Two projectiles are anyhow projected simultaneously from a point, what is the relation between their vertical heights at any instant?

This simple inquiry, which was instituted in consequence of some results recently obtained from thermo-electric experiments (see ante p. 311) carried on at high temperatures, where the indications given by two separate circuits, immersed in the same hot and cold bodies. were used as ordinate and abscissa, leads to a very curious consequence.

Let

and

be any two parabolas whose axes are vertical, and which pass through the origin.