I have changed a few things but nothing has helped. I installed CrossPack (development environment for AVR which includes a more recent build of AVRDUDE than the one I was using previously (from Arduino)) and the 10uF capacitor is now between RESET and GND. Strangely AVRDUDE will not work unless I first short the capacitor. I also cleaned some flux residue off the 6-pin to 10-pin adaptor but that didn't do anything – it was worth a shot.
AVRDUDE output:
Richards-MacBook-Pro:~ Richard$ avrdude -P /dev/tty.usbmodem411 -b 19200 -c arduino -p atmega8 -B 1 -U flash:w:usbasp.atmega8.2011-05-28.hex -v -v -v -v
avrdude: Version 6.0.1, compiled on Dec 16 2013 at 17:26:24
Copyright (c) 2000-2005 Brian Dean, http://www.bdmicro.com/
Copyright (c) 2007-2009 Joerg Wunsch
System wide configuration file is "/usr/local/CrossPack-AVR-20131216/etc/avrdude.conf"
User configuration file is "/Users/Richard/.avrduderc"
User configuration file does not exist or is not a regular file, skipping
Using Port : /dev/tty.usbmodem411
Using Programmer : arduino
Overriding Baud Rate : 19200
Setting bit clk period : 1.0
avrdude: Send: 0 [30] [20]
avrdude: Send: 0 [30] [20]
avrdude: Send: 0 [30] [20]
avrdude: Recv: . [14]
avrdude: Recv: . [10]
AVR Part : ATmega8
Chip Erase delay : 10000 us
PAGEL : PD7
BS2 : PC2
RESET disposition : dedicated
RETRY pulse : SCK
serial program mode : yes
parallel program mode : yes
Timeout : 200
StabDelay : 100
CmdexeDelay : 25
SyncLoops : 32
ByteDelay : 0
PollIndex : 3
PollValue : 0x53
Memory Detail :
Block Poll Page Polled
Memory Type Mode Delay Size Indx Paged Size Size #Pages MinW MaxW ReadBack
----------- ---- ----- ----- ---- ------ ------ ---- ------ ----- ----- ---------
eeprom 4 20 128 0 no 512 4 0 9000 9000 0xff 0xff
Block Poll Page Polled
Memory Type Mode Delay Size Indx Paged Size Size #Pages MinW MaxW ReadBack
----------- ---- ----- ----- ---- ------ ------ ---- ------ ----- ----- ---------
flash 33 10 64 0 yes 8192 64 128 4500 4500 0xff 0x00
Block Poll Page Polled
Memory Type Mode Delay Size Indx Paged Size Size #Pages MinW MaxW ReadBack
----------- ---- ----- ----- ---- ------ ------ ---- ------ ----- ----- ---------
lfuse 0 0 0 0 no 1 0 0 2000 2000 0x00 0x00
Block Poll Page Polled
Memory Type Mode Delay Size Indx Paged Size Size #Pages MinW MaxW ReadBack
----------- ---- ----- ----- ---- ------ ------ ---- ------ ----- ----- ---------
hfuse 0 0 0 0 no 1 0 0 2000 2000 0x00 0x00
Block Poll Page Polled
Memory Type Mode Delay Size Indx Paged Size Size #Pages MinW MaxW ReadBack
----------- ---- ----- ----- ---- ------ ------ ---- ------ ----- ----- ---------
lock 0 0 0 0 no 1 0 0 2000 2000 0x00 0x00
Block Poll Page Polled
Memory Type Mode Delay Size Indx Paged Size Size #Pages MinW MaxW ReadBack
----------- ---- ----- ----- ---- ------ ------ ---- ------ ----- ----- ---------
calibration 0 0 0 0 no 4 0 0 0 0 0x00 0x00
Block Poll Page Polled
Memory Type Mode Delay Size Indx Paged Size Size #Pages MinW MaxW ReadBack
----------- ---- ----- ----- ---- ------ ------ ---- ------ ----- ----- ---------
signature 0 0 0 0 no 3 0 0 0 0 0x00 0x00
Programmer Type : Arduino
Description : Arduino
avrdude: Send: A [41] . [80] [20]
avrdude: Recv: . [14]
avrdude: Recv: . [02]
avrdude: Recv: . [10]
avrdude: Send: A [41] . [81] [20]
avrdude: Recv: . [14]
avrdude: Recv: . [01]
avrdude: Recv: . [10]
avrdude: Send: A [41] . [82] [20]
avrdude: Recv: . [14]
avrdude: Recv: . [12]
avrdude: Recv: . [10]
avrdude: Send: A [41] . [98] [20]
avrdude: Recv: . [14]
avrdude: Recv: . [00]
avrdude: Recv: . [10]
Hardware Version: 2
Firmware Version: 1.18
Topcard : Unknown
avrdude: Send: A [41] . [84] [20]
avrdude: Recv: . [14]
avrdude: Recv: . [00]
avrdude: Recv: . [10]
avrdude: Send: A [41] . [85] [20]
avrdude: Recv: . [14]
avrdude: Recv: . [00]
avrdude: Recv: . [10]
avrdude: Send: A [41] . [86] [20]
avrdude: Recv: . [14]
avrdude: Recv: . [00]
avrdude: Recv: . [10]
avrdude: Send: A [41] . [87] [20]
avrdude: Recv: . [14]
avrdude: Recv: . [00]
avrdude: Recv: . [10]
avrdude: Send: A [41] . [89] [20]
avrdude: Recv: . [14]
avrdude: Recv: . [00]
avrdude: Recv: . [10]
Vtarget : 0.0 V
Varef : 0.0 V
Oscillator : Off
SCK period : 0.1 us
avrdude: Send: A [41] . [81] [20]
avrdude: Recv: . [14]
avrdude: Recv: . [01]
avrdude: Recv: . [10]
avrdude: Send: A [41] . [82] [20]
avrdude: Recv: . [14]
avrdude: Recv: . [12]
avrdude: Recv: . [10]
avrdude: Send: B [42] p [70] . [00] . [00] . [01] . [01] . [01] . [01] . [02] . [ff] . [00] . [ff] . [ff] . [00] @ [40] . [02] . [00] . [00] . [00] [20] . [00] [20]
avrdude: Recv: . [14]
avrdude: Recv: . [10]
avrdude: Send: E [45] . [05] . [04] . [d7] . [c2] . [00] [20]
avrdude: Recv: . [14]
avrdude: Recv: . [10]
avrdude: Send: P [50] [20]
avrdude: ser_recv(): programmer is not responding
avrdude: stk500_recv(): programmer is not responding