Quinn, JohnO'Faolain de Bhroithe, AnnaAnnaO'Faolain de Bhroithe2015-08-142015-08-142014 the a2014http://hdl.handle.net/10197/6804This thesis concerns the study of inverse-Compton emission from two astrophysical sources. The first object, 1ES 1959+650, is a nearby active galactic nucleus. This source was observed as part of the VERITAS blazar monitoring programme in the hopes of detecting it in the midst of a dramatic flaring event. Over the course of these monitoring observations which span four years, a significant detection of the source in its low state was accumulated. The spectral energy distribution of this source was analysed from optical to VHE and was modelled with a synchrotron self-Compton model with an additional external Compton component. The parameters obtained cannot be fully explained by first-order Fermi acceleration at parallel shocks, and instead may suggest particle acceleration at oblique subluminal shocks, or that 1ES 1959+650 may consist of an inhomogeneous jet with a fast inner spine and slower-moving outer cocoon.The second source is the famous Crab Nebula, for years considered the standard candle of X-ray to VHE gamma-ray astronomy. VERITAS observed the Crab Nebula during the recent flare of the high-energy synchrotron component of the source in March 2013. No enhanced VHE emission was detected, but the observations facilitated the calculation of upper limits on any extra VHE spectral component emerging during the flare. A wealth of archival VHE Crab Nebula data also exists, spanning many years. An extended VHE data set of the source from 2000 to 2013 was compiled from Whipple 10m Telescope and VERITAS observations. This data set was searched for short-term flaring activity, but no evidence of this behaviour was found. A slight decrease in the long-term flux of the nebula was detected in the VERITAS data in 2011. This could possibly be correlated with increasing instability of the aerosol content of the local atmosphere around the VERITAS site.en1ES 1959+650BL Lacertae objectsCrab NebulaGamma raysPulsar wind nebulaeVERITASDoctoral Thesis2015-08-04#0|aCrab Nebula.#0|aBL Lacertae objects.#0|aGamma ray telescopes.#0|aGamma ray astronomy|xObservations.https://creativecommons.org/licenses/by-nc-nd/3.0/ie/