Peculiarly and particularly can have the same meaning - in fact, you could use either in your sentence. Peculiar usually means unusual or strange, but it can also mean ' belonging exclusively to' or 'particular, special. He was looking at me rather peculiarly. [strangely, oddly] Peculiar 'to' New Zealand, the kiwi is a remarkable bird. [belonging only to NZ - note you need the 'to'] The Archers is a peculiarly English soap-opera. [particularly, uniquely] Both words can also mean 'very': It is a peculiarly/particularly difficult word to understand.

Hello! Unfortunately, you cannot interchange peculiarly as particularly because they are not the same word nor do they give the same definitions. Peculiarly could mean "more than usually; especially" or "oddly", however it is more commonly used as "oddly"-- as in to say something is weird/not normal. ( i.e. given the situation that: It was odd that he went to the store on Monday because he usually goes on Sunday. ) "Therefore, he peculiarly went to the store on Monday." Particularly means "to a higher degree than is usual or average" or "so as to give special emphasis to a point; specifically". Basically you use when you want to emphasis that you are talking about a particular object/thing/noun/etc. ( i.e. given the situation that he does not want to talk about that particular subject during class, because he finds it boring. ) Therefore, he does not want to talk about that subject in particular.

‘Particular’ [adj.] or the adverb ‘particularly’ are used to specify i.e. state something distinctive or special : ‘It was the particular conditions of geography in England that enabled the Industrial Revolution’. ‘Peculiar’ [adj.] , the noun ‘peculiarity’, or the adverb ‘peculiarly’ denote something unusual, unexpected, or strange. In the sentence you quote, the author suggests that normally an event of this kind [the Industrial Revolution’ ] would be expected to have occurred in an urban environment i.e. towns and cities, and that its ‘roots’ in the English countryside are particular to the peculiar conditions that existed at that place and time. The event is ‘particular’ and is due to the prevailing conditions which were peculiar. In this case you can use ‘particularly’ in place of ‘peculiarly’. You need to write that ‘. . . is that it is rooted in the countryside.’ I hope this helps you get a better understanding of the use of these words, which in most cases are used in different contexts and are not interchangeable.

peculiarly and particularly? unusual or odd vs. unique