From John Conwill   September 1842

<beginning of letter missing>

The velocity of bodies descending in this manner is quite different from that of bodies falling through vacuum to the earth – in the latter case the body receives no impulse in any direction save that which goes through the earth’s centre, while in the former case the moment the body enters the earth it is pulled back by a force due to the distance between it and the earth’s surface (vide¹ A) hence we draw two queries:–

1. To determine the velocity of a body at any point between the earth’s surface and her centre supposing it could pass in vacuo² to that centre without taking away attraction or extension

2. Will the momentum of the body be completely destroyed when it arrives at the earth’s centre? If not, how far will it move beyond that centre?

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- - Now to your queries, and 1st with regard to light, heat &c. We must premise the following observation – If a substance of any density be spread over a surface of any given dimensions, when that substance is spread on a surface of twice, three times, four times &c that of the given one, its density will be only one half, one third, one fourth &c of its first density.

Let ‘a’ be a luminous body whence rays of light issue on the surfaces ‘nrmo’ ‘SRQT’ which are similar but one surface being one fourth the other,³

From what has been premised the density of light on ‘or’ is four times its density on ‘TR’, that is to say

surface or : surface TR :: dens[ity of light] on ‘TR’ : dens[ity of light] on ‘or’

— Again, from the similar [triangle]s Arm, ARQ & ANR, ASR we have

Ar : rm:: AR : RQ

Ar : rn :: AR : RS

Multiplying these proportions

Ar² : rm x rn :: AR² : RQ x RS – Alternately

Ar² : AR² :: or : TR :: dens[ity of light] on TR : dens[ity of light] on or

Q E D.⁴

RI MS JT 1/11/3526