in the sample, D0 is number of atoms of the daughter isotope in the original or initial composition, n is number of atoms of the parent isotope in the sample at the present, λ is the decay constant of the parent isotope, equal to the inverse of the radioactive half-life of the parent isotope times the natural logarithm of 2, and (eλt-1) is the slope of the isochron which defines the age of the system. Because the isotopes are measured by mass spectrometry, ratios are used instead of absolute concentrations since mass spectrometers usually measure the former rather than the latter. (See the section on isotope ratio mass spectrometry.) As such, isochrons are typically defined by the following equation, which normalizes the concentration of parent and radiogenic daughter isotopes to the concentration of a non-radiogenic isotope of the daughter element that is assumed to be constant: where is the concentration of the non-radiogenic isotope of the daughter element (assumed constant), is the present concentration of the radiogenic daughter isotope, is the initial concentration of the radiogenic daughter isotope, and is the present concentration of the parent isotope that has decayed over time . To perform dating, a rock is crushed to a fine powder, and minerals are separated by various physical and magnetic means. Each mineral has different ratios between parent and daughter concentrations. For each mineral, the ratios are related by the following equation: (1) where is the initial concentration of the parent isotope, and is the total amount of the parent isotope which has decayed by time . The proof of (1) amounts to simple algebraic manipulation. It is useful in this form because it exhibits the relationship between quantities that actually exist at present. To wit, , and respectively correspond to the concentrations of parent, daughter and non-radiogenic isotopes found in the rock at the time of measurement. The ratios or (relative concentration of present daughter and non-radiogenic isotopes) and or (relative concentration of present parent and non-radiogenic isotope) are measured by mass spectrometry and plotted against each other in a three-isotope plot known as an isochron plot. If all data points lie on a straight line, this line is called an isochron. The better the fit of the data points to a line, the more reliable the resulting age estimate. Since the ratio of the daughter and non-radiogenic isotopes is proportional to the ratio of the