## 1 Introduction  
The rich history of food adulteration since the fourteenth century is well described in [1]. The relevance of detecting product falsification, including butter, is only growing; see, for example, [2; 3; 4; 5]. There is an international regulatory Council Regulation (EC) No. 1234/2007 dated 22 October 2007, which defines butter as a product with a mass fraction of milk fat of at least 82% [6]. However, a large amount of \"butter\" appears on the market, in which butter fat is replaced by vegetable one, most often palm oil. This is due to the fact that palm oil is the cheapest available and the most affordable among the cheap ones. Therefore, when demonstrating the proposed methods for detecting falsification, we limited ourselves to various brands of palm oil. It is well known that the addition of palm oil to butter causes substantial changes in fat constants, fatty acid composition, and sterol andtocopherol contents. The changes depend on the addition level [2]. There are a number of chemical and physical methods to estimate these changes, described in [7]: the iodine value (IV) measurement, saponification value (SV) measurement, Reichert-Meissl method (RM, that is, analysis of soluble volatile fatty acids) and Polenske value method (PV, that is, analysis of insoluble fatty acids). Fatty acid profiles are usually analyzed by gas chromatography equipped with a flame ionization detector (FID) [8]. The most common standardized methods for studying the fatty phase of dairy products to detect the presence of vegetable fats are chromatography [1; 8; 9; 10] and spectroscopy [11]. Both high-performance liquid chromatography (HPLC) [12] and gas chromatography (GC) [9] give the content of bulk components, especially triacylglycerglycerols (TAGs), fatty acids, sterols, tocopherols, and some other fat components. The method is suitable for identifying vegetable additives to butter because it contains other styrene instead of cholesterol. However, it does not apply to the detection of animal fat (like lard) and to the study of milk fat in some cases [1]. Additionally, the method is quite expensive and gives the chemical composition of butter from which it is hard to obtain a quantitative content of adulterants in butter. Gas chromatography analysis of fatty acids and sterols showed that the minimum detectable additive of palm oil in the spread was 10 wt% [9; 10]. Therefore, other methods have recently been proposed for determining additives to butter, such as Raman spectroscopy [13; 14] and its variety--method of laser-induced breakdown spectroscopy [15], Fourier Transform Infrared (FTIR) spectroscopy [16], method of temperature-controlled attenuated total reflectance-mid-infrared (ATR-MIR) spectroscopy [17] and differential scanning calorimetry (DSC) [18]. The method of Raman spectroscopy is based on measuring the intensity of radiation lines of individual chemical elements and gives a good result for margarine used as an adulterant of butter. However, since different margarine brands have different content of these elements, the quantitative determination of the adulterant may be difficult. The same applies to the method of laser-induced breakdown spectroscopy. Additionally, these methods require expensive spectrometers. The FTIR method is designed to determine the presence of animal fat in butter, but this technique, similar to ATR-MIR and Fourier spectroscopy (FS) techniques, requires a complicated procedure for extracting fat from the butter. Violation of such a procedure or change of adulterant composition can lead to errors in determining the composition of the falsified butter. Moreover, these methods involve the use of expensive equipment too. The simplest and cheap method seems to be the DSC. Addition of palm oil to butterfat results in an altered shape of the melting curve. But it still requires a set of data for different adulterants and is applicable for the quantitative detection of palm oil (PO) in butter within the range of palm oil concentrations from 2 to 35% [18].