I found this after some Google-fu. Two interesting points:
It sounds like they were not fully conscious past about 25,000' and another account I read reported that the actual max altitude is unknown because they neither were able to operate the instruments at the time
The ascent rate was something like 500-800 fpm, so they would have gotten to 25,000' in less than an hour
Either way, it sounded like things were pretty hairy and depended on one guy's teeth...
The watching crowds were bigger on September 5th, 1862, and the weather kinder. What was different was the gas that filled "Mars". Mr Thomas Proud, Manager of the Wolverhampton Gas Works, had 'brewed' a particularly potent supply, capable of much more 'lift' than normal.
There was a fully-controlled launch within a couple of minutes of the 1.00 pm target, and Coxwell and Glaisher were elated to find themselves at a height of two miles in only 19 minutes.
The soaring rate of climb continued past the three and four mile mark.
Because the balloon's basket was unevenly loaded, the balloon canopy began to revolve, tangling the net. And, along with it, the valving rope that enabled gas to be released so that the balloon could descend.
As Glaisher patiently recorded what his instruments told him, the four mile and five mile mark were passed. Both men knew they are in line for a record. As Coxwell climbed into the rigging to free the valve line, Glaisher's eyesight began to deteriorate. He began to lose the power to move his arms and legs. His voice goes, his hearing fades. He passes out, his head sagging over the rim of the basket.
Coxwell, in the rigging, is frozen almost helpless with the cold. His hands are turning blue and black. He tumbles, rather than climbs down into the basket. The balloon is still rising. Coxwell seizes the gas valve rope in his teeth and pulls. The valve opens and the balloon begins to descend.
Neither man appreciates the situation until afterwards when the instruments are read. But they have reached the 37,000 feet mark. They are the first men into the Stratosphere.
Without oxygen, without pressure suits, without a protective cabin, seven miles high, they have penetrated into Jumbo Jet country. Unconscious and frozen under a balloon that would have gone on climbing until it burst.
What follows, as the balloon plunges downwards, is a classic British understatement*.
'Out of a thick darkness Glaisher hears the voice of his companion trying to rouse him: "Do try; now do". The darkness lightens. Dimly Glaisher sees the barometer tube, the other instruments, then the form of Coxwell bending over him, then gladness driving the anxiety from Coxwell's face.
"He sits upright, stretches himself as if awaking from a deep sleep and says:
"I have been insensible".
"You have", answers Coxwell, "and I too, very nearly".
"The first thing Glaisher does when he rises to his feet is to take a pencil and resume his observations.
'But he lays it aside as soon as he notices Coxwell's black, frost-bitten hands, and rubs them with brandy until the circulation is restored'.
All this time the balloon is racing downwards.
By throwing out ballast the descent is brought under control for a severe but safe landing at Cold Weston under the shadow of the Brown Clee Hill in Shropshire. In a straight line, the pair are only about twenty miles from their launch point.
As Coxwell begins to recover the balloon, Glaisher begins a six mile trudge into nearby Ludlow to get help. Perhaps he spends the time wondering about the fate of the pigeon that was thrown out when the balloon had fallen to the four mile mark.
It merely circled the balloon and finally perched on top of the envelope. Perhaps it was the one that returned to Wolverhampton two days later.
Glaisher made many more flights for the British Association, but never another like the September 5th, 1862 ascent from Wolverhampton.
* "Adventures Above The Clouds", Monk & Winter, Blackie, 1933