From G. H. Darwin to Horace Darwin 21 February 1875

By the principle of virtual velocities all actions at hinges go out *P [DIAG HERE that is presumably meant to show that all actions at hinges go out, diagram is annotated with 2 arrows and the letters 'T' and 'P'] *Q

& T x its v:v: = P x its v.v:

or Tdr = Pdr′

But rr′ = k¹ ∴ logr + logr′ | = logh˘

Diff^g.

∴ $\frac{\mathrm{dr}}{\mathrm{r}}$ = - $\frac{\mathrm{dr\prime }}{\mathrm{r\prime }}$

∴ Tr = -Pr′

∴ $\frac{\mathrm{TK˘}}{\mathrm{r12}}$ = -P

or P is attractive & $\frac{1}{\mathrm{r12}}$

if T is constant

This proves that my dodge gives this reverse sq: force

Otherwise

From symmetry T & P are the only reactions at A & C

*P [DIAG HERE] *Q

Then Y= Y′+Y'″

X =X′+X'″

Y′sinθ = X′cosθ

Oh its too awful I can’t work it it out thus & its no use whatever to find out the reactions at the joints

The other way is very simple & correct.

I have got wooden cells wh seem to do better than metal, [founded] with paper binders

*P [DIAG HERE] *Q

GHD

FB comes to Down on the 6^th.