The author is interested in practical algorithms for finding a grammar of a language, using a finite sample of strings marked to show whether or not the string is in the language. He proposes an algorithm for obtaining linear grammars from finite sample sets. First, for all strings u and v over the alphabet of language L, he defines the derivative language of L, \(\bar uL\bar v=\{x; uxv\in L\}\). (Think of these sets as containing the ''centre'' of each string of L.) Next, he creates a diagram D(L). It is a network whose nodes are \(\bar uL\bar v,\) for all u and v, and which has labels on the arcs between nodes X and Y indicating \(Y=\bar sX\) or \(X\bar s,\) for s a character of the alphabet of L. Then, he gives a procedure for constructing a ''structural tree of depth k'', for the strings of L of at most length k. He uses this structural tree to create a finite structural diagram \(D(L,k,h)\), analogous to D(L), with nodes that are sets of strings of at most length h, drawn from languages with a structural tree of depth k. From this finite structural diagram, he synthesizes a linear grammar. To illustrate the method, he uses the example of \(L=\{a^ nba^ n\), \(n\geq 0\}\). In this case, the language L can be synthesized from \(D(L,1,2)\). The algorithm is complete for harmonic linear languages, where any regular language is harmonic, but not all linear languages are. For harmonic linear languages, a grammar of L can be inferred from a finite sample of L. The necessary and sufficient condition is that the sample include the characteristic set of L, C(L). C(L) is a set of strings with ''centres'' up to a certain length h and with an associated structural tree of a certain depth k, h and k dependent on L. The paper concludes with a flow-chart for the algorithm for inferring harmonic linear grammars from a sample of strings that are marked as in or not in the language.