The Comparative Method I

The phonological change that languages undergo over time is at present probably the best understood aspect of language change. Phonology is the component of speech that deals with the sounds utilized in a particular language and how they are combined to produce lexical items (words).
All spoken human languages have a set of speech sounds that they utilize, known as a phoneme inventory (each sound in the set is known as a phoneme). Out of the total number of sounds that humans can produce and regularly use in language production, only a subset is utilized by any particular language, though languages differ on which set of sounds they utilize. An important distinction must be made between phonetic differences and phonemic ones. A phonetic difference within a language does not contribute to differences in meaning (though it may mark differences in regional accent or dialect). For example, in English, the pronunciation of the 't' in 'top' is slightly different from the pronunciation of the 't' in 'stop'; the first 't' is pronounced with a slight puff of air (known as aspiration), while the second 't' is not. This difference is a phonetic one, since the two sounds are not identical in an absolute sense, but is not a phonemic difference, since pronouncing 'top' without the puff of air, or pronouncing 'stop' with it, will not change the fact that we're still saying the words 'top' and 'stop - that is, there'll be no confusion on the part of the listener. However, if we changed the 't' in 'top' to a 'p', it would result in saying a different word, 'pop'; the difference between 't' and 'p' in English is therefore a phonemic one, because it serves to distinguish different words from each other. We say, then, that 't' and 'p' are different phonemes in the phonemic inventory of English, while 't' with aspiration and 't' without aspiration are known as different allophones (essentially different phonetic versions) of the common phoneme 't'.
The phoneme inventory of any given language is unstable over time; some phonemes are lost, some gained, some become differentiated in different contexts. For example, Old English (the variety of English that was spoken in Britain between the 5th and 12th centuries AD) did not utilize the sound 'zh', as in the word 'seizure', in its phoneme inventory. This sound was only added later through the addition of words from Old French and through a phonological process called 'palatalization' (the process that causes 't' to be pronounced 'ch' in combinations such as 'what you'). Similarly, Old English had a phoneme 'kh' in its inventory (the sound of 'ch' German 'Bach' or Scottish 'loch'), but this phoneme was eventually lost by the Modern English period (roughly 1500 to the present), although it is maintained in the related Scots language.
So, we know that a language's phoneme inventory changes over time. But how did we figure this out? Through a process called the Comparative Method, we're able to reconstruct earlier stages of a language (most easily earlier phonological stages), even in the absence of any written records from those earlier stages. In the comparative method, we compare the vocabulary between different languages to find regular phonological correspondences between them.
The first step in this process is to figure out if a set of languages is genetically related (i.e. evolved from a common ancestral language). If we know nothing about the languages beforehand, we more or less have to start from scratch, choosing a group of languages that are in close geographical proximity, and comparing very basic vocabulary items in each of them. In part II of this post, I'll illustrate this process first with some imaginary data, then with some data from a group of European languages.