n,i}^{(k)}$ and $n$ is clearly the
degree of the harmonic and $i$ its order, because you refer
to its becoming

$$A{({\rho}^{2}-{e}^{2})}^{\frac{1}{2}i}{D}^{i+n}{({p}^{2}-{e}^{2})}^{n}$$ |

in the case of the spheroid. Hence where in y^{r} M.S. you write
${R}_{0,2}^{\prime}$ and ${R}_{0,3}^{\prime}$ you mean ${R}_{2,0}^{\prime}$ and ${R}_{3,0}^{\prime}$.
Accordingly I propose (with your consent) to correct
this.^{3}^{3}Darwin’s note was inserted in Poincaré’s paper
(Poincaré 1902, 336). I then
obtain the following for your new $R$’s.

${R}_{1}$ | $={\U0001d513}_{0}(v),$ | ${R}_{2}$ | $={\U0001d513}_{1}^{1}(v),$ | ||

${R}_{3}$ | $={\U0001d513}_{2}(v),$ | ${R}_{4}$ | $={\U0001d513}_{2}^{2}(v),$ | ||

${R}_{4}$ | $={\U0001d513}_{3}(v),$ |

Of course if in any case you dislike the mode of printing which I shall suggest it will be open to you to correct it in proof.

I do not think our printers have any type for your except one like this $\backsim $ which has been used by some writers to denote a difference without regard to sign. On the other hand we have $\propto $ which has been used as equivalent to “varies as” & this is your meaning. I suggest therefore $\propto $ to replace .

Our printers always make such a thing as $\frac{\xi}{2}$ look very ugly, & so I write $\frac{1}{2}\xi $. This moreover saves the compositor much trouble. I have suggested this in many places.

I am afraid the French will be very badly set up & so I will look over a first proof before sending it on to you. I will write again if anything occurs to me. I have not yet had time to master your method. I am besides very busy for some days to come.

Yours sincerely,

G. H. Darwin

ALS 4p. Collection particulière, Paris.

Time-stamp: "25.01.2016 19:54"

## References

- Sur la stabilité de l’équilibre des figures piriformes affectées par une masse fluide en rotation. Philosophical Transactions of the Royal Society A 198, pp. 333–373. External Links: Link Cited by: 3-15-40. George Howard Darwin to H. Poincaré.