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Gas cells containing ammonia and methane at atmospheric pressure were custom-made in our chemical laboratory. Low-resolution near-infrared spectroscopy of these gas cells were collected in our optical laboratory. They are compared with simulated spectra using the high-resolution transmission molecular absorption database (HITRAN) for temperatures of 300 K and 500 K, and with near-infrared spectra of late-T and Y dwarfs, Jupiter and Saturn. We selected for this investigation the spectral region between 1.5 and 1.7 microns (H-band) because it is covered by the Euclid red grism, it is particularly sensitive to the relative proportions of ammonia and methane opacity, and it is free from strong contributions of other abundant molecules such as water vapour. The laboratory spectra showed that the ammonia and methane features that are present in the simulations using the HITRAN database are incomplete. Using our laboratory spectra, we propose a modified version of the NH3-H spectral ratio with expanded integration limits that increases the amplitude of variation of the index with respect to spectral type. Combinations of our laboratory spectra were used to find the best fits to the observed spectra with the relative absorption ratio of ammonia to methane as a free parameter. A relationship was found between the T$\rm_{eff}$ and the ratio of ammonia to methane from spectral classes T5 to Y2 (1100 K -- 350 K), in qualitative fairly good agreement with theoretical predictions for high gravity objects and temperatures from 1100 K to 500 K. The ammonia to methane ratios in late-T and Y dwarfs are similar to that of Jupiter, suggesting a similar chemical composition. Simulations of the spectroscopic performance of Euclid suggest that it will yield T$\rm_{eff}$ values and ratios of ammonia to methane for over 10$^3$ late T dwarfs in the whole wide survey., Comment: 5 pages, 5 figures, accepted for publication in Astronomy & Astrophysics Letters